ELASTICITY

by J. R. BARBER

Since the first edition of this book was published, there have been major improvements in symbolic mathematical languages such as Maple and Mathematica and this has opened up the possibility of solving considerably more complex and hence interesting and realistic elasticity problems as classroom examples. It also enables the student to focus on the formulation of the problem (e.g. the appropriate governing equations and boundary conditions) rather than on the algebraic manipulations, with a consequent improvement in insight into the subject and in motivation. During the past 10 years I have developed files in Maple and Mathematica to facilitate this process, notably electronic versions of the Tables in the present Chapters 19 and 20 and of the recurrence relations for generating spherical harmonics. One purpose of this new edition is to make this electronic material available to the reader through the Kluwer website . I hope that readers will make use of this resource and report back to me any aspects of the electronic material that could benefit from improvement or extension. Some hints about the use of this material are contained in Appendix A. Those who have never used Maple or Mathematica will find that it takes only a few hours of trial and error to learn how to write programs to solve boundary value problems in elasticit

TABLE OF CONTENTS

I: GENERAL CONSIDERATIONS

CHAPTER 1 INTRODUCTION

CHAPTER 2 EQUILIBRIUM AND COMPATIBILITY

II: TWO-DIMENSIONAL PROBLEMS

CHAPTER 3 PLANE STRAIN AND PLANE STRESS

CHAPTER 4 STRESS FUNCTION FORMULATION

CHAPTER 5 PROBLEMS IN RECTANGULAR COORDINATES

CHAPTER 6 END EFFECTS

CHAPTER 7 BODY FORCES

CHAPTER 8 PROBLEMS IN POLAR COORDINATES

CHAPTER 9 CALCULATION OF DISPLACEMENTS

CHAPTER 10 CURVED BEAM PROBLEMS

CHAPTER 11 WEDGE PROBLEMS

CHAPTER 12 PLANE CONTACT PROBLEMS

CHAPTER 13 FORCES, DISLOCATIONS AND CRACKS

CHAPTER 14 THERMOELASTICITY

CHAPTER 15 ANTIPLANE SHEAR

III: END LOADING OF THE PRISMATIC BAR

CHAPTER 16 TORSION OF A PRISMATIC BAR

CHAPTER 17 SHEAR OF A PRISMATIC BAR

IV: THREE-DIMENSIONAL PROBLEMS

CHAPTER 18 DISPLACEMENT FUNCTION SOLUTIONS

CHAPTER 19 THE BOUSSINESQ POTENTIALS

CHAPTER 20 THERMOELASTIC DISPLACEMENT POTENTIALS

CHAPTER 21 SINGULAR SOLUTIONS

CHAPTER 22 SPHERICAL HARMONICS

CHAPTER 23 CYLINDERS AND CIRCULAR PLATES

CHAPTER 24 PROBLEMS IN SPHERICAL COORDINATES

CHAPTER 25 AXISYMMETRIC TORSION

CHAPTER 26 FRICTIONLESS CONTACT

CHAPTER 27 THE BOUNDARY-VALUE PROBLEM

CHAPTER 28 THE PENNY-SHAPED CRACK

CHAPTER 29 THE INTERFACE CRACK

CHAPTER 30 THE RECIPROCAL THEOREM

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