1. Finite Element Method
Weak form
Monday, 11/4/2002

2. Interpolation
displacements
strains
stresses

3. Shape function for triangular element
If:

4. FEM Discretization
Cantilever Beam

5. Equilibrium Equations
Static problem.
Goal: Find displacements under the applied load
2D problem
Force boundary conditions
Displacement boundary conditions

6. Equilibrium Equation (Weak Form)
Force boundary conditions
Displacement boundary conditions
: arbitrary spatial function

7. Variational Equation
x direction equation
Divergence theorem

8. Element Discretization

9. Interpolation

10. Arbitrary Spatial Function

11. Arbitrary function in Matrix
: arbitrary value

12. Force Terms

13. Stresses Related to Displacement

14. F=Ku Stiffness Matrix

15. Stiffness Matrix

16. FEM Linear Equations