AME 50541: Finite Element for Structural Analysis

CATALOG DATA:
 An introduction to the finite element method with applications to problems in structural analysis. Basics of linear and non-linear finite element formulation and programming, applications to bars, beams and simple continuum problems, use of commercially available codes with advanced input/output capabilities.

Prerequisites: AME 20241 and MATH 20580

TEXTBOOK:
TR Chandrupatla and AS Belegundu, Introduction to Finite Elements in Engineering, 3 rd Edition, Prentice Hall, 2002.

COURSE OBJECTIVES :
 To give an introduction to the finite element method, with emphasis on the approximate solution of problems in structural mechanics. The course seeks to present a balanced view between coverage of the fundamentals of the method, implementation in computer programs, and the use of current commercial finite element programs.

TOPICS COVERED:

  1. Introduction to boundary –value problems
  2. Strong and weak formulation of boundary-value problems
  3. Approximate solutions using the Galerkin method
  4. Approximate solutions using the finite element method
  5. Introduction to floating-point computation
  6. Solution of linear equations systems by Gauss elimination and back substitution
  7. Principle of minimum potential energy in structural mechanics
  8. The Rayleigh-Ritz method
  9. Formulation and exact solutions for axial load and bending of bars
  10. Finite element formulation and solutions for bars under axial load
  11. Finite element formulation and solution for trusses
  12. Finite element formulation and solutions for beams under bending
  13. Introduction to solution of nonlinear problems using Newton ’s method
  14. Introduction to basic stress and strain concepts in linear elasticity
  15. Finite element formulation and solutions for plane problems in elasticity
  16. Use of commercial finite element codes.

SCHEDULE:
 The class meets for 50 minutes three times a week or 75 minutes twice a week. Laboratory exercises are conducted at other times.

CONTRIBUTION TO PROFESSIONAL COMPONENT :
This class is 100% devoted to engineering science.

CONTRIBUTION TO PROGRAM LEARNING OUTCOMES :
 The course uses lectures, homework assignments, programming assignments and the use of commercially available program to achieve the objective state above. The students’ progress is assed through the grading of homework, computer assignments and exams in the following areas:

a. Knowledge of the basic formulation of the finite element method

  1. be able to recognize boundary value problems and distinguish between strong and weak formulations.
  2. be able to use the Galerkin method to find approximate solutions to simple ordinary differential equations.
  3. be able to use the principle of minimum potential energy to develop approximate solutions to simple structural problems using the Rayleigh-Ritz method or the finite element method.
  4. be able to implement boundary conditions using the penalty or the elimination approaches
  5. be able to distinguish between linear and nonlinear problems.

b. Implementation and programming of finite element solutions for a class of problems

  1. be able to take a finite element formulation, develop an algorithm and program a computer to obtain and output solutions.
  2. be able to develop a user’s manual for the finite element implementations that has been developed

c. Use of commercially available finite element programs

  1. be aware of the current state-of-the-art regarding the pre-processing, processing and post-processing of finite element solutions using commercially available programs.

In order to assess the students’ progress in the class, all homework assignments, programming assignments and computer work are graded and recorded, and all exams are graded by the instructor. Some evaluation is by peer review, where on student is asked to use another’s program to solve a new problem. That student then reports the quality of the manual and service provided as well as the ease-of-use of the program and the accuracy of the solution.

Prepared by:Edmundo Corona, May 21,2004

Direct comments, questions, and corrections to amedept@nd.edu