Stanford University Fall 2001

ME235A Finite Element Analysis

Professor Peter M. Pinsky

Welcome to the ME235A web site for the Fall 2001 quarter!

Announcements

The take home final exam will be available for pickup at 9:00 am Monday (Dec. 10) outside Prof. Pinsky's office. It will be due Wednesday (Dec.12) by 10:30 a.m. There will be a drop-in box outside Prof. Pinsky's office for the finished exams.
Problem set #7 (the last problem set) is due Dec. 7 (Fri).
There will not be a lecture this Friday, and we will have classes next week as usual.
Problem set #6 is due Dec. 3 (Mon).
Computing assignment #2 is now available for download and will be due Nov. 28 (Wed).
The due date for problem set #5 has been changed to Nov. 19 (Mon). There are some changes to the problems as well. See below for the problems.
There will be an extra class this Friday (Nov. 9) due to Prof. Pinsky being away next week. Next week, the Monday (Nov. 12) class is cancelled, and on Wednesday (Nov. 14), there will be a guest lecture.
The midterm is due Nov. 5 (Mon).
Computing assignment #1 is due Nove. 7 (Wed). See below for problem statement and files.
Problem set #4 is due Oct. 31 (Wed).
Problem set #3 is due Oct. 24 (Wed).
Problem set #2 is due Oct. 17 (Wed).
Problem set #1 is due Oct. 10 (Wed).
The course text book is now available at the bookstore.
You will automatically be included in the ME235A class mailing list when you register for the class on Axess. Please register ASAP so that you don't miss out on any course information.

Assignments

    Reading Assignment

Lecture 1 (Sep. 26) : 1.1 - 1.4
Lecture 2 (Oct. 1) : 1.5 - 1.7
Lecture 3 (Oct. 3) : 1.8
Lecture 4 (Oct. 8) : 1.9 - 1.10
Lecture 5 (Oct. 10) : 1.10
Lecture 6 (Oct. 15) : 1.10
Lecture 7 (Oct. 17) : 1.10 - 1.16
Lecture 8 (Oct. 22) : 1.10 - 1.16
Lecture 9 (Oct. 24) : 2.1 - 2.3
Lecture 10 (Oct. 29) : 2.1 - 2.6
Lecture 11 (Oct. 31) : 2.1 - 2.6
Lecture 12 (Nov. 5) : 2.1 - 2.6
Lecture 13 (Nov. 7) : Ch 2
Lecture 14 (Nov. 9) : Ch 2
Lecture 15 (Nov. 19) : Ch 3
Lecture 16 (Nov. 21) : 3.1 - 3.7
Lecture 17 (Nov. 26) : 3.1 - 3.7 (3.8 - 3.10)
Lecture 18 (Nov. 28) : Ch 3

    Problem Set #1 (due Oct. 10)

Exercise 1 on page 7
Exercise 1 on page 22
Additional problem as described in class (see here for problem statement)
Solution to problem set 1.

    Problem Set #2 (due Oct. 17)

Exercise 1 on page 36.
Solution to problem set 2

    Problem Set #3 (due Oct. 24)

Exercise 2 on page 46
Page 49, a and b only
Solution to problem set 3

    Problem Set #4 (due Oct. 31)

Exercise 1 on page 63
Exercise 2 on page 64
Exercise 1 in page 68
Solution to problem set 4

    Computing Assignment #1 (due Nov. 7)

The problem statement is here.
Download files.

    Problem Set #5 (due Nov. 19)

Exercises 1, 2 on page71
Exercise 1 on page75
Exercise 8 (parts i and ii only) on page 107
Exercise 1 on page 81
Exercise 2, 3, 4 on page 82
Exercise 5 on page 83
Exercise 1 on page 87
Exercise 1 on page 91
Exercise 1 on page 98
Solution to problem set #5.

    Computing Assignment #2 (due Nov. 28)

The problem statement is here.
Download files.

    Problem Set #6 (due Dec. 3)

Exercise 6 on page 84
Exercise 1 on page 114
Exercise 1 on page 123
Exercise 1 on page 128
Exercise 2, 3, 4 on page 130
Exercise 1, 2, 3 on page 135
Solution to problem set #6.

    Problem Set #7 (due Dec. 7)

Exercise 1 on page 142
Exercise 3, 4 on page 145
Exercise 1 on page 156
Exercise 2 a - d on page 157
Solution to problem set #7.

Course Overview

ME235A Introduces fundamental concepts and technologies of primal finite element methods for linear elliptic boundary value problems. Topics covered include : overview of finite element method for a one-dimensional model problem including the weak, Galerkin and matrix forms, error analysis and superconvergence; extension of the finite element method for heat equation and elasticity in two and three space dimensions; element formulations and data structures; analysis of errors and convergence of approximation; treatment of constraints and variational crimes. For computing assignments, students will work with and extend a simple but effective finite element code using Matlab and use the Matlab PDE Toolnox for convenient pre- and post-processing features.

ME235B Treats the development and analysis of finite element methods for linear parabolic (time-dependent heat equation), linear hyperbolic (structural dynamics) and eigenvalue (free vibration and stability) problems.

ME235C Introduction to finite element formulations for nonlinear elliptic, parabolic and hyperbolic problems; methods for solving nonlinear algebraic systems.

Staff

        pinsky@stanford.edu

        Phone : 3-9327

        TA : Jee Rim

        jrim@stanford.edu

        Office : Durand 266

        Phone : 3-8104

        Office Hours : Tues 4:15 - 6:15, Fri 1:00 - 3:00

        Grader: To be announced

    MW 2:15 - 3:30

     McCullough 122

Text (Required)

    The Finite Element Method : Linear Static and Dynamic Finite Element Analysis

    Thomas J. R. Hughes, Dover, 2000

Other Reading

   The Finite Element Method, Zienkiewicz and Taylor, two volumes, McGraw-Hill, 2000

    Computational Differential Equations, Eriksson et al., Cambridge, 1996

    An Analysis of FEM, Strang and Fix, Prentice-Hall, 1974

    FEM for Elliptic Problems, Ciarlet, North-Holland, 1978

    Mathematical Theory of FEM, Brenner and Scott, Springer, 1994

    Numerical Solution of PDE by FEM, Johnson, Cambridge, 1990

    Finite Element Procedures, K-J Bathe, Prentice-Hall, 1996

    Concepts and Applications of FEM, Cook et al., Wiley, 1988

Prerequisites

• Elementary calculus and linear algebra.
• Knowledge of Matlab is helpful but not essential (see Matlab tutorial).

Matlab Help

• Matlab 6.1 is available in the unix machines in Sweet Hall and Terman. Type matlab at the command prompt.
• Matlab is also availble in the Macintosh computers in Terman. Find it under the math applications folder.
• A tutorial for matlab can be found here.
• For residential computing, you will need an x-server program that will enable you to open an x-window on your screen. Otherwise, you won't be able to display the graphs. There is a software MI/X that you can try out for 15 days (if you are a Mac user, it is completely free).