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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