1) O documento descreve a formulação de modelos unidimensionais de ordem superior para análise estrutural de vigas de parede fina.
2) Foram desenvolvidos modelos para análise de vigas considerando distorção da seção, seção deformável ou rígida e geometria arbitrária, assim como para vigas de seção compacta.
3) O trabalho inclui aplicações dos modelos e aponta tópicos futuros de desenvolvimento.
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
Creative operations teams expect increased AI use in 2024. Currently, over half of tasks are not AI-enabled, but this is expected to decrease in the coming year. ChatGPT is the most popular AI tool currently. Business leaders are more actively exploring AI benefits than individual contributors. Most respondents do not believe AI will impact workforce size in 2024. However, some inhibitions still exist around AI accuracy and lack of understanding. Creatives primarily want to use AI to save time on mundane tasks and boost productivity.
Organizational culture includes values, norms, systems, symbols, language, assumptions, beliefs, and habits that influence employee behaviors and how people interpret those behaviors. It is important because culture can help or hinder a company's success. Some key aspects of Netflix's culture that help it achieve results include hiring smartly so every position has stars, focusing on attitude over just aptitude, and having a strict policy against peacocks, whiners, and jerks.
PEPSICO Presentation to CAGNY Conference Feb 2024Neil Kimberley
PepsiCo provided a safe harbor statement noting that any forward-looking statements are based on currently available information and are subject to risks and uncertainties. It also provided information on non-GAAP measures and directing readers to its website for disclosure and reconciliation. The document then discussed PepsiCo's business overview, including that it is a global beverage and convenient food company with iconic brands, $91 billion in net revenue in 2023, and nearly $14 billion in core operating profit. It operates through a divisional structure with a focus on local consumers.
Content Methodology: A Best Practices Report (Webinar)contently
This document provides an overview of content methodology best practices. It defines content methodology as establishing objectives, KPIs, and a culture of continuous learning and iteration. An effective methodology focuses on connecting with audiences, creating optimal content, and optimizing processes. It also discusses why a methodology is needed due to the competitive landscape, proliferation of channels, and opportunities for improvement. Components of an effective methodology include defining objectives and KPIs, audience analysis, identifying opportunities, and evaluating resources. The document concludes with recommendations around creating a content plan, testing and optimizing content over 90 days.
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
Creative operations teams expect increased AI use in 2024. Currently, over half of tasks are not AI-enabled, but this is expected to decrease in the coming year. ChatGPT is the most popular AI tool currently. Business leaders are more actively exploring AI benefits than individual contributors. Most respondents do not believe AI will impact workforce size in 2024. However, some inhibitions still exist around AI accuracy and lack of understanding. Creatives primarily want to use AI to save time on mundane tasks and boost productivity.
Organizational culture includes values, norms, systems, symbols, language, assumptions, beliefs, and habits that influence employee behaviors and how people interpret those behaviors. It is important because culture can help or hinder a company's success. Some key aspects of Netflix's culture that help it achieve results include hiring smartly so every position has stars, focusing on attitude over just aptitude, and having a strict policy against peacocks, whiners, and jerks.
PEPSICO Presentation to CAGNY Conference Feb 2024Neil Kimberley
PepsiCo provided a safe harbor statement noting that any forward-looking statements are based on currently available information and are subject to risks and uncertainties. It also provided information on non-GAAP measures and directing readers to its website for disclosure and reconciliation. The document then discussed PepsiCo's business overview, including that it is a global beverage and convenient food company with iconic brands, $91 billion in net revenue in 2023, and nearly $14 billion in core operating profit. It operates through a divisional structure with a focus on local consumers.
Content Methodology: A Best Practices Report (Webinar)contently
This document provides an overview of content methodology best practices. It defines content methodology as establishing objectives, KPIs, and a culture of continuous learning and iteration. An effective methodology focuses on connecting with audiences, creating optimal content, and optimizing processes. It also discusses why a methodology is needed due to the competitive landscape, proliferation of channels, and opportunities for improvement. Components of an effective methodology include defining objectives and KPIs, audience analysis, identifying opportunities, and evaluating resources. The document concludes with recommendations around creating a content plan, testing and optimizing content over 90 days.
How to Prepare For a Successful Job Search for 2024Albert Qian
The document provides guidance on preparing a job search for 2024. It discusses the state of the job market, focusing on growth in AI and healthcare but also continued layoffs. It recommends figuring out what you want to do by researching interests and skills, then conducting informational interviews. The job search should involve building a personal brand on LinkedIn, actively applying to jobs, tailoring resumes and interviews, maintaining job hunting as a habit, and continuing self-improvement. Once hired, the document advises setting new goals and keeping skills and networking active in case of future opportunities.
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
The document provides career advice for getting into the tech field, including:
- Doing projects and internships in college to build a portfolio.
- Learning about different roles and technologies through industry research.
- Contributing to open source projects to build experience and network.
- Developing a personal brand through a website and social media presence.
- Networking through events, communities, and finding a mentor.
- Practicing interviews through mock interviews and whiteboarding coding questions.
Google's Just Not That Into You: Understanding Core Updates & Search IntentLily Ray
1. Core updates from Google periodically change how its algorithms assess and rank websites and pages. This can impact rankings through shifts in user intent, site quality issues being caught up to, world events influencing queries, and overhauls to search like the E-A-T framework.
2. There are many possible user intents beyond just transactional, navigational and informational. Identifying intent shifts is important during core updates. Sites may need to optimize for new intents through different content types and sections.
3. Responding effectively to core updates requires analyzing "before and after" data to understand changes, identifying new intents or page types, and ensuring content matches appropriate intents across video, images, knowledge graphs and more.
A brief introduction to DataScience with explaining of the concepts, algorithms, machine learning, supervised and unsupervised learning, clustering, statistics, data preprocessing, real-world applications etc.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
Unlocking the Power of ChatGPT and AI in Testing - A Real-World Look, present...Applitools
During this webinar, Anand Bagmar demonstrates how AI tools such as ChatGPT can be applied to various stages of the software development life cycle (SDLC) using an eCommerce application case study. Find the on-demand recording and more info at https://applitools.info/b59
Key takeaways:
• Learn how to use ChatGPT to add AI power to your testing and test automation
• Understand the limitations of the technology and where human expertise is crucial
• Gain insight into different AI-based tools
• Adopt AI-based tools to stay relevant and optimize work for developers and testers
* ChatGPT and OpenAI belong to OpenAI, L.L.C.
The document discusses various AI tools from OpenAI like GPT-3 and DALL-E 2, as well as ChatGPT. It explores how search engines are using AI and things to consider around AI-generated content. Potential SEO uses of ChatGPT are also presented, such as generating content at scale, conducting topic research, and automating basic coding tasks. The document encourages further reading on using ChatGPT for SEO purposes.
More than Just Lines on a Map: Best Practices for U.S Bike Routes
This session highlights best practices and lessons learned for U.S. Bike Route System designation, as well as how and why these routes should be integrated into bicycle planning at the local and regional level.
Presenters:
Presenter: Kevin Luecke Toole Design Group
Co-Presenter: Virginia Sullivan Adventure Cycling Association
Ride the Storm: Navigating Through Unstable Periods / Katerina Rudko (Belka G...DevGAMM Conference
Has your project been caught in a storm of deadlines, clashing requirements, and the need to change course halfway through? If yes, then check out how the administration team navigated through all of this, relocating 160 people from 3 countries and opening 2 offices during the most turbulent time in the last 20 years. Belka Games’ Chief Administrative Officer, Katerina Rudko, will share universal approaches and life hacks that can help your project survive unstable periods when there seem to be too many tasks and a lack of time and people.
This presentation was designed to provide strategic recommendations for a brand in decline. The deck also incorporates a situational assessment, including a brand identity, positioning, architecture, and portfolio strategy for the Brand.
Presentation originally created for NYU Stern's Brand Strategy course. Design by Erica Santiago & Chris Alexander.
Good Stuff Happens in 1:1 Meetings: Why you need them and how to do them wellSaba Software
According to the latest State of the American Manager report from Gallup, employees who have regular meetings with their managers are almost three times as likely to be engaged as those who don’t. These regular check-ins keep managers and employees in sync and aligned. Want to see better manager/employee relationships in your organisation? Then make an all-in commitment to 1:1 meetings. Not sure how? You’ve come to the right place.
In this webinar with Jamie Resker, Founder and Practice Leader for Employee Performance Solutions (EPS), and Teala Wilson, Talent Management Consultant at Saba Software, you’ll get the inside track on how to hold effective 1:1 meetings, including tips for getting managers on board.
• Go beyond discussing the status of everyday work to higher level topics, including recognition, performance, development, and career aspirations
• Learn how to decide meeting frequency, what to cover, as well as roles and responsibilities of the manager and employee
• Understand how managers can build trust and make it comfortable for employees to provide upward feedback
• Unite your organisation with a unified approach to 1:1 meetings
Join us for this 1-hour webinar to get practical tips for building better manager-employee relationships with intention and purpose.
About the Speakers
Jamie Resker - Founder and Practice Leader for Employee Performance Solutions (EPS)
Jamie Resker, Practice Leader and Founder of Employee Performance Solutions, is a recognized innovator in performance management. She is the originator of the-the Performance Continuum Feedback Method® and Conversations to Optimize Employee Performance training program; tools and training that reshape communications between managers and employees to drive and align performance. Jamie is on the faculty for the Northeast Human Resources Association, is a contributor to Halogen Software's Talent Space Blog, and is an editorial advisory board member for HR Examiner.
Teala Wilson - Senior Consultant, Strategic Services, Saba Software
Teala is a Talent Management Consultant at Halogen Software, now a part of Saba Software. She has worked with teams on a national and global level supporting human resources in areas such as performance management, recruitment, employee benefit programs, training and talent development, workforce planning and internal communications. Teala also has a personal passion for visual arts and design.
Want to learn more? Join us for an upcoming Product Tour!
http://bit.ly/2yitfqu
This video by Simplilearn will explain to you Introduction to C Programming Language. Introduction to C Programming Language Tutorial For Beginners will explain to you the C language's history, C's importance, its features, real-world applications, and some of its advantages and disadvantages.
00:00 Introduction to C
1:42-History of C language
Dennis Ritchie, a computer scientist, could identify the gaps and tap out the best features from both B and BCPL languages to invent a new hybrid.
Hence, C was born in 1972 at Bell Laboratories. A remarkably simple and highly readable programming language resulted in groundbreaking advancements in the IT industry.
2:48-Importance and unraveling the powerful capabilities of C,
The widespread use of C started to take over the IT industry. Unraveling the potential of C, the designers began to discover new possibilities that led them to focus on the big picture.
3:56-C's cutting-edge features
The designers at Bell Laboratories ensured that their programming language solved the issues with B and BCPL and the ones they had foreseen.
6:35-The popular real-world applications of C
-UNIX operating system
-google file system
-Mozilla
-Graphical user interface
8:30-The advantages and disadvantages of C
10:34-The popular IT companies and their domains that employ C
· MasterCard
· IBM
· Flipkart
· Dell
· Twitter
· GitHub and twitch
11:09-First c program.
🔥 Explore our FREE courses with completion certificates: https://www.simplilearn.com/skillup-f...
✅Subscribe to our Channel to learn more about the top Technologies: https://bit.ly/2VT4WtH
⏩ Check out the C++ Programming training videos: https://www.youtube.com/playlist?list...
#IntroductiontoCProgrammingLanguage #CLanguage #CProgramming #CProgram #CProgrammingLanguage #LearnCProgramming #HowToCodeInCForBeginners #CTutorialForBeginners #LearnCProgramming #Simplilearn
Dennis Ritchie, a computer scientist, was able to identify the gaps and tap out the best features from both B and BCPL languages to invent a new hybrid.
Hence, C was born in 1972 at Bell Laboratories. A remarkably simple and highly readable programming language resulted in groundbreaking advancements in the IT industry.
✅What is C++ Programming?
C++ is an enhanced and extended version of C programming language, developed by Bjarne Stroustrup in 1979 as part of his Ph.D. project. Bjarne developed what he called ‘C with Classes’ (later renamed C++) because he felt limited by the existing programming languages that were not ideal for large scale projects. He used C to build what he wanted because C was already a general-purpose language that was efficient and fast in its operations.
✅C++ Career Prospects:
With just C++ programming expertise, you will have excellent job opportunities, salaries, and career prospects. However, for a career based on programming languages such as Java and Python (which are in more demand than C++) or for careers based on front-end, back-end, and full-stack
How to Prepare For a Successful Job Search for 2024Albert Qian
The document provides guidance on preparing a job search for 2024. It discusses the state of the job market, focusing on growth in AI and healthcare but also continued layoffs. It recommends figuring out what you want to do by researching interests and skills, then conducting informational interviews. The job search should involve building a personal brand on LinkedIn, actively applying to jobs, tailoring resumes and interviews, maintaining job hunting as a habit, and continuing self-improvement. Once hired, the document advises setting new goals and keeping skills and networking active in case of future opportunities.
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
The document provides career advice for getting into the tech field, including:
- Doing projects and internships in college to build a portfolio.
- Learning about different roles and technologies through industry research.
- Contributing to open source projects to build experience and network.
- Developing a personal brand through a website and social media presence.
- Networking through events, communities, and finding a mentor.
- Practicing interviews through mock interviews and whiteboarding coding questions.
Google's Just Not That Into You: Understanding Core Updates & Search IntentLily Ray
1. Core updates from Google periodically change how its algorithms assess and rank websites and pages. This can impact rankings through shifts in user intent, site quality issues being caught up to, world events influencing queries, and overhauls to search like the E-A-T framework.
2. There are many possible user intents beyond just transactional, navigational and informational. Identifying intent shifts is important during core updates. Sites may need to optimize for new intents through different content types and sections.
3. Responding effectively to core updates requires analyzing "before and after" data to understand changes, identifying new intents or page types, and ensuring content matches appropriate intents across video, images, knowledge graphs and more.
A brief introduction to DataScience with explaining of the concepts, algorithms, machine learning, supervised and unsupervised learning, clustering, statistics, data preprocessing, real-world applications etc.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
Unlocking the Power of ChatGPT and AI in Testing - A Real-World Look, present...Applitools
During this webinar, Anand Bagmar demonstrates how AI tools such as ChatGPT can be applied to various stages of the software development life cycle (SDLC) using an eCommerce application case study. Find the on-demand recording and more info at https://applitools.info/b59
Key takeaways:
• Learn how to use ChatGPT to add AI power to your testing and test automation
• Understand the limitations of the technology and where human expertise is crucial
• Gain insight into different AI-based tools
• Adopt AI-based tools to stay relevant and optimize work for developers and testers
* ChatGPT and OpenAI belong to OpenAI, L.L.C.
The document discusses various AI tools from OpenAI like GPT-3 and DALL-E 2, as well as ChatGPT. It explores how search engines are using AI and things to consider around AI-generated content. Potential SEO uses of ChatGPT are also presented, such as generating content at scale, conducting topic research, and automating basic coding tasks. The document encourages further reading on using ChatGPT for SEO purposes.
More than Just Lines on a Map: Best Practices for U.S Bike Routes
This session highlights best practices and lessons learned for U.S. Bike Route System designation, as well as how and why these routes should be integrated into bicycle planning at the local and regional level.
Presenters:
Presenter: Kevin Luecke Toole Design Group
Co-Presenter: Virginia Sullivan Adventure Cycling Association
Ride the Storm: Navigating Through Unstable Periods / Katerina Rudko (Belka G...DevGAMM Conference
Has your project been caught in a storm of deadlines, clashing requirements, and the need to change course halfway through? If yes, then check out how the administration team navigated through all of this, relocating 160 people from 3 countries and opening 2 offices during the most turbulent time in the last 20 years. Belka Games’ Chief Administrative Officer, Katerina Rudko, will share universal approaches and life hacks that can help your project survive unstable periods when there seem to be too many tasks and a lack of time and people.
This presentation was designed to provide strategic recommendations for a brand in decline. The deck also incorporates a situational assessment, including a brand identity, positioning, architecture, and portfolio strategy for the Brand.
Presentation originally created for NYU Stern's Brand Strategy course. Design by Erica Santiago & Chris Alexander.
Good Stuff Happens in 1:1 Meetings: Why you need them and how to do them wellSaba Software
According to the latest State of the American Manager report from Gallup, employees who have regular meetings with their managers are almost three times as likely to be engaged as those who don’t. These regular check-ins keep managers and employees in sync and aligned. Want to see better manager/employee relationships in your organisation? Then make an all-in commitment to 1:1 meetings. Not sure how? You’ve come to the right place.
In this webinar with Jamie Resker, Founder and Practice Leader for Employee Performance Solutions (EPS), and Teala Wilson, Talent Management Consultant at Saba Software, you’ll get the inside track on how to hold effective 1:1 meetings, including tips for getting managers on board.
• Go beyond discussing the status of everyday work to higher level topics, including recognition, performance, development, and career aspirations
• Learn how to decide meeting frequency, what to cover, as well as roles and responsibilities of the manager and employee
• Understand how managers can build trust and make it comfortable for employees to provide upward feedback
• Unite your organisation with a unified approach to 1:1 meetings
Join us for this 1-hour webinar to get practical tips for building better manager-employee relationships with intention and purpose.
About the Speakers
Jamie Resker - Founder and Practice Leader for Employee Performance Solutions (EPS)
Jamie Resker, Practice Leader and Founder of Employee Performance Solutions, is a recognized innovator in performance management. She is the originator of the-the Performance Continuum Feedback Method® and Conversations to Optimize Employee Performance training program; tools and training that reshape communications between managers and employees to drive and align performance. Jamie is on the faculty for the Northeast Human Resources Association, is a contributor to Halogen Software's Talent Space Blog, and is an editorial advisory board member for HR Examiner.
Teala Wilson - Senior Consultant, Strategic Services, Saba Software
Teala is a Talent Management Consultant at Halogen Software, now a part of Saba Software. She has worked with teams on a national and global level supporting human resources in areas such as performance management, recruitment, employee benefit programs, training and talent development, workforce planning and internal communications. Teala also has a personal passion for visual arts and design.
Want to learn more? Join us for an upcoming Product Tour!
http://bit.ly/2yitfqu
This video by Simplilearn will explain to you Introduction to C Programming Language. Introduction to C Programming Language Tutorial For Beginners will explain to you the C language's history, C's importance, its features, real-world applications, and some of its advantages and disadvantages.
00:00 Introduction to C
1:42-History of C language
Dennis Ritchie, a computer scientist, could identify the gaps and tap out the best features from both B and BCPL languages to invent a new hybrid.
Hence, C was born in 1972 at Bell Laboratories. A remarkably simple and highly readable programming language resulted in groundbreaking advancements in the IT industry.
2:48-Importance and unraveling the powerful capabilities of C,
The widespread use of C started to take over the IT industry. Unraveling the potential of C, the designers began to discover new possibilities that led them to focus on the big picture.
3:56-C's cutting-edge features
The designers at Bell Laboratories ensured that their programming language solved the issues with B and BCPL and the ones they had foreseen.
6:35-The popular real-world applications of C
-UNIX operating system
-google file system
-Mozilla
-Graphical user interface
8:30-The advantages and disadvantages of C
10:34-The popular IT companies and their domains that employ C
· MasterCard
· IBM
· Flipkart
· Dell
· Twitter
· GitHub and twitch
11:09-First c program.
🔥 Explore our FREE courses with completion certificates: https://www.simplilearn.com/skillup-f...
✅Subscribe to our Channel to learn more about the top Technologies: https://bit.ly/2VT4WtH
⏩ Check out the C++ Programming training videos: https://www.youtube.com/playlist?list...
#IntroductiontoCProgrammingLanguage #CLanguage #CProgramming #CProgram #CProgrammingLanguage #LearnCProgramming #HowToCodeInCForBeginners #CTutorialForBeginners #LearnCProgramming #Simplilearn
Dennis Ritchie, a computer scientist, was able to identify the gaps and tap out the best features from both B and BCPL languages to invent a new hybrid.
Hence, C was born in 1972 at Bell Laboratories. A remarkably simple and highly readable programming language resulted in groundbreaking advancements in the IT industry.
✅What is C++ Programming?
C++ is an enhanced and extended version of C programming language, developed by Bjarne Stroustrup in 1979 as part of his Ph.D. project. Bjarne developed what he called ‘C with Classes’ (later renamed C++) because he felt limited by the existing programming languages that were not ideal for large scale projects. He used C to build what he wanted because C was already a general-purpose language that was efficient and fast in its operations.
✅C++ Career Prospects:
With just C++ programming expertise, you will have excellent job opportunities, salaries, and career prospects. However, for a career based on programming languages such as Java and Python (which are in more demand than C++) or for careers based on front-end, back-end, and full-stack
1. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Higher Order Thin-Walled Beam Models
Ricardo Vieira
ICIST, DECivil - Departmento de Engenharia Civil e Arquitectura
Instituto Superior T´cnico
e
Semin´rio de Doutoramento
a
Orientadores: Prof. Francisco Virtuoso e Prof. Eduardo Pereira
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
2. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Higher Order Thin-Walled Beam Models
Motiva¸˜o e enquadramento do tema;
ca
1
Sintese do trabalho desenvolvido e em desenvolvimento;
2
Formula¸˜o de modelos unidimensionais de ordem superior,
ca
An´lise da sec¸˜o, desacoplamento dos modos da solu¸˜o;
a ca ca
An´lise longitudinal, desenvolvimento do elemento finito.
a
Modelos desenvolvidos;
An´lise vigas de parede fina - a distor¸˜o ´ considerada,
a ca e
sec¸˜o transversalmente deform´vel ou indeform´vel, sec¸˜o
ca a a ca
de geometria arbitr´ria, (abertas, fechadas e ramificadas);
a
An´lise de vigas de sec¸˜o compacta.
a ca
Aplica¸˜es dos modelos propostos;
co
Trabalho por desenvolver.
3
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
3. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Higher Order Thin-Walled Beam Models
Motiva¸˜o e enquadramento do tema;
ca
1
Sintese do trabalho desenvolvido e em desenvolvimento;
2
Formula¸˜o de modelos unidimensionais de ordem superior,
ca
An´lise da sec¸˜o, desacoplamento dos modos da solu¸˜o;
a ca ca
An´lise longitudinal, desenvolvimento do elemento finito.
a
Modelos desenvolvidos;
An´lise vigas de parede fina - a distor¸˜o ´ considerada,
a ca e
sec¸˜o transversalmente deform´vel ou indeform´vel, sec¸˜o
ca a a ca
de geometria arbitr´ria, (abertas, fechadas e ramificadas);
a
An´lise de vigas de sec¸˜o compacta.
a ca
Aplica¸˜es dos modelos propostos;
co
Trabalho por desenvolver.
3
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
4. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Higher Order Thin-Walled Beam Models
Motiva¸˜o e enquadramento do tema;
ca
1
Sintese do trabalho desenvolvido e em desenvolvimento;
2
Formula¸˜o de modelos unidimensionais de ordem superior,
ca
An´lise da sec¸˜o, desacoplamento dos modos da solu¸˜o;
a ca ca
An´lise longitudinal, desenvolvimento do elemento finito.
a
Modelos desenvolvidos;
An´lise vigas de parede fina - a distor¸˜o ´ considerada,
a ca e
sec¸˜o transversalmente deform´vel ou indeform´vel, sec¸˜o
ca a a ca
de geometria arbitr´ria, (abertas, fechadas e ramificadas);
a
An´lise de vigas de sec¸˜o compacta.
a ca
Aplica¸˜es dos modelos propostos;
co
Trabalho por desenvolver.
3
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
5. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Higher Order Thin-Walled Beam Models
Motiva¸˜o e enquadramento do tema;
ca
1
Sintese do trabalho desenvolvido e em desenvolvimento;
2
Formula¸˜o de modelos unidimensionais de ordem superior,
ca
An´lise da sec¸˜o, desacoplamento dos modos da solu¸˜o;
a ca ca
An´lise longitudinal, desenvolvimento do elemento finito.
a
Modelos desenvolvidos;
An´lise vigas de parede fina - a distor¸˜o ´ considerada,
a ca e
sec¸˜o transversalmente deform´vel ou indeform´vel, sec¸˜o
ca a a ca
de geometria arbitr´ria, (abertas, fechadas e ramificadas);
a
An´lise de vigas de sec¸˜o compacta.
a ca
Aplica¸˜es dos modelos propostos;
co
Trabalho por desenvolver.
3
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
6. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Higher Order Thin-Walled Beam Models
Motiva¸˜o e enquadramento do tema;
ca
1
Sintese do trabalho desenvolvido e em desenvolvimento;
2
Formula¸˜o de modelos unidimensionais de ordem superior,
ca
An´lise da sec¸˜o, desacoplamento dos modos da solu¸˜o;
a ca ca
An´lise longitudinal, desenvolvimento do elemento finito.
a
Modelos desenvolvidos;
An´lise vigas de parede fina - a distor¸˜o ´ considerada,
a ca e
sec¸˜o transversalmente deform´vel ou indeform´vel, sec¸˜o
ca a a ca
de geometria arbitr´ria, (abertas, fechadas e ramificadas);
a
An´lise de vigas de sec¸˜o compacta.
a ca
Aplica¸˜es dos modelos propostos;
co
Trabalho por desenvolver.
3
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
7. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Higher Order Thin-Walled Beam Models
Motiva¸˜o e enquadramento do tema;
ca
1
Sintese do trabalho desenvolvido e em desenvolvimento;
2
Formula¸˜o de modelos unidimensionais de ordem superior,
ca
An´lise da sec¸˜o, desacoplamento dos modos da solu¸˜o;
a ca ca
An´lise longitudinal, desenvolvimento do elemento finito.
a
Modelos desenvolvidos;
An´lise vigas de parede fina - a distor¸˜o ´ considerada,
a ca e
sec¸˜o transversalmente deform´vel ou indeform´vel, sec¸˜o
ca a a ca
de geometria arbitr´ria, (abertas, fechadas e ramificadas);
a
An´lise de vigas de sec¸˜o compacta.
a ca
Aplica¸˜es dos modelos propostos;
co
Trabalho por desenvolver.
3
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
8. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modelos unidimensionais de pe¸as prism´ticas (Modelos de viga)
c a
Simplicidade na an´lise e na interpreta¸˜o do comportamento
a ca
1
estrutural;
Redu¸˜o das equa¸˜es fundamentais de elasticidade de 3-D
ca co
2
para 1-D,
Teoria t´cnica de vigas - hip´teses admitidas “ab initio”
e o
(experimentalmente validadas e de conhecimento emp´ ırico);
An´lise assimpt´tica adoptando como perturba¸˜o grandeza
a o ca
f´
ısica ou geom´trica adequada;
e
M´todos de projec¸˜o do campo de deslocamentos.
e ca
Perda de exactid˜o relativamente a formula¸oes 3-D
a c˜
3
dependente das hip´teses admitidas, do tipo de sec¸˜o e de
o ca
an´lise estrutural pretendida;
a
Enriquecimento de formula¸˜o refinando a aproxima¸˜o do
ca ca
4
campo de deslocamentos.
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
9. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modelos unidimensionais de pe¸as prism´ticas (Modelos de viga)
c a
Simplicidade na an´lise e na interpreta¸˜o do comportamento
a ca
1
estrutural;
Redu¸˜o das equa¸˜es fundamentais de elasticidade de 3-D
ca co
2
para 1-D,
Teoria t´cnica de vigas - hip´teses admitidas “ab initio”
e o
(experimentalmente validadas e de conhecimento emp´ ırico);
An´lise assimpt´tica adoptando como perturba¸˜o grandeza
a o ca
f´
ısica ou geom´trica adequada;
e
M´todos de projec¸˜o do campo de deslocamentos.
e ca
Perda de exactid˜o relativamente a formula¸oes 3-D
a c˜
3
dependente das hip´teses admitidas, do tipo de sec¸˜o e de
o ca
an´lise estrutural pretendida;
a
Enriquecimento de formula¸˜o refinando a aproxima¸˜o do
ca ca
4
campo de deslocamentos.
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
10. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modelos unidimensionais de pe¸as prism´ticas (Modelos de viga)
c a
Simplicidade na an´lise e na interpreta¸˜o do comportamento
a ca
1
estrutural;
Redu¸˜o das equa¸˜es fundamentais de elasticidade de 3-D
ca co
2
para 1-D,
Teoria t´cnica de vigas - hip´teses admitidas “ab initio”
e o
(experimentalmente validadas e de conhecimento emp´ ırico);
An´lise assimpt´tica adoptando como perturba¸˜o grandeza
a o ca
f´
ısica ou geom´trica adequada;
e
M´todos de projec¸˜o do campo de deslocamentos.
e ca
Perda de exactid˜o relativamente a formula¸oes 3-D
a c˜
3
dependente das hip´teses admitidas, do tipo de sec¸˜o e de
o ca
an´lise estrutural pretendida;
a
Enriquecimento de formula¸˜o refinando a aproxima¸˜o do
ca ca
4
campo de deslocamentos.
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
11. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modelos unidimensionais de pe¸as prism´ticas (Modelos de viga)
c a
Simplicidade na an´lise e na interpreta¸˜o do comportamento
a ca
1
estrutural;
Redu¸˜o das equa¸˜es fundamentais de elasticidade de 3-D
ca co
2
para 1-D,
Teoria t´cnica de vigas - hip´teses admitidas “ab initio”
e o
(experimentalmente validadas e de conhecimento emp´ ırico);
An´lise assimpt´tica adoptando como perturba¸˜o grandeza
a o ca
f´
ısica ou geom´trica adequada;
e
M´todos de projec¸˜o do campo de deslocamentos.
e ca
Perda de exactid˜o relativamente a formula¸oes 3-D
a c˜
3
dependente das hip´teses admitidas, do tipo de sec¸˜o e de
o ca
an´lise estrutural pretendida;
a
Enriquecimento de formula¸˜o refinando a aproxima¸˜o do
ca ca
4
campo de deslocamentos.
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
12. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modelos unidimensionais de pe¸as prism´ticas (Modelos de viga)
c a
Simplicidade na an´lise e na interpreta¸˜o do comportamento
a ca
1
estrutural;
Redu¸˜o das equa¸˜es fundamentais de elasticidade de 3-D
ca co
2
para 1-D,
Teoria t´cnica de vigas - hip´teses admitidas “ab initio”
e o
(experimentalmente validadas e de conhecimento emp´ ırico);
An´lise assimpt´tica adoptando como perturba¸˜o grandeza
a o ca
f´
ısica ou geom´trica adequada;
e
M´todos de projec¸˜o do campo de deslocamentos.
e ca
Perda de exactid˜o relativamente a formula¸oes 3-D
a c˜
3
dependente das hip´teses admitidas, do tipo de sec¸˜o e de
o ca
an´lise estrutural pretendida;
a
Enriquecimento de formula¸˜o refinando a aproxima¸˜o do
ca ca
4
campo de deslocamentos.
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
13. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modelos unidimensionais de pe¸as prism´ticas (Modelos de viga)
c a
Simplicidade na an´lise e na interpreta¸˜o do comportamento
a ca
1
estrutural;
Redu¸˜o das equa¸˜es fundamentais de elasticidade de 3-D
ca co
2
para 1-D,
Teoria t´cnica de vigas - hip´teses admitidas “ab initio”
e o
(experimentalmente validadas e de conhecimento emp´ ırico);
An´lise assimpt´tica adoptando como perturba¸˜o grandeza
a o ca
f´
ısica ou geom´trica adequada;
e
M´todos de projec¸˜o do campo de deslocamentos.
e ca
Perda de exactid˜o relativamente a formula¸oes 3-D
a c˜
3
dependente das hip´teses admitidas, do tipo de sec¸˜o e de
o ca
an´lise estrutural pretendida;
a
Enriquecimento de formula¸˜o refinando a aproxima¸˜o do
ca ca
4
campo de deslocamentos.
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
14. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modelos unidimensionais de pe¸as prism´ticas (Modelos de viga)
c a
Simplicidade na an´lise e na interpreta¸˜o do comportamento
a ca
1
estrutural;
Redu¸˜o das equa¸˜es fundamentais de elasticidade de 3-D
ca co
2
para 1-D,
Teoria t´cnica de vigas - hip´teses admitidas “ab initio”
e o
(experimentalmente validadas e de conhecimento emp´ ırico);
An´lise assimpt´tica adoptando como perturba¸˜o grandeza
a o ca
f´
ısica ou geom´trica adequada;
e
M´todos de projec¸˜o do campo de deslocamentos.
e ca
Perda de exactid˜o relativamente a formula¸oes 3-D
a c˜
3
dependente das hip´teses admitidas, do tipo de sec¸˜o e de
o ca
an´lise estrutural pretendida;
a
Enriquecimento de formula¸˜o refinando a aproxima¸˜o do
ca ca
4
campo de deslocamentos.
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
15. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modelos 1-D de pe¸as lineares de parede fina
c
O comportamento de estruturas de parede fina enquanto vigas ´
e
complexo.
empenamento da sec¸˜o,
ca
1
tor¸˜o n˜o uniforme em vigas de sec¸˜o aberta ou fechada
ca a ca
com sec¸˜o deform´vel;
ca a
fen´meno de shear-lag.
o
deformabilidade por corte no plano do folheto m´dio;
e
2
deformabilidade transversal da sec¸˜o (flex˜o e distor¸˜o
ca a ca
3
global);
modos de encurvadura local;
4
efeito das cargas concentradas na direc¸˜o.
ca
5
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
16. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modelos 1-D de pe¸as lineares de parede fina
c
O comportamento de estruturas de parede fina enquanto vigas ´
e
complexo.
empenamento da sec¸˜o,
ca
1
tor¸˜o n˜o uniforme em vigas de sec¸˜o aberta ou fechada
ca a ca
com sec¸˜o deform´vel;
ca a
fen´meno de shear-lag.
o
deformabilidade por corte no plano do folheto m´dio;
e
2
deformabilidade transversal da sec¸˜o (flex˜o e distor¸˜o
ca a ca
3
global);
modos de encurvadura local;
4
efeito das cargas concentradas na direc¸˜o.
ca
5
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
17. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modelos 1-D de pe¸as lineares de parede fina
c
O comportamento de estruturas de parede fina enquanto vigas ´
e
complexo.
empenamento da sec¸˜o,
ca
1
tor¸˜o n˜o uniforme em vigas de sec¸˜o aberta ou fechada
ca a ca
com sec¸˜o deform´vel;
ca a
fen´meno de shear-lag.
o
deformabilidade por corte no plano do folheto m´dio;
e
2
deformabilidade transversal da sec¸˜o (flex˜o e distor¸˜o
ca a ca
3
global);
modos de encurvadura local;
4
efeito das cargas concentradas na direc¸˜o.
ca
5
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
18. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modelos 1-D de pe¸as lineares de parede fina
c
O comportamento de estruturas de parede fina enquanto vigas ´
e
complexo.
empenamento da sec¸˜o,
ca
1
tor¸˜o n˜o uniforme em vigas de sec¸˜o aberta ou fechada
ca a ca
com sec¸˜o deform´vel;
ca a
fen´meno de shear-lag.
o
deformabilidade por corte no plano do folheto m´dio;
e
2
deformabilidade transversal da sec¸˜o (flex˜o e distor¸˜o
ca a ca
3
global);
modos de encurvadura local;
4
efeito das cargas concentradas na direc¸˜o.
ca
5
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
19. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modelos 1-D de pe¸as lineares de parede fina
c
O comportamento de estruturas de parede fina enquanto vigas ´
e
complexo.
empenamento da sec¸˜o,
ca
1
tor¸˜o n˜o uniforme em vigas de sec¸˜o aberta ou fechada
ca a ca
com sec¸˜o deform´vel;
ca a
fen´meno de shear-lag.
o
deformabilidade por corte no plano do folheto m´dio;
e
2
deformabilidade transversal da sec¸˜o (flex˜o e distor¸˜o
ca a ca
3
global);
modos de encurvadura local;
4
efeito das cargas concentradas na direc¸˜o.
ca
5
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
20. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modelos 1-D de pe¸as lineares de parede fina
c
O comportamento de estruturas de parede fina enquanto vigas ´
e
complexo.
empenamento da sec¸˜o,
ca
1
tor¸˜o n˜o uniforme em vigas de sec¸˜o aberta ou fechada
ca a ca
com sec¸˜o deform´vel;
ca a
fen´meno de shear-lag.
o
deformabilidade por corte no plano do folheto m´dio;
e
2
deformabilidade transversal da sec¸˜o (flex˜o e distor¸˜o
ca a ca
3
global);
modos de encurvadura local;
4
efeito das cargas concentradas na direc¸˜o.
ca
5
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
21. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Referenciais e nota¸˜o
ca
Referencial global (x, y, z);
1
Referencial local (x, s, n);
2
Deslocamentos no referencial local,
3
u(x, s, n), v(x, s, n), w(x, s, n)
y
s(v)
n(ω)
z
x(u)
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
22. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Teorias cl´ssicas - Contributos avulsos na primeira metade do
a
s´culo XX
e
Timoshenko1910
Wagner1926
Despreza distor¸˜o associada ao empenamento da sec¸˜o
ca ca
Umansky1939
Aplica¸˜o a sec¸˜es de perfil fechado
ca co
Empenamento da sec¸˜o atrav´s de fun¸˜o independente da
ca e ca
rota¸˜o
ca
Argyris1947
Tor¸˜o n˜o uniforme sec¸˜es fechadas;
ca a co
von Karman1946
Tor¸˜o de sec¸˜es fechadas multi-celulares;
ca co
Fl¨gge e Marguerre1948
u
Empenamento de vigas de parede fina com sec¸˜o aberta ou
ca
fechada.
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
23. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Adurorov1947 ,Panokvo1948 e Vorobiev1955
Consideram deformabilidade por corte em vigas de parede fina;
Benscoter1958
Tor¸˜o n˜o uniforme de sec¸˜es fechadas multi-celulares;
ca a co
Teoria de Vlassov1940,1968
despreza a deformabilidade por corte do folheto m´dio, ie. γxs = 0;
e
obt´m empenamento da sec¸˜o uω (x, s) = − θ (x)ω(s);
e ca
considera a flex˜o transversal atrav´s de modelo p´rtico articulado,
a e o
a compatibilidade dos n´s apenas se verifica para sec¸˜es de forma
o co
quadrada.
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
24. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Teoria t´cnica generalizada de vigas, Schardt1989
e
Teoria de Schardt1966−1989 ,TU - Darmstadt
admite hip´tese de Vlassov, ie. γxs = 0;
o
baseada numa discretiza¸˜o de deslocamentos axiais;
ca
considera o empenamento da sec¸˜o;
ca
considera a deformabilidade transversal atrav´s de
e
deslocamentos adicionais normais ` parede;
a
v´lida apenas para sec¸˜es abertas n˜o ramificadas;
a co a
Teoria de Sedlacek1968 , TU - Berlin
empenamentos de tor¸˜o e de distor¸˜o;
ca ca
v´lida para sec¸˜es abertas, fechadas e ramificadas.
a co
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
25. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Teoria t´cnica generalizada de vigas, Schardt1989
e
Teoria de Schardt1966−1989 ,TU - Darmstadt
admite hip´tese de Vlassov, ie. γxs = 0;
o
baseada numa discretiza¸˜o de deslocamentos axiais;
ca
considera o empenamento da sec¸˜o;
ca
considera a deformabilidade transversal atrav´s de
e
deslocamentos adicionais normais ` parede;
a
v´lida apenas para sec¸˜es abertas n˜o ramificadas;
a co a
Teoria de Sedlacek1968 , TU - Berlin
empenamentos de tor¸˜o e de distor¸˜o;
ca ca
v´lida para sec¸˜es abertas, fechadas e ramificadas.
a co
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
26. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Teoria t´cnica generalizada de vigas, Schardt1989
e
Teoria de Schardt1966−1989 ,TU - Darmstadt
admite hip´tese de Vlassov, ie. γxs = 0;
o
baseada numa discretiza¸˜o de deslocamentos axiais;
ca
considera o empenamento da sec¸˜o;
ca
considera a deformabilidade transversal atrav´s de
e
deslocamentos adicionais normais ` parede;
a
v´lida apenas para sec¸˜es abertas n˜o ramificadas;
a co a
Teoria de Sedlacek1968 , TU - Berlin
empenamentos de tor¸˜o e de distor¸˜o;
ca ca
v´lida para sec¸˜es abertas, fechadas e ramificadas.
a co
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
27. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Aplica¸˜o `s estruturas met´licas
ca a a
Hip´teses,
o
γxs = 0 e s = 0
γsn = 0 e γxn = 0
Aproxima¸˜o de deslocamentos axiais de membrana
ca
u(x, s) = φ(s) Va (x);
Deslocamentos tangenciais obtidos por
v(x, s) = ψ(s) Va (x) donde γxs = 0 ⇒ ψ(s) = φ,s .
Deslocamentos normais obtidos por
wa (x, s) = χa (s) Va (x) em que χa (s) ´ definida atrav´s
e e
de,
φ,s para garantir continuidade de deslocamentos dos n´s;
o
e da rigidez transversal da sec¸˜o de modo a garantir
ca
continuidade de rota¸˜es dos n´s.
co o
Campo de deslocamentos escrito apenas em termos de graus de
liberdade axiais. Schardt- Cap´ 2
ıtulo
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
28. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Para considerar a flex˜o transversal da sec¸˜o, introduzem-se graus
a ca
de liberdade adicionais que correspondem a deslocamentos normais
`s paredes da sec¸˜o. Miosga1976
a ca
wn (x, s) = χn (s) Vn (x)
A equa¸˜o geral da GBT escrita em fun¸˜o do vector que agrupa
ca ca
as amplitudes das fun¸˜es de aproxima¸˜o adoptadas ´ escrita na
co ca e
forma
em que Vt = [Va (x), Vn (x)]
− G DV + BV = p
EC V
Os modos de deforma¸˜o s˜o obtidos atrav´s da resolu¸˜o de um
ca a e ca
problema linear de valores e vectores pr´prios,
o
(C − µB) q = 0 µ = 0 com multiplicidade alg´brica
e
α = 4, os quais representam os modos de extens˜o axial,
a
flex˜o e tor¸˜o.
a ca
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
29. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Desenvolvimentos da GBT
TU Darmstadt
Saal1974
Miosga1976
Inclus˜o de graus de liberdade de flex˜o transversal (normais `
a a a
parede);
Desenvolvimento de an´lise geometricamente n˜o linear.
a a
M¨ller1982
o
Desenvolvimento para aplica¸˜o a sec¸oes fechadas e sec¸oes
ca c˜ c˜
ramificadas.
Heinz1994
Macro-elementos para a resolu¸˜o do sistema de equa¸oes
ca c˜
Couchon2001
Desenvolvimento para aplica¸˜o da GBT ` an´lise de lajes.
ca aa
Salford University, Leach1989
An´lise de estabilidade de perfis enformados a frio
a
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
30. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Desenvolvimentos da GBT em Portugal
IST, DECivil
Silvestre2005
Defini¸˜o de modos de corte;
ca
Defini¸˜o de modos de extens˜o transversal;
ca a
Aplica¸˜o a sec¸oes de materiais comp´sitos.
ca c˜ o
Gon¸alves2007
c
Inclui a formula¸˜o da GBT no contexto de uma teoria
ca
geometricamente n˜o linear (Simmo, Ritto);
a
Aplica¸˜o a sec¸oes arbitr´rias, M¨ller1982 ;
ca c˜ a o
Aplica¸˜o a an´lise fisicamente n˜o linear de pe¸as em
ca a a c
alum´ınio.
FCTUC Coimbra Sim˜o2005
a
Considera distor¸˜o do folheto m´dio sec¸˜o para sec¸˜es
ca e ca co
fechadas;
Define modos de extens˜o transversal;
a
Desenvolve an´lise de p´s-encurvadura.
a o
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
31. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Teoria de Sedlacek1968
V´lida para sec¸˜es abertas, sec¸˜es fechadas e sec¸˜es
a co co co
ramificadas.
Sec¸˜es abertas
co
Hip´teses, γxs = 0 e
o =0
s
Gradiente axial do deslocamento tangencial ´ dado por,
e
v (x, s) = Ψ(s) V (x)
Deslocamento axial ´ obtido a partir de,
e
Ω=−
u(x, s) = Ω V (x) em que Ψ(s) ds
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
32. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Sec¸˜es fechadas
co
Hip´teses,
o
SV ω
γxs = γxs por que γxs = 0 e =0
s
Gradiente axial do deslocamento tangencial ´ dado por,
e
v (x, s) = [Ψ(s) − Θ(s)] V (x)
Deslocamento axial ´ obtido a partir de,
e
Ω=−
u(x, s) = Ω V (x) em que Θ(s) ds
Equa¸˜o fundamental do modelo
ca
− G JV + LV = p
EF V
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
33. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Desacoplamento considera duas fases,
Desacoplamento do empenamento de distor¸˜o relativamente
ca
aos modos cl´ssicos;
a
(F − λ L)v = 0.
Desenvolvimentos e aplica¸˜es da teoria de Sedlacek1968
co
Maisel1974
1
Usuki1976
2
Hangang Li1994
3
Bogensperger2000
4
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
34. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Enquadramento - An´lise de tabuleiros de pontes
a
Analogia de viga em meio el´stico para a an´lise de distor¸˜o,
a a ca
Vlassov1941 , Knittel1965 , Wrigth1968 e Oliveira Pedro1994
despreza a distor¸˜o no folheto m´dio, γxs = 0, admite “medida”
ca e
de distor¸˜o generalizada da sec¸˜o, γd (x);
ca ca
define empenamento de distor¸˜o devido ` deforma¸˜o transversal
ca a ca
n˜o uniforme da sec¸˜o, uω d → γd (x);
a ca
tens˜es de empenamento σω d , → γd (x) implicam por equil´
o ıbrio a
existˆncia de tens˜es de corte τω d → γd (x);
e o
o gradiente longitudinal das tens˜es de corte, γd (x) induz
o
resistˆncia ao empenamento de distor¸˜o;
e ca
resistˆncia ` distor¸˜o por flex˜o transversal da sec¸˜o, κ γd .
e a ca a ca
EΓ γd + G κ γd = 0
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
35. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Enquadramento - An´lise de tabuleiros de pontes
a
Bazant1968,1974
Maisel1974,1980 Tem o m´rito de produzir uma extensa revis˜o da
e a
literatura sobre o assunto, divulgando ` comunidade cient´
a ıfica
M´todo de K¨llbrunner, empenamento de tor¸˜o n˜o uniforme;
e o ca a
M´todo de Sedlacek empenamento de distor¸˜o;
e ca
M´todo de Schmackpfeffer efeito de shear-lag;
e
Kristek1979 Considera deformabilidade da sec¸˜o em 2 passos
ca
Sec¸˜o r´
ca ıgida atrav´s de uma “escora” na diagonal;
e
Aplica¸˜o do esfor¸o da “escora” num modelo de p´rtico da
ca c o
sec¸˜o.
ca
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
36. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Enquadramento - An´lise de tabuleiros de pontes
a
Paavola1990
Virtuoso1991
An´lise de pontes curvas em caix˜o;
a a
Define coordenadas generalizadas associadas a deslocamentos
perpendiculares ao plano da sec¸ao e a deslocamentos no
c
plano da sec¸˜o;
ca
Considera shear-lag, empenamento de tor¸˜o e de distor¸˜o.
ca ca
Hangang Li1991
An´lise de pontes curvas em caix˜o;
a a
Considera m´todos propostos por Maisel.
e
Bogensperger2000
“M´todo dos empenamentos adicionais”
e
Considera a sec¸˜o r´
ca ıgida no seu pr´prio plano;
o
Processo de desacoplamento baseado em Sedlacek;
Aplica¸˜o a pontes com secc˜o de in´rcia vari´vel.
ca a e a
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
37. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Enquadramento - An´lise de p´s de helic´ptero
a a o
An´lise de p´s de helic´ptero
a a o
Giavotto1983 ;
Solu¸˜es centrais, solu¸˜es de extremidade
co co
Deslocamentos como soma de duas parcelas
parcela que n˜o “deforma” a sec¸˜o;
a ca
parcela que produz empenamento e distor¸˜o da sec¸˜o
ca ca
resolvida atrav´s de problema quadr´tico de valores e vectores
e a
pr´prios.
o
Bauchau1985 - Eigenwarpings;
Considera sec¸˜o r´
ca ıgida transversalmente;
= φ(s) F (x) γ = Γ(s) F(x)
F (x) − µ2 F(x) = 0
Hodges2002 M´todo variacional assimpt´tico - VABS.
e o
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
38. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Enquadramento - An´lise de sec¸˜es compactas
a co
Modelos 1-D de pe¸as lineares de sec¸˜o compacta
c ca
Vlassov1941 - An´lise de sec¸˜es sujeitas ` tor¸˜o, considera o
a co a ca
1
empenamento proporcional a uma fun¸˜o independente da
ca
rota¸˜o da sec¸˜o;
ca ca
Teorema de Toupin (3D), teorema de Knowles (2D)
2
Quantifica¸˜o do principio de Saint-Venant U ≤ U0 eλ x ;
ca
1968 - Determina¸˜o de factores de corte;
Cowper ca
3
Adopta deslocamento m´dio da sec¸˜o, solu¸˜es de Saint-Venant.
e ca co
Massonet1983 - Flex˜o n˜o uniforme;
aa
4
Ie e Kosmatka - Empenamento da sec¸˜o; ca
5
Empenamentos de 1a ordem, solu¸˜es de Saint-Venant.
co
Kazic - An´lise da tor¸˜o n˜o uniforme em sec¸˜es compactas;
a ca a co
6
EBR Pereira1994
7
Desenvolvimento em s´rie da aproxima¸˜o do campo de
e ca
deslocamentos na sec¸˜o;
ca
Considera distor¸˜o da sec¸˜o.
ca ca
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
39. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Caracter´
ısticas da formula¸˜o desenvolvida
ca
Formula¸˜o desenvolvida
ca
Na formula¸˜o desenvolvida os deslocamentos s˜o projectados na
ca a
sec¸˜o transversal, adoptando um conjuntos de fun¸˜es base
ca co
linearmente independentes em cada direc¸˜o do espa¸o.
ca c
ˆ
u(x, y, z) = B(y, z) u(x)
A formula¸˜o ´ gen´rica face ` flexibilidade adoptada para a
ca e e a
aproxima¸˜o do campo de deslocamentos, permitindo de forma
ca
natural considerar
A deformabilidade transversal da sec¸˜o (flex˜o e distor¸˜o
ca a ca
1
global);
A deforma¸˜o por corte da sec¸˜o;
ca ca
2
Sec¸˜o de geometria arbitr´ria (aberta, fechada, ramificada).
ca a
3
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
40. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Caracter´
ısticas da formula¸˜o desenvolvida
ca
Equa¸˜es de equil´
co ıbrio Condi¸˜es de compatibilidade
co
= D∗ u
Dσ + f = 0
Nσ = ˆ ˆ
uΓ = u
t
Rela¸˜o constitutiva
ca σ=C
DCD∗ u + f = 0
Equa¸˜o equl´
ca ıbrio, formula¸˜o forte
ca
M´todo dos res´
e ıduos pesados
t (D C D∗ B u + f ) dΩ = 0
ˆ
ΩB
D∗ = D∗ + D∗
Decomposi¸˜o do operador diferencial
ca x yz
Obten¸˜o da equa¸˜o diferencial de equl´
ca ca ıbrio definida em
termos das fun¸˜es de deslocamentos ao longo do eixo da
co
ˆ
pe¸a - u(x)
c
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
41. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Caracter´
ısticas da formula¸˜o desenvolvida
ca
Aplica¸˜o a vigas de parede fina, sec¸˜o transversal unidimensional
ca ca
- an´lise 2D
a
Sistema de Equa¸oes diferenciais de 2a ordem
c
K2 u + K1 u + K0 u + p = 0 em que u = [ˆ x , us ]t
¯ˆ
ˆ ˆ ˆ uˆ
ˆ ˆ
ux = φ ux e us = ψ us
φ e ψ definidas de forma independente;
Distor¸˜o do folheto m´dio e deformabilidade transversal
ca e
consideradas de forma natural;
Considera-se um estado plano de tens˜o.
a
K2 e K0 sim´tricas, positivas definidas, K1 anti-sim´trica;
e e
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
42. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Caracter´
ısticas da formula¸˜o desenvolvida
ca
Aplica¸˜o a vigas de parede fina, an´lise 3D - hip´tese de Kirchhoff
ca a o
Sistema de equa¸˜es diferenciais de 4a ordem
co
u = [ˆ x , us , un ]t
¯ˆ
ˆ ˆ ˆ ˆ uˆˆ
K4 u + K2 u + K1 u + K0 u + p = 0
ux = φ ux − n χˆ n us = ψ us − n χ,s un
ˆ ˆ ˆ ˆ
un = χ un u
χ, φ e ψ definidas de forma independente;
Considera a deformabilidade por corte do folheto m´dio.
e
K4 K2 K1 K0
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
43. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Caracter´
ısticas da formula¸˜o desenvolvida
ca
Aplica¸˜o a vigas de sec¸˜o compacta
ca ca
Sistema de equa¸˜es diferenciais de 2a ordem
co
K2 u + K1 u + K0 u + p = 0 u = [ˆ x , uy , uz ]t
¯ˆ
ˆ ˆ ˆ uˆˆ
ˆ ˆ ˆ
ux = ψ ux uy = φ uy uz = χ uz
ψ, φ e χ definidas de forma independente;
Consideradas todas as componentes de deforma¸˜o.
ca
K2 K1 K0
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
44. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
An´lise da solu¸˜o homog´nea da equa¸˜o diferencial para a
a ca e ca
obten¸˜o de modos de deforma¸˜o
ca ca
Obten¸˜o de modos de deforma¸˜o com base na an´lise da solu¸˜o
ca ca a ca
homog´nea da equa¸˜o diferencial.
e ca
Da solu¸˜o geral, u = u0 eλ x obtˆm-se as seguintes equa¸˜es
ˆ ˆ
ca e co
alg´bricas,
e
ˆ
Q(λ) u0 = 0 Problema quadr´tico de valores pr´prios;
a o
ˆ
P(λ) u0 = 0 Problema qu´rtico de valores pr´prios;
a o
uma vez que eλ x > 0 e sendo Q(λ) e P(λ) as matrizes
polinomiais definidas por,
Q(λ) = K2 λ2 + K1 λ + K0
P(λ) = K4 λ4 + K2 λ2 + K1 λ + K0
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
45. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Modos de deforma¸˜o
ca
Obten¸˜o dos modos de deforma¸˜o
ca ca
Problema quadr´tico
a
1
An´lise 3D de vigas de parede fina;
a
Vigas de sec¸˜o compacta.
ca
Problema qu´rtico An´lise 3D de vigas de parede fina -
a a
2
formula¸˜o de Kirchhoff.
ca
Os vectores pr´prios caracterizam a forma dos modos na sec¸˜o
o ca
3
transversal;
Os valores pr´prios caracterizam o comportamento ao longo do eixo
o
4
da pe¸a.
c
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
46. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Formula¸˜o geral
ca
Caracter´
ısticas espectrais do problema
Pares de valores pr´prios reais, ±a (sim´tricos)
o e
Qu´druplos de valores pr´prios complexos, ±a ± b ı
a o
(sim´tricos e conjugados)
e
Valor pr´prio zero como raiz m´ltipla da equa¸˜o
o u ca
caracter´
ıstica;
An´lise 2D λ = 0 → α = 6;
a
An´lise 3D λ = 0 → α = 12.
a
O conjunto de vectores pr´prios n˜o ´ linearmente
o ae
independente, e.g. existem mais de 2 n vectores para um
problema com n graus de liberdade ;
Existem vectores pr´prios com componente complexas;
o
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
47. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Formula¸˜o geral
ca
Modos fundamentais
Correspondem a λ = 0, pelo que n˜o tˆm decaimento ao longo do
ae
eixo da pe¸a.
c
Definem-se com base nos vectores pr´prios determinados por:
o
K0 q = 0 i.e. q ∈ N (K0 ) | Dim N (K0 ) = β < α em que β
´ a multiplicidade geom´trica de K0
e e
C´lculo de cadeias de Jordan;
a
Solu¸˜es polinomiais da equa¸˜o diferencial;
co ca
x3 x2
u(x) = 3! u0 + 2! u1 + x u2 + u3
Os movimentos de corpo r´ ıgido da pe¸a;
c
Os modos de deforma¸˜o associados `: extens˜o axial, tor¸˜o
ca a a ca
uniforme, flex˜o circular, flex˜o simples;
a a
Determina¸˜o do centro el´stico (cg), do centro de tor¸˜o e
ca a ca
dos eixos principais de flex˜o atrav´s da ortogonaliza¸˜o dos
a e ca
modos.
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
48. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Formula¸˜o geral
ca
Modos de ordem superior
1 Os modos de ordem superior λ = 0 tˆm um comportamento
e
de decaimento, determinado por Re(λ), ao longo do eixo da
viga, podendo ter car´cter oscilat´rio, definido com base em
a o
Im(λ).
Modos superiores s˜o ortogonais entre si e em rela¸˜o aos
a ca
2
modos fundamentais numa m´trica que est´ associada ao
e a
problema n˜o linear de valores pr´prios.
a o
Viga em meio el´stico EI w(x) + k w(x) = p(x)
a
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
49. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Formula¸˜o geral
ca
Nova base para a aproxima¸˜o de deslocamentos na sec¸˜o
ca ca
Atrav´s do valor do decaimento identificam-se os modos de
e
1
ordem superior com maior significado;
Seleccionados os modos, adopta-se uma nova base para o
2
espa¸o das fun¸˜es de aproxima¸˜o na defini¸˜o das equa¸˜es
c co ca ca co
de equil´
ıbrio;
A mudan¸a de base dever´ ser isoespectral, de modo a
c a
3
garantir de que se reproduzem os modos seleccionados.
A nova base das fun¸˜es de aproxima¸˜o ´ obtida
co ca e
4
considerando uma transforma¸˜o linear
ca
No operador da transforma¸˜o T, as colunas representam a
ca
5
base do espa¸o vectorial dos modos solu¸˜o da equa¸˜o de
c ca ca
equil´
ıbrio.
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
50. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Formula¸˜o geral
ca
A aproxima¸˜o do campo de deslocamentos ´ efectuada de forma
ca e
independente em cada direc¸˜o do referencial adoptado, pelo que:
ca
·
Tx
T=
· Tyz
|T − λ I| = |Tx − λ Ix | |Tyz − λ Iyz | ⇒ Isoespectral
Tx base para os deslocamento axiais;
1
Tyz base para os deslocamento transversais.
2
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
51. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Formula¸˜o geral
ca
Desenvolvimento de um elemento finito
Dom´ınio Fronteira N s = tσ in Γσ
D K D∗ u(x) + p=0
ˆ ˆ ˆ
u = uu in Γu
Formula¸˜o elemento finito
ca
Aproxima¸˜o do campo de deslocamentos
ca
u(x) ∼ Ω(x)˜
ˆ q
=
M´todo dos res´
e ıduos pesados
ΩT (D K D∗ Ω q + p) dV = 0 ⇒ Kb q = Q0 + Q
˜ ˜
V
˜
q conjunto de inc´gnitas;
o
Ω matriz que agrupa as fun¸˜es de aproxima¸˜o ao longo do
co ca
eixo da pe¸a.
c
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
52. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Exemplo de aplica¸˜o - an´lise 2D
ca a
u(x, z) = Φ(z) u(x) em que u(x, z) = [ux , uz ]t
ˆ
ˆ
ϕ(z) 0 ux (x)
ˆ
Φ= u(x) =
ˆ
0 ψ(z) uz (x)
Viga de sec¸˜o transversalmente indeform´vel;
ca a
Discretiza¸˜o da sec¸˜o;
ca ca
Fun¸˜es de aproxima¸˜o, Lagrange lineares ou Hermite;
co ca
Determina¸˜o das matrizes globais, K0 , K1 e K2 .
ca
Resolu¸˜o do problema quadr´tico (K2 λ2 + K1 λ + K0 )q = 0
ca a
ϕ1 (z) ϕ2 (z) ϕ3 (z) ϕn (z) ψ(z)
˜
δx1 (x)
˜
ho δx2 (x)
o ˜
x δx3 (x)
z
˜
δz (x)
h
˜
δxn (x)
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
53. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Primeiro modo de ordem superior
3
2.5
2
Cross section height
Lagrange functions, 3 elements
Hermite functions, 1 element
1.5
Hermite functions, 3 elements
1
0.5
0
−1.5 −1 −0.5 0 0.5 1
Symmetric warping mode
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
54. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Segundo modo de ordem superior
3
2.5
Lagrange functions, 3 elements
Hermite functions, 1 element
2
Cross section height
Hermite functions, 3 elements
1.5
1
0.5
0
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2
Skew−symmetric warping mode
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
55. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Compara¸˜o dos modos obtidos
ca
Even axial stress comparison between models
4
3.5
3
Cross section height
2.5
2
Analytical solution
1.5
Hermite − 4 elements
Hermite − 1 element
1
Lagrange − 4 elements
0.5
0
−1 −0.5 0 0.5 1
Even stress distribution
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
56. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Exemplo de aplica¸˜o - sec¸˜o fechada transversalmente indeform´vel
ca ca a
Exemplo de aplica¸˜o - an´lise 3D
ca a
Aplica¸˜o ` an´lise de uma viga de parede fina de sec¸˜o fechada
ca a a ca
Deslocamentos axiais aproximados por fun¸˜es de Lagrange
co
quadr´ticas;
a
Deslocamentos transversais aproximados por fun¸˜es de
co
Hermite na direc¸˜o normal ` parede e por fun¸˜es de
ca a co
lagrange lineares na direc¸˜o tangencial;
ca
Considera-se a sec¸˜o discretizada em 4 elementos - 20 graus
ca
de liberdade;
Admite-se a sec¸˜o transversalmente indeform´vel - 11 graus
ca a
de liberdade.
Y
X
Z
t
s
n
H x
t
B
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
57. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Exemplo de aplica¸˜o - sec¸˜o fechada transversalmente indeform´vel
ca ca a
Primeiro modo de ordem superior
1º Modo de empenamento
λ = 2.3
1
0.8
Altura H = 1.0 m
0.6
0.4
0.2
0
2
1.5 1
0.5
1
0
0.5 −0.5
Largura B = 2.0 m Eixo da viga
0 −1
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
58. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Exemplo de aplica¸˜o - sec¸˜o fechada transversalmente indeform´vel
ca ca a
Segundo modo de ordem superior
2º Modo de empenamento
λ = 2.8
1
0.8
Altura H = 1.0 m
0.6
0.4
0.2
0
2
1.5 0.6
0.4
1 0.2
0
0.5
−0.2
Largura B = 2.0 m Eixo da viga
0 −0.4
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
59. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Exemplo de aplica¸˜o - sec¸˜o fechada transversalmente indeform´vel
ca ca a
Terceiro modo de ordem superior
3º Modo de empenamento
λ = 3.5
1
0.8
Altura H = 1.0 m
0.6
0.4
0.2
0
2
1.5 1
0.5
1
0
0.5 −0.5
0 −1
Largura B = 2.0 m Eixo da viga
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models
60. Motiva¸˜o
ca Formula¸˜o
ca Modos de deforma¸˜o
ca Exemplo 2D Exemplo 3D Trabalho por desenvolver
Exemplo de aplica¸˜o - sec¸˜o fechada transversalmente indeform´vel
ca ca a
Quarto modo de ordem superior
4º Modo de empenamento
λ = 7.0
1
0.8
Altura H = 1.0 m
0.6
0.4
0.2
0
2
1.5 1
0.5
1
0
0.5
Largura B = 2.0 m −0.5
Eixo da viga
0 −1
Semin´rio Doutoramento
a IST, DECivil - Higher Order Thin-Walled Beam Models