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

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Presentation transcript:

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

Interpolation displacements strains stresses

Shape function for triangular element If:

FEM Discretization Cantilever Beam

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

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

Variational Equation x direction equation Divergence theorem

Element Discretization

Interpolation

Arbitrary Spatial Function

Arbitrary function in Matrix : arbitrary value

Force Terms

Stresses Related to Displacement

F=Ku Stiffness Matrix

Stiffness Matrix

FEM Linear Equations