Elements of Elasticity

The Commonwealth and International Library: Structures and Solid Body Mechanics Division

D. S. Dugdale, B. G. Neal

• Publisher: Pergamon
• Year: 2014
• Print ISBN: 9780082034957
• eBook ISBN: 9781483191201
• Topic: Technology & Engineering
• Subtopic: Engineering General
• Index: Technology & Engineering

Elements of Elasticity details the fundamental concepts in the theory of elasticity. The title emphasizes discussing the essential formulas, along with elementary matters. The text first covers stress and strain, and then proceeds to tackling the elasticity equation. Next, the selection covers plane stress and strain, along with curvilinear coordinates and polar coordinates. The next chapter deals with rotating discs and thick cylinders. Chapter 8 details strain energy in plates, while Chapter 9 discusses torsion. The last chapter covers stress propagation. The book will be of great interest to engineers, particularly those who deal with fracture mechanics.

CHAPTER 1

STRAIN

Publisher Summary

This chapter discusses strain examination in coordinate systems. Rectangular or Cartesian coordinates are suitable and sufficient for expressing the general physical relationships that hold at points in the interior of a solid body. The process of solution of a problem consists of selecting mathematical expressions for the distribution of stress and strain that not only satisfy these differential equations but also give the required values at the boundaries of the body. In the typical boundary-value problem, stresses or displacements or both are specified over the surface of a body, or over part of its surface. In selecting a coordinate system for conveniently describing boundary conditions, it must be remembered that differential equations in rectangular coordinates must be recast into a new form appropriate to the new coordinates.

1.1 Coordinate systems

Neither stress nor strain can be examined in a precise way without first defining a system of coordinates. Rectangular or Cartesian coordinates are suitable and sufficient for expressing the general physical relationships that hold at points in the interior of a solid body. Alternative coordinate systems may be preferable when one has to describe a boundary of some particular shape or to specify what happens at the boundary.

Whatever the shape of the body may be, stresses and strains are known to be distributed within the interior of the body in accordance with certain differential equations derived from the physical properties of the material from which the body is made. The process of solution of a problem consists of selecting mathematical expressions for the distribution of stress and strain that not only satisfy these differential equations, but also give the required values at the boundaries of the body. In the typical “boundary-value problem”, stresses or displacements or both are specified over the surface of a body, or over part of its surface. When expressions for stress and displacement have been found, and it has been shown that these are satisfactory both on the boundaries and at interior points, the problem has been solved.

In selecting a coordin...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• AUTHOR’S PREFACE
• Chapter 1: STRAIN
• Chapter 2: STRESS
• Chapter 3: ELASTICITY EQUATIONS
• Chapter 4: PLANE STRESS AND STRAIN
• Chapter 5: CURVILINEAR COORDINATES
• Chapter 6: POLAR COORDINATES
• Chapter 7: ROTATING DISCS AND THICK CYLINDERS
• Chapter 8: STRAIN ENERGY IN PLATES
• Chapter 9: TORSION
• Chapter 10: STRESS PROPAGATION
• APPENDIX: CONDENSED SUFFIX NOTATION
• INDEX