Nonlinear Analysis

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

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