2. FINITE ELEMENT ANALYSIS
Finite element analysis (FEA) is a computer
based numerical method for solving problems in a
wide range of engineering areas such as stress
analysis, thermal analysis and fluid flow, diffusion,
and magnetic field interactions.
3. NUMERICAL METHODS
• Functional approximating method
• Finite element method
• In this method the physical problems are first written in
terms of differential equations or any possible
• By integrating and applying boundary condition the
approximate solution can be obtained by this method.
4. FINITE ELEMENT METHOD
Finite element method instead of solving the
problems for entire body in one operation we
formulate the equation for each finite element and
combined them to obtained solution of whole body.
5. GENERAL STEPS OF FEA
• Numbering of nodes and elements
• Selection of displacement function
• Deviation of element stiffness matrix
• Assemble of element equations
• Applying boundary conditions
• Solution of unknown displacement
• Computation of stress and strain
• Predict the results
6. GENERALAPPROACHES OF FEA
• h –refinement
• p- refinement
h- refinement :
• h is for the linear dimension that characterizes the
size of an element.
• The size of the element may be its largest span, or
square root of area, or cubic root of the area.
7. p - refinement :
• p is for the degree of the highest complete polynomial in
the elements field quantity. p- refinements consists of
increasing the degree of polynomial with in elements
without changing the number of elements.
This may be achieved by the following ways :
• Adding degrees of freedom to the existing nodes
• Adding nodes on the existing inter element boundaries
• Adding internal degrees of freedom
10. TO FIND OUT THE MAXIMUM DEFLECTION OF CANTILEAVER BEAM
The steps will be followed are :
1. Change Job name.
2. Define element type. (“BEAM3”, which is a 2-D beam element)
3. Define real constants. (Area, Moment of Inertia, Height, SHEARZ)
4. Define material properties. (Young’s Modulus, EX -- only property required for this
5. Create nodes. (21 total)
6. Create beam elements between nodes. (20 total)
7. Apply constraints and loads to the model.
9. Plot deformed shape.
10. List reactions.
11. List the deflections at each node.
12. Define element table items for plotting and listing
of various stress components.
13. List element table items.
14. Plot element table items.
15. Exit the ANSYS program.
13. • The maximum deflection of the cantilever beam
• The von-mises stress is 286.19 N/m
Analytically this problem may be carried out
by some variation method such that Rayleigh ritz
method or weight residual method by using their
formulas and boundary conditions
In this experiment I have to find out
maximum deflection of cantilever beam and
stresses created in fixed area by using ansys
software from finite elements approaches.