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