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Finite Element Method

Introduction

The field of Mechanics can be subdevided into three major areas, namely Theoretical, Applied and Computational Mechanics.
The finite element method (FEM), or finite element analysis (FEA) which is a branch of computational mechanics is based on the idea of building a complicated object with simple blocks, or, dividing a complicated object into small and manageable pieces. Application of this simple idea can be found everywhere in everyday life as well as in engineering.
The objective of the course is to teach in a unified manner the fundamentals of finite element analysis of solids, and structures. This includes the theoretical foundations and computer implementation of finite element in Matlab environment. The course is divided into three parts:

  1. Basic and fundamental concepts of structural modeling
  2. Formulation of Finite Elements
  3. Computer Implementation of the Finite Element Method

 

Syllabus

  1. Introduction to Finite Element Method
  2. The direct method
  3. Linear static analysis of bar elements
  4. Bar elements in 2D and 3D space
  5. Beam elements
  6. 3D beam elements
  7. Introduction to Matlab
  8. Computer implementation of bar and beam elements
  9. Two-dimensional problems
  10. Constant and linear strain triangles elements
  11. Other types of 2D elements
  12. Solid elements for 3D problems
  13. Multi-freedom constraints
  14. Finite element modeling and solution techniques
  15. Methods of solving FEM equations
  16. Interpolation models
  17. Numerical integration
  18. Automatic renumbering of FE models
  19. Computer implementation of 2D problems
  20. Bending behavior of plates
  21. Finite element modeling of plates
Prerequisites: 

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Grading Policy: 

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Time: 

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Term: 
Fall 2012
Grade: 
Graduate