University of Washington
Aeronautics and Astronautics Department
AA 540 - Finite Element Analysis, Part 1
Winter 2016
Instructor: Dr. Marco Salviato, (206) 543-2170, salviato@aa.washington.edu
Teaching Assistant: Hyunryung Kim, hryungk@uw.edu
Classroom: Loew Hall, Room 206
Time: Monday, Wednesday and Friday 10:30-11:20 AM
Office Hours: TBA
Reference Textbooks:
Logan D.L., A First Course in the Finite Element Method, Cengage Learning,
2011.
Kim, N. and Sankar, B.V., Introduction to Finite Element Analysis and Design,
Wiley Publication, 2009.
Zienkiewicz, O.C., Taylor, R.L. and Zhu, J.Z., The Finite Element Method, Its
Basis & Fundamentals, B-H Elsevier, 2013; 7th edition.
Course Description:
This course aims at introducing and discussing the fundamentals of finite element
analysis (FEA). Formulation of the finite element method (FEM) using variational
and weighted residual methods will be discussed. Details of several element types and
interpolation functions will be covered. Application to solve implicit problems such
as in elasticity, thermal conduction, and other problems of engineering and physics
will be used to enforce the principles of FEM. The course uses the finite element code
HyperWorks/OptiStruct for the applications and problems, examples of various types
will be given as homework.
Course Outline
(Subject to change and adjustment)
1. Overview
2. Preliminary Remarks on Stress-Strain Analysis
a. Stress, strain
b. Stress-strain relationship
c. Boundary value problem definitions
d. Failure criteria
3. Direct Method -Uniaxial Bar and Truss
a. Bar element
b. 2D truss element
c. 3D truss element
4. Weighted Residual and Energy Methods for 1-D Problems
a. Exact and approximate solutions
b. Galerkin method
c. Differential equations
d. FE approximation
e. Formal procedures
f. Energy method
5. Beams and Frames FEA
a. Beam theory review
b. Rayleigh-Ritz method
c. Element interpolation
d. Beam element
e. Bending moment and shear force
f. Plane frame
6. Heat Transfer FEA
a. Introduction
b. Fourier equation
c. Direct method
d. Galerkin method
e. Convection boundary condition
7. Finite Elements for Plane Solids
a. Differential equation
b. Minimum Potential Energy
c. Constant strain triangular element
d. Lagrange interpolation for rectangular element
e. Iso-parametric quadrilateral element
f. Numerical integration
8. FE Procedures and Modeling
a. Analysis Procedures
b. Problem definition
c. Problem physical fundamentals
d. Problem set-up
e. Solution technique
f. Post-processing
g. Modeling Techniques
h. Meshing
i. Connectivity
j. Boundary conditions
9. Using FEM in Structural Design
a. Consideration of FEM in Structural Design
b. Consideration of FEA in Structural analysis
c. Safety margin
d. Load cases
e. Design optimization
10. Finite Element Analysis, Verification, Validation and Documentation
Using HyperWorks/OptiStruct.
a. Problem definition
b. Preprocessing
c. Solution
d. Post-processing
e. Verification
f. Validation
g. Documentation
11. Conclusion
Grading Criteria:
Grades will be calculated accounting for a) homework assignments, b) the midterm exam
and c) the final exam. Each will contribute to the final grade as it follows:
Homework
Midterm
Final
15%
35%
50%
Grades will be curved if necessary.
For the remote EDGE students, the midterm exam will be posted on the class website at
the time of the exam, to be downloaded and returned by the student via electronic means
(fax, or scan+email). Please be sure you will have access to the internet at that time.