# Course - Finite Element Procedures for Solids and Structures: Nonlinear Analysis

Course Level: Senior

This video series 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 videos, Professor K. J. Bathe, a researcher of world renown in the field of finite element analysis, builds upon the concepts developed in his previous video course on Linear Analysis. 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.

Prerequisites
• Lecture 1 - Introduction to Nonlinear Analysis
• Lecture 2 - Basic Considerations in Nonlinear Analysis
• Lecture 3 - Lagrangian Continuum Mechanics Variables for Analysis
• Lecture 4 - Total Lagrangian Formulation-Incremental Analysis
• Lecture 5 - Updated Lagrangian Formulation-Incremental Analysis
• Lecture 6 - Formulation of Finite Element Matrices
• Lecture 7 - 2D and 3D Solid Elements; Plane Stress-Strain Conditions
• Lecture 8 - 2-Node Truss Element - Updated Lagrangian Formulation
• Lecture 9 - 2-Node 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 - Solutions 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