Lecture 2: Basic Considerations in Nonlinear Analysis

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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

Related Resources

Study Guide (PDF)

Readings

Section 6.1

Examples

Problems 6.1-6.4

References

Sussman, T., and K. J. Bathe. “Studies of Finite Element Procedures: On Mesh Selection.Computers & Structures 21 (1985): 257-264.

Sussman, T., and K. J. Bathe. “Studies of Finite Element Procedures: Stress Band Plots and the Evaluation of Finite Element Meshes.Engineering Computations 3 (1986): 178-191.