Lecture 10: Solution of Nonlinear Static FE Equations I

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Topics: Solution of the nonlinear finite element equations in static analysis I

  • Short review of Newton-Raphson iteration for the root of a single equation
  • Newton-Raphson iteration for multiple degree of freedom systems
  • Derivation of governing equations by Taylor series expansion
  • Initial stress, modified Newton-Raphson and full Newton-Raphson methods
  • Demonstrative simple example
  • Line searches
  • The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method
  • Computations in the BFGS method as an effective scheme
  • Flowcharts of modified Newton-Raphson, BFGS, and full Newton-Raphson methods
  • Convergence criteria and tolerances

Instructor: Klaus-Jürgen Bathe

Related Resources

Study Guide (PDF)


Sections 6.1, 8.4


Problems 6.1-6.4, 8.23, 8.24


Bathe, K. J., and A. P. Cimento. “Some Practical Procedures for the Solution of Nonlinear Finite Element Equations.Computer Methods In Applied Mechanics and Engineering 22 (April 1980): 59-85.