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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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Lecture 01 - Introduction to Nonlinear Analysis
Lecture 02 - Basic Considerations in Nonlinear Analysis
Lecture 03 - Lagrangian Continuum Mechanics Variables for Analysis
Lecture 04 - Total Lagrangian Formulation - Incremental Analysis
Lecture 05 - Updated Lagrangian Formulation - Incremental Analysis
Lecture 06 - Formulation of Finite Element Matrices
Lecture 07 - 2D & 3D Solid Elements; Plane Stress/Strain Conditions
Lecture 08 - 2-Noded Truss Element - Updated Lagrangian Formulation
Lecture 09 - 2-Noded Truss Element - Total Lagrangian Formulation
Lecture 10 - Solution of Nonlinear Static FE Equations I
Lecture 11 - Solution of Nonlinear Static FE Equations II
Lecture 12 - Demonstrative Example Solutions in Static Analysis
Lecture 13 - Solution of Nonlinear Dynamic Response I
Lecture 14 - Solution of Nonlinear Dynamic Response II
Lecture 15 - Elastic Constitutive Relations in T. L. Formulation
Lecture 16 - Elastic Constitutive Relations in U. L. Formulation
Lecture 17 - Modeling of Elasto-Plastic and Creep Response I
Lecture 18 - Modeling of Elasto-Plastic and Creep Response II
Lecture 19 - Beam, Plate, and Shell Elements I
Lecture 20 - Beam, Plate, and Shell Elements II
Lecture 21 - Demonstration Using ADINA - Linear Analysis
Lecture 22 - Demonstration Using ADINA - Nonlinear Analysis