University of Pennsylvania
School of Engineering and Applied Science
Department of Mechanical Engineering and Applied Mechanics

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MEAM 527
Finite Element Analysis
Spring 2000/ S. Turteltaub

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Table of Contents

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Course description and syllabus

This is an introductory course for finite element methods used for elliptic and parabolic problems. Typical applications are equilibrium and diffusion problems such as elasticity, heat and mass transfer, potential flow, diffusion of chemical species, etc. Topics covered include: classical and variational formulations, Ritz and Galerkin methods for one and two-dimensional elliptic problems, finite element discretization, direct and iterative methods (Cholesky, gradient and conjugate gradient methods), application to optimization of continuous systems, finite element formulation for parabolic systems, time-integration schemes, stability analysis.

Prerequisites

Students planning on taking this course are expected to be familiar with partial differential equations, linear algebra and elementary calculus. Programming experience is useful.

Course Meeting Time

Tuesdays and Thursdays, 4:30 - 6:00 PM. Towne 309.

Grading Policy

• Homeworks: 20%
• Project: 20%
• Midterm exams: 60% (2x30%)
• Homework: Unless otherwise specified, homeworks are due in class one week after they have been assigned. Late homeworks will not be accepted.
• Collaboration: Collaboration on homeworks is allowed, however each student must submit his/her own work. "Identical"  (i.e., very similar) homeworks would not be allowed.

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Online Schedule

 Week Topics covered Notes 1 [1/18-20] Review of PDEs. Strong and weak formulations for one-dimensional boundary value problems 2 [1/25-27] Galerkin method. Finite element method with piecewise linear functions. 3 [2/1-3] Finite element methods for the two-dimensional heat equation. 4 [2/8-10] Direct methods for linear systems of equations. Cholesky's method. 5 [2/15-17] Element formulation. Assembly of stiffness matrix and load vector. Numerical integration. 6 [2/22-24] FEM for linear elasticity. 7 [2/29-3/2] General formulation of elliptic problems. Introduction to finite element spaces. 8 [3/7-9] Examples of discrete spaces and common finite elements. Triangulations. Error estimates Midterm 1: March 9 9 Spring break 10 [3/21-23] Iterative methods for linear systems of equations. 11 [3/23-25] Gradient and conjugate gradient methods. 12 [3/28-30] Finite element methods for parabolic problems. Semi-discrete variational formulation 13 [4/4-6] Discretization in time: alpha-methods (forward and backward Euler, Crank-Nicolson). Stability analysis. 14 [4/11-13] Asymptotic behavior; Gear method. 15 [4/18-20] Special topics Midterm 2: April 20 16 [4/25-27] Special topics Final

Textbooks

Recommended Textbook:
• Reddy, J. N., An Introduction to the Finite Element Method, McGraw-Hill
Additional references:
• Johnson, C., Numerical solution of partial differential equations by the finite element method, Cambridge University Press, 1987
• Hughes, T. J. R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, 1987
• K. Eriksson, D. Estep, P. Hansbo, C. Johnson, Computational Differential Equations, Cambridge University Press, 1996
• Carey, G. F. and Oden, J. T., Finite Elements (Vols. I-VI; The Texas Finite Element Series), Prentice-Hall
A comprehensive database for finite element books can be found at http://ohio.ikp.liu.se/fe/

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General Information

Instructor Office Hours:

Monday            11:00-12:00 am
Wednesday    11:00-12:00 am
Friday                3:00-  4:00 pm
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Handouts

PDF version
Notes on finite element formulation for linear elasticity
PS version
PDF version

Homework

Homework Assignments and  Due Dates:

1

HW1: PDF version
2

HW2: PDF version
3

HW3: PDF version
4

HW4: PDF version
5

HW5: PDF version
6

HW6: PDF version

Homework Solutions:

PDF version
1
Solution: HW1: PDF version
2
Solution: HW2: PDF version
3 Solution: HW3: PDF version
4 Solution: HW4: PDF version

Exams

Exam Dates:

Midterm 1: March 9 -- 4:30 - 6:00 PM (T309)
Midterm 2: April 20 -- 4:30 - 6:00 PM (T309)

Links

CETS

Created: 1/99
Last Updated: 3/99