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 09 - 2-Noded Truss Element - Total Lagrangian Formulation |
Derivation of total Lagrangian truss element displacement and strain-displacement matrices from continuum mechanics equations. Mathematical and physical explanation that only one component of the 2nd Piola-Kirchhoff stress tensor is nonzero. Physical explanation of the matrices obtained directly by application of the principle of virtual work. Discussion of initial displacement effect. Comparison of updated and total Lagrangian formulations.
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