MECH 303



MECH 303 Advanced Stress Analysis (Fall 2004/2005)

Course Description:

Introduce the basic concepts, equations and methods used to perform stress, strain and displacement analysis of an elastically deformed body.

Prerequisites: MECH 101 Mechanics of Solids I, MECH 202 Mechanics of Solids II

Textbook: Lecture notes

Rreference books:

1. Zhilun Xu, Applied Elasticity, John Wiley & Sons, 1992.

2. S. Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw-Hill, New York, 1970.

Instructor: Dr. Qing-Ping SUN

(Office room 2551, e-mail meqpsun, Tel. 8655)

Tutorial: Dr. Qing-Ping SUN (my office Room 2551)

Grade Policy: Homework 30%

Mid-exam 30%

Fin-exam 40%

Contents:

1. Introduction

• Content, Concepts and Basic Assumptions

2. Theory of Plane Problems

• Plane Stress and Plane Strain Equation of Equilibrium

• Stress and Strain at a point

• Stress-strain relations and Geometrical equations

• Boundary conditions and Saint-Venant's principal

• Solution of plane problem in terms of displacements

• Solution of plane problem in terms of stress

• Airy's stress function, Inverse and semi-inverse methods

3. Solution of Plane Problems in Rectangular Coordinates

• Solution by polynomials

• Determination of displacements

• Bending of a simple beam under uniform load

• Solution by trigonometric series

4. Solution of Plane Problems in Polar Coordinates

• Equilibrium equations in polar coordinates

• Geometrical and Physical equations in polar coordinates

• Stress function and compatibility equations in polar coordinates

• Axisymmetrial stress and corresponding displacements

• Pure bending of curved beams, hollow cylinder and Rotating disks

• Effect of circular holes on stress distribution and wedge

(Mid-term examination)

5. Torsion

• Stress function solution for torsion

• Membrane analogy

• Examples of practical interest

6. Plane Problems on Thermal Stress

• Thermoelastic physical equations

• Solution in terms of displacement, displacement potential

• Solution in terms of stress, stress function

7. Theory of Spacial Problems

• Stress and Strain at a point

• Basic equations of spacial problems

• Displacement and stress solutions

• Some simple examples

(Final Examination)

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