CEVE - MECH
527 COMPUTATIONAL METHODS
IN STRUCTURAL
MECHANICS
FALL
2005
Ryon
231 MW
Instructor: Prof. S. Nagarajaiah
Dept.
of Civil & Env.
216
Ryon
713-348-6207
Course Description: Introduction to differential and integral formulations.
Minimum principles, variational principles, weighted residuals, and principle
of virtual work. Simple boundary, initial, and eigenvalue problems. Finite
element method and finite difference methods for structural mechanics. Study of
nonlinearities. Computational methods for geometric and material nonlinear
analysis. Applications to static and dynamic problems. Programming and computer
software. Also offered as MECH 527.
Knowledge
Prerequisite: Basic knowledge of linear algebra, ODE and PDE, application of equilibrium,
compatibility, and stress-strain constitutive relationships in elasticity
problems from the mechanics of solids course. Knowledge of basic analysis of
trusses, beams, and frames.
Textbooks and/or other
required Material:
Text Book: No Required Text
Detailed lecture notes
will be handed out each class
Recommended References:
1. Gilbert Strang, Introduction to Applied
Mathematics, First Edition, Wellesley-Cambridge Press
2. Gilbert Strang & Fix, An Analysis of the Finite Element
Method, Second Edition,
3. Hughes T. R., The Finite Element Method: Linear Static and
Dynamic Finite Element Analysis,
Prentice
Hall, 1st Edition, 1987
4. Reddy, J. N., Applied Functional Analysis
and Variational Methods in Engineering, McGraw-Hill, Second Edition, 1999
5. Akin, J. E., Finite Element Analysis with
Error Estimation,
http://www.owlnet.rice.edu/~mech517/
6. Kwon & Bang, The Finite Element Method using MATLAB,
Second Edition, CRC
(For
MATLAB m-files)
Grading Policy:
Home Work and
Computer
Assignments - 20%
First Exam (in
class) - 25%
Second Exam (Take
Home) - 25%
Final Project - 30%
Homework Policy:
Homework due date will be announced in class.
Homework submitted late will receive partial grade at the discretion of the
instructor.
Course Topics
1. Introductory Concepts in Structural Mechanics
1) Linear Algebra: Matrices,
Determinants, Vector Spaces; 2) Introduction to MATLAB; 3) Introduction to
differential and integral formulations: simple boundary, initial, and
eigenvalue problems; 4) Positive/Negative/Semi Definite/Indefinite Systems; 5)
Minimum Principles, Variational Principles, Weighted Residuals, Energy
Principles, Principal of Virtual Work; 6) Strong form, Weak form, Variational
form; and 7) Dynamic Systems: Eigenvalue Analysis, State Space Solution
2. One Dimensional Problems
1) Introduction to the Finite Element Method; 2) Finite Element Analysis
of One Dimensional Static Systems; 3) Element Equations, Boundary Conditions,
Solution of Equations; 4) Isoparametric Elements and Numerical Integration; 5)
Hyperbolic PDE—Wave Equation, Dynamic Systems and Eigenvalue Analysis; and 6)
Finite Difference Methods for Solution of Dynamic Systems
3. Two Dimensional Problems
1) Elasticity Equations; 2) Elliptic PDE—
4. Introduction to Nonlinear Problems
5. Computer Programs
Study computer programs based on MATLAB,
FEMLAB, and SAP2000
CEVE 527 Course Objectives and Outcomes
Course Objectives:
The objective of CEVE 527 is to learn
the fundamental concepts of finite element and finite difference methods for
solving ordinary differential equations and partial differential equations that
arise in simple boundary, initial, and eigenvalue problems. Static and dynamic
one-dimensional and two-dimensional problems (elasticity problems based on
Laplace and Poisson equations) are of primary interest. The goal is to learn
concepts of minimum principles, variational principles, and methods of weighted
residual. The course builds on the fundamental concepts of stiffness method.
The students will:
1.
Gain
a fundamental understanding of the finite element method for solving boundary
value problems and finite difference techniques for solving initial value
problems.
2.
Learn
important concepts of strong form, weak form, variational form, minimum
principles, and method of weighted residuals
3.
Study
one-dimensional problems such as truss, beam, and frame members, two-dimensional
problems such as plain stress and plain strain elasticity problems, torsion
problem.
4.
Learn
finite element and finite difference analysis of static and dynamic problems
5.
Study
linear and simple nonlinear problems in structural mechanics
Course Outcomes:
Students successfully completing CEVE
527 course will have a clear and thorough understanding of the fundamental
concepts of finite element and finite difference methods and sufficient
analysis skills for successful professional practice. The students will have
the ability to perform advanced finite element analysis by hand and by using
modern computer software. The students will be able to:
1.
Apply
the concepts of minimum principles and linear algebra to solve structural
mechanics problems
2.
Compute
eigenvalues and eigenvectors of simple dynamic systems
3.
Obtain
state space solutions of simple dynamic systems
4.
Learn
to obtain weak form from strong form and total potential, and recognize
similarities between such solutions, and those obtained by variational
principles and principal of virtual work
5.
Obtain
Ritz solution and finite element solution and compare with exact solution of
simple one dimensional problems
6.
Solve
simple truss and beam problems using finite element method
7.
Solve
two dimensional plane stress problems
8.
Learn
to perform comprehensive finite element analysis of structural mechanics
problems using FEMLAB and SAP2000
9.
Document
analysis results, write detailed reports, and communicate the project findings
by making PowerPoint presentations to the class
Contribution to Meeting the Professional Component:
Engineering Content, 100%, 3 credit
hours
Although not a required course, the
students are advised to take this course as an essential preparation for
professional practice