Nonlinear Analysis

Lecture 2: Basic Considerations in Nonlinear Analysis

Topics: Basic considerations in nonlinear analysis

  • The principle of virtual work in general nonlinear analysis, including all material and geometric nonlinearities
  • A simple instructive example
  • Introduction to the finite element incremental solution, statement and physical explanation of governing finite element equations
  • Requirements of equilibrium, compatibility, and the stress-strain law
  • Nodal point equilibrium versus local equilibrium
  • Assessment of accuracy of a solution
  • Example analysis: Stress concentration factor calculation for a plate with a hole in tension
  • Example analysis: Fracture mechanics stress intensity factor calculation for a plate with an eccentric crack in tension
  • Discussion of mesh evaluation by studying stress jumps along element boundaries and pressure band plots

Instructor: Klaus-Jürgen Bathe

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