Lecture 6: Formulation of Finite Element Matrices

Topics: Formulation of finite element matrices

• Summary of principle of virtual work equations in total and updated Lagrangian formulations
• Deformation-independent and deformation-dependent loading
• Materially-nonlinear-only analysis
• Dynamic analysis, implicit and explicit time integrations
• Derivations of finite element matrices for total and updated Lagrangian formulations, materially-nonlinear-only analysis
• Displacement and strain-displacement interpolation matrices
• Stress matrices
• Numerical integration and application of Gauss and Newton-Cotes formulas
• Example analysis: Elasto-plastic beam in bending
• Example analysis: A numerical experiment to test for correct element rigid body behavior

Instructor: Klaus-Jürgen Bathe