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Non-Linear Finite Element Method

Introduction

This course describes, besides the physical and mathematical background of the finite element method, special discretization techniques and algorithms which have to be applied for nonlinear problems of solid mechanics.
The course will describe the theory and computer implementation of nonlinear finite element method. The implementation will be carried out on simple heat transfer and solid mechanics problems.
The focus is on geometric nonlinearities; however some material nonlinearity will also be discussed. Both static and transient (time-dependent) problems will be studied.
The main textbook of the course is the book “An Introduction to nonlinear finite element analysis” by J.N. Reddy. The book is suitable as a text book for a first course as nonlinear finite elements in mechanical, civil, aerospace engineering departments.

Syllabus

  1. Introduction
  2. A review of finite element method
    1. 1D problems
    2. 2D problems
    3. Library of 2D finite elements
    4. Numerical Integration
    5. Computer Implementation
  3. 1D heat transfer problems
  4. Governing differential equation
  5. Weak formulation
  6. Finite element model
  7. Solution procedure
  8. Computer implementation
  9. Euler-Bernouli beams
  10. Timoshenko beams
  11. Model equation
  12. Weak form
  13. Finite element method
  14. Solution procedure
  15. Computer implementation
  16. Classical plate theory (CPT)
  17. Variational formulation of CPT
  18. Finite element models of CPT
  19. Computer Implementation of CPT
  20. Time approximation
  21. Stability and accuracy
  22. Transient analysis of nonlinear problems
  23. Computer implementation
  24. Numerical examples
  25. Introduction
  26. Strain and stress measures
  27. Strain and stress measures between configurations
  28. Constitutive equations
  29. Total and updated Lagrangian formulations
  30. Finite element methods of 2D continua
  31. Nonlinear elastic problems
  32. Small deformation theory of plasticity
  33. Numerical examples
  34. Nonlinear bending of beams
  35. 2D heat transfer problems
  36. Nonlinear bending of elastic plates
  37. Nonlinear analysis of 2D problems
  38. Finite element formulation of solid continua
  39. Material nonlinearity
پیش نیازها: 

Finite Element I

Continuum Mechanics

سیاست نمره دهی: 
Midterm 30% Final Exam 40% Homeworks and Projects 30%
زمان بندی کلاس: 

Saturday 11:00 - 12:30

Monday  11:00 - 12:30

Class 1 Mechanical Engineering Department

Term: 
Spring 2015
Grade: 
Graduate