MEAM 527

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

Announcements

Handouts

General Information

Instructor

Course Description

Syllabus

Prerequisites

Meeting Time

Online Schedule

Grading Policy

Textbook

Homework

Homework Due Dates

Homework Problems

Homework Solutions

Exam

Exam Schedule

Links

CETS

Library

SEAS

Announcements

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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.

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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.

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Course Meeting Time

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

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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

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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