FEA Basic Introduction Training By Praveen conducted in 2008

1. Finite Element Analysis
Praveen Patil
Y
Z X

2. Contents
• Introduction to the Finite Element Method
(FEM)
• Future Trends

3. FEM Applied to Solid Mechanics Problems
• A FEM model in solid mechanics
can be thought of as a system of
assembled springs. When a load
is applied, all elements deform
until all forces balance.
• F = Kd
Create elements
of the beam • K is dependant upon Young’s
modulus and Poisson’s ratio,
as well as the geometry.
• Equations from discrete elements
are assembled together to form
Nodal displacement and forces the global stiffness matrix.
dxi 1 dxi 2 • Deflections are obtained by
solving the assembled set of
dyi 1 1 2 linear equations.
dyi 2
• Stresses and strains are
4 3 calculated from the deflections.

4. Classification of Solid-Mechanics Problems
Analysis of solids
Static Dynamics
Elementary Advanced
Behavior of Solids Stress Stiffening
Large Displacement
Geometric
Instability
Linear Nonlinear
Fracture
Plasticity
Material
Viscoplasticity
Geometric
Classification of solids
Skeletal Systems Plates and Shells Solid Blocks
1D Elements 2D Elements 3D Elements
Trusses Plane Stress Brick Elements
Cables Plane Strain Tetrahedral Elements
Pipes Axisymmetric General Elements
Plate Bending
Shells with flat elements
Shells with curved elements

5. Governing Equation for Solid Mechanics Problems
• Basic equation for a static analysis is as follows:
[K] {u} = {Fapp} + {Fth} + {Fpr} + {Fma} + {Fpl} + {Fcr} + {Fsw}
+ {Fld}
[K] = total stiffness matrix
{u} = nodal displacement
{Fapp} = applied nodal force load vector
{Fth} = applied element thermal load vector
{Fpr} = applied element pressure load vector
{Fma} = applied element body force vector
{Fpl} = element plastic strain load vector
{Fcr} = element creep strain load vector
{Fsw} = element swelling strain load vector
{Fld} = element large deflection load vector

6. Six Steps in the Finite Element Method
• Step 1 - Discretization: The problem domain is discretized
into a collection of simple shapes, or elements.
• Step 2 - Develop Element Equations: Developed using the
physics of the problem, and typically Galerkin’s Method or
variational principles.
• Step 3 - Assembly: The element equations for each element
in the FEM mesh are assembled into a set of global equations
that model the properties of the entire system.
• Step 4 - Application of Boundary Conditions: Solution
cannot be obtained unless boundary conditions are applied.
They reflect the known values for certain primary unknowns.
Imposing the boundary conditions modifies the global
equations.
• Step 5 - Solve for Primary Unknowns: The modified global
equations are solved for the primary unknowns at the nodes.
• Step 6 - Calculate Derived Variables: Calculated using the
nodal values of the primary variables.

7. Process Flow in a Typical FEM Analysis
Problem Analysis and
Start Stop
Definition design decisions
Processor/Solver Post-processor
Pre-processor • Prints or plots
• Generates
contours of stress
• Reads or generates element shape
components.
nodes and elements functions
• Prints or plots
(e.g. MD-Patran) • Calculates master
contours of
• Reads or generates element equations
displacements.
material property data. • Calculates
• Evaluates and
• Reads or generates transformation
prints error
boundary conditions matrices
bounds.
(loads and • Maps element
equations into
constraints.)
global system
Step 6
• Assembles
element equations
Step 1, Step 4 • Introduces
boundary Steps 2, 3, 5
conditions
• Performs solution
procedures

8. Step 1: Discretization - Mesh Generation
surface model
airfoil geometry
(from CAD program e.g CATIA)
e.g. MD-Patran
ET,1,SOLID45
N, 1, 183.894081 , -.770218637 , 5.30522740
N, 2, 183.893935 , -.838009645 , 5.29452965
.
.
TYPE, 1
E, 1, 2, 80, 79, 4, 5, 83, 82
E, 2, 3, 81, 80, 5, 6, 84, 83
.
.
.
meshed model

9. Step 4: Boundary Conditions for a Solid Mechanics Problem
• Displacements ⇒ DOF constraints usually
specified at model boundaries to define rigid
supports.
• Forces and Moments ⇒ Concentrated loads on
nodes usually specified on the model exterior.
• Pressures ⇒ Surface loads usually specified on
the model exterior.
• Temperatures ⇒ Input at nodes to study the
effect of thermal expansion or contraction.
• Inertia Loads ⇒ Loads that affect the entire
structure (ex: acceleration, rotation).

10. Step 4: Applying Boundary Conditions (Thermal Loads)
300
Nodes from 300
275
FE Modeler 275
250
250 bf, 1,temp, 149.77
225
225 bf, 2,temp, 149.78
Temp .
200 .
mapper 200
.
175 bf, 1637,temp, 303.64
bf, 1638,temp, 303.63
Thermal 150
Soln Files 150
175

11. Step 4: Applying Boundary Conditions (Other Loads)
• Speed, temperature and hub fixity applied to sample
problem.
• FE Modeler used to apply speed and hub constraint.
antype,static
omega,10400*3.1416/30
d,1,all,0,0,57,1
Z
Y X

12. Information Available from Various Types of FEM Analysis
• Static analysis • Heat transfer analysis
» Deflection »Temperature
» Stresses » Heat fluxes
» Strains
» Thermal gradients
» Forces
» Heat flow from
» Energies convection faces
• Dynamic analysis
• Fluid analysis
» Frequencies
» Deflection (mode » Pressures
shape) » Gas temperatures
» Stresses » Convection coefficients
» Strains » Velocities
» Forces
» Energies

13. Example FEM Application Areas
• Automotive industry • Aerospace industry
» Static analyses » Static analyses
» Modal analyses » Modal analyses
» Transient dynamics » Aerodynamics
» Heat transfer » Transient dynamics
» Mechanisms » Heat transfer
» Fracture mechanics » Fracture mechanics
» Metal forming » Creep and plasticity analyses
» Crashworthiness » Composite materials
• Architectural » Aeroelasticity
» Soil mechanics » Metal forming
» Rock mechanics » Crashworthiness
» Hydraulics
» Fracture mechanics
» Hydroelasticity

14. Variety of FEM Solutions is Wide and Growing Wider
• The FEM has been applied to a richly diverse array of scientific
and technological problems.
• FEM is increasingly applied to a variety of real-world design and
analysis problems.

15. Technologies That Compete With the FEM
• Other numerical solution methods:
– Finite differences
» Approximates the derivatives in the differential equation using
difference equations.
» Useful for solving heat transfer and fluid mechanics problems.
» Works well for two-dimensional regions with boundaries parallel
to the coordinate axes.
» Cumbersome when regions have curved boundaries.
– Weighted residual methods (not confined to a small subdomain):
» Collocation
» Subdomain
» Least squares*
» Galerkin’s method*
– Variational Methods* (not confined to a small subdomain)
* Denotes a method that has been used to formulate finite element
solutions.

16. Technologies that Compete With the FEM (cont.)
• Prototype Testing
» Reliable. Well-understood.
» Trusted by regulatory agencies (FAA, DOT, etc.)
» Results are essential for calibration of simulation software.
» Results are essential to verify modeled results from simulation.
» Non destructive testing (NDT) is lowering costs of testing in
general.
» Expensive, compared to simulation.
» Time consuming.
» Development programs that rely too much on testing are
increasingly less competitive in today’s market.
» Faster product development schedules are pressuring the quality of
development test efforts.
» Data integrity is more difficult to maintain, compared to
simulation.

17. Contents
• Introduction to the Finite Element Method
(FEM)
• Future Trends

18. Future Trends in the FEM and Simulation
• The FEM in particular, and simulation in general, are becoming
integrated with the entire product development process (rather than just
another task in the product development process):
– FEM cannot become the bottleneck.
• A broader range of people are using the FEM:
– Not just hard-core analysts. Future (?? Word excel??)
• Increased data sharing between analysis data sources (CAD, testing,
FEM software, ERM software.)
• FEM software is becoming easier to use:
– Improved GUIs, automeshers.
– Increased use of sophisticated shellscripts and “wizards.(??)”

19. Conflicting Variables . . .with Reduci ng time
NVH & Crash Optimization of Vehicle Body Overnight
• Ford body-in-prime (BIP) model of 390K DOF
• MSC.Nastran for NVH, 30 design variables
• RADIOSS for crash, 20 design variables Achieved overnight
• 10 design variables in common BIP optimization on
SGI 2800/256, with
• Sensitivity based Taylor approx. for NVH equivalent yield of 9
months CPU time
• Polynomial response surface for crash

20. Future Trends in the FEM and Simulation (cont.)
• Enhanced multiphysics capabilities are coming:
– Coupling between numerous physical phenomena.
» Ex: Fluid-structural interaction is the most common example.
» Ex: Semiconductor circuits, EMI and thermal buildup vary with current
densities.
• Improved life predictors, improved service estimations.
• Increasing use of non-deterministic analysis and design methods:
– Statistical modeling of material properties, tolerances, and anticipated loads.
– Sensitivity analyses.
• Faster and more powerful computer hardware. Massively parallel processing.
• FEM and simulation software available via Internet subscription.
• Decreasing reliance on testing. But (??)

21. Economics: Physical prototyping costs continue Increasi ng
Engineer more expensive than simulation tools
MSC/NASTRAN 1960 2006
Mainframes Simulation Costs $30,000 $0.02
(Source: General Motors)
Cost of CAE CAE Engineer Engineer System
vs. System Costs $36/hr $1.5/hr
Simulation (Source: Detroit Big3)
Cost of CAE
Engineer
Cost of Physical
Prototyping Workstations
and Servers
1960 Years 2006

22. Thanks.