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Massachusetts Institute of Technology

Finite Element Procedures for Solids and Structures

Massachusetts Institute of Technology via MIT OpenCourseWare

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Overview

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Finite element analysis is now widely used for solving complex static and dynamic problems encountered in engineering and the sciences. In these two video courses, {{% resource_link "b3b04b67-272b-4cc1-941f-24dcb363c343" "Professor K. J. Bathe" %}}, a researcher of world renown in the field of finite element analysis, teaches the basic principles used for effective finite element analysis, describes the general assumptions, and discusses the implementation of finite element procedures for linear and nonlinear analyses. These videos were produced in 1982 and 1986 by the MIT Center for Advanced Engineering Study.

Syllabus

  • Lecture 1: Introduction to Nonlinear Analysis
  • Lecture 1: Some Basic Concepts of Engineering Analysis
  • Lecture 2: Analysis of Continuous Systems
  • Lecture 2: Basic Considerations in Nonlinear Analysis
  • Lecture 3: Lagrangian Continuum Mechanics Variables for Analysis
  • Lecture 3: The Displacement-Based Finite Element Method
  • Lecture 4: Generalized Coordinate Finite Element Models
  • Lecture 4: Total Lagrangian Formulation - Incremental Analysis
  • Lecture 5: Implementation of Methods in Computer Programs
  • Lecture 5: Updated Lagrangian Formulation - Incremental Analysis
  • Lecture 6: Formulation and Calculation of Isoparametric Models
  • Lecture 6: Formulation of Finite Element Matrices
  • Lecture 7: 2D & 3D Solid Elements; Plane Stress/Strain Conditions
  • Lecture 7: Formulation of Structural Elements
  • Lecture 8: 2-Noded Truss Element - Updated Lagrangian Formulation
  • Lecture 8: Numerical Integrations, Modeling Considerations
  • Lecture 9: 2-Noded Truss Element - Total Lagrangian Formulation
  • Lecture 9: Solution of Equilibrium Equations in Static Analysis
  • Lecture 10: Solution of Equilibrium Equations in Dynamic Analysis
  • Lecture 10: Solution of Nonlinear Static FE Equations I
  • Lecture 11: Mode Superposition Analysis; Time History
  • Lecture 11: Solution of Nonlinear Static FE Equations II
  • Lecture 12: Demonstrative Example Solutions in Static Analysis
  • Lecture 12: Solution Methods for Frequencies and Mode Shapes
  • 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

Taught by

Klaus-Jürgen Bathe

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