Res.2-002 Nonlinear Finite Element Analysis
Res.2-002 Nonlinear Finite Element Analysis (MIT OCW). Instructor: Professor K. J. Bathe. This course presents effective finite element procedures for the nonlinear analysis of solids and structures. The finite element method is the ideal tool for solving complex static and dynamic problems in engineering and the sciences. Nonlinear analysis models kinematic and/or materially nonlinear effects. In these lectures, general nonlinear analysis techniques are presented by emphasizing physical concepts. The mathematical foundation of nonlinear finite element techniques is given in light of these physical requirements. A wide range of questions in engineering and the sciences can be addressed with these methods. (from ocw.mit.edu)
| Lecture 10 - Solution of Nonlinear Static FE Equations 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. 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.
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