MCE 561 Computational Methods in Solid Mechanics
Professor M. H. Sadd,  208 Wales, X5548, sadd@egr.uri.edu
Text: An Introduction to the Finite Element Method (3rd Edition) by J.N. Reddy


Objective and Course Structure
The course will provide a basic treatment of finite and boundary element methods applied to problems of stress analysis and potential/diffusion.  Both static and dynamic problems will be covered, and an introduction to finite element methods for non-linear problems will also be given.  The course will emphasize basic formulations and will develop element equations based upon variational and weighted residual techniques. Computer implementation issues will also be discussed.  In-class mid-term and final exams will be given, and homework will be assigned and collected for  evaluation.  A course project will involve individual study of a computational related topic of student choice with a written project report due at the end of the semester. 

Course Outline, Resources and Homework
 
Topic     Text Sections Resources  Homework
Basic Concepts and Field  Equations of Interest Handout, Chapter 1 Introduction
References
 
Integral Formulations & Variational Methods 2.1 - 2.6 Variational Methods HW1
FEA of One-Dimensional Problems  Chapters 3, 4 & 5 1-D Problems   Text 1-D   Beams
Trusses
   Frames
Axisymetric Problems
Timoshenko Beams
HW2
HW3

4.15
, 4.24
HW4
Computer Implementation & Related Issues Chapter 7 Computer Implementation  
Single Variable Two-Dimensional Problems Chapters 8 & 9 2-D Problems
Additional 2D
2D Scalar Example
Evaluation of Boundary Integrals
2D Computer Implementation
HW5
HW6
Plane Elasticity Problems Chapter 11 Basic Elasticity  
2-D Elasticity
  
Analytical Elasticity Solutions

FEA-Elasticity

Computational Issues

PDETool Box
Cantilever Beam Example.m
HW7
HW8

HW8 Solution
Time Dependent Problems    6.2, Handout Time Dependent
1st Order Example
2nd Order Example
Eigenvalue Problems
HW9
9-1Solution

9-2 Extended Solution
Non-Linear Problems  Handout Nonlinear PPT
Nonlinear Problems

Nonlinear Example

Nonlinear Cubic.m
HW10
Boundary Element Methods Handout Boundary Element 1
Boundary Element 2

BEM Potential Example

BEM Torsion Example
-

Grading
    Homework             30%
    Mid-Term Exam     20%
    Final Exam            30%
    Project                  20%

Text Resources
        Project Descriptions

ABAQUS Tutorials (Donated by Prof. Taggart)
Beam Truss
Column Buckling Plane Stress
Plate Bending Axisymmetric Stress
3D Stress Analysis Plate With Hole.SAT

Mid-Term Exam & Solutions

Final Exam: Friday, May 6, 3-6pm
Semester Project Papers Due: Thursday, May 12