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 04 - Total Lagrangian Formulation - Incremental Analysis |
Review of basic principle of virtual work equation, objective in incremental solution. Incremental stress and strain decompositions in the total Lagrangian form of the principle of virtual work. Linear and nonlinear strain increments. Considerations for finite element discretization with continuum elements and structural elements. Consistent linearization of terms in the principle of virtual work for the incremental solution. Derivation of iterative equations. The modified Newton-Raphson iteration, flowchart of complete solution.
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