Lecture 10: Solution of Nonlinear Static FE Equations I

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