Stanford University Winter 2001-2002

ME235B Finite Element Analysis

Professor Peter M. Pinsky

Welcome to the ME235B web site for the Winter 2001-2002 quarter!

Announcements

The final will be take-home, from Monday (Mar. 18) 10 a.m. to Wednesday (Mar. 20) 10 a.m. For alternate time (Saturday (Mar. 16) 10 a.m. to Monday 10 a.m.), email Prof. Pinsky and he'll send you the final exam by email.
Problem set 6 is due on Mar 12 (Tues).
Computing assignment 2 is due on Mar 12 (Tues).
Problem set 5 is due on Feb 28 (Thur).
Problem set 4 is due on Feb 14 (Thur).
Problem set 3 is due on Feb 7 (Thur).
Computing assignment 1 is due on Feb 14 (Thur).
There will be no class on Feb 5 (Tues).
Problem set 2 is due on Jan 29 (Tues).
Problem set 1 is due on Jan 17 (Thurs).
You will automatically be included in the ME235B 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

    Problem Set 1. (due Jan 17)  

        Exercise 1 on page 169

        Exercise 1 on page 420

    Problem Set 2. (due Jan 29)

        Exercise 1 (page 424)

        Show symmetry and positive-definiteness of the element and global mass matrices (elastodynamics).

        Exercise 1 (page 432)

        Exercise 2 (page 433)

        Exercise 7 and 8 (page 445)

    Problem Set 3 (due Feb 7)

        Exercise 1 (page 462)

        Derive the v-, d-, d'-forms of the generalized trapezoidal rule.

        Derive (8.2.21).

        Commutative diagram (page 465) - show the details of modal decomposition of the fully discrete equations and the                                                              temporal discretization of the semidiscrete modal equations.

    Problem Set 4 (due Feb 14)

        Exercise 3, 4 (page 474)

        Exercise 6 (page 475)

    Problem Set 5 (due Feb 28)

        Exercise 1 (page 492)

        Exercise 2, 3 (page 495)

        Exercise 4 (page 498)

    Problem Set 6 (due Mar 12)

        Exercise 5 (page 501)

        Exercise 7 (page 502)

        Exercise 1, 2 (page 518)

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 : TBA

    TTH 2:45 - 4:00

     530-127

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

• ME235A
• 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).