In this post, we will see the book *Manual of the Theory of Elasticity* by *V. G. Rekach*.

About the book

This book is designed to be used as an aid to solving elasticity problems in college and university courses in engineering.

The book covers all subjects of the mathematical theory of elasticity. It contains material which forms the basis for structural analysis and design. Numerous problems illustrate the text and somewhat complete it. Along with classical problems, they include cases of practical significance.

The author does not emphasize any particular procedure of solution, but instead considerable emphasis is placed on the solution of problems by the use of various methods. Most of the problems are worked out and those which are left as an exercise to the student are provided with answers or references to the original works.

**About the author**

Professor Vladimir Germanovich Rekach, D.Sc., is the Head of the Department of Strength of Materials at the Patrice Lumumba Peoples’ Friendship University in Moscow.

His main scientific interests are structural design, analysis of curved bars and vibration problems. The title of his doctoral thesis was “The Analysis of Spherical Shells”. He is the author of 28 articles and 3 books (3 as coauthor).

The book was translated from the Russian by *M. Konyaeva* and was published by Mir in 1979.

Many thanks to *Akbar Azimi* for the raw scans.

Note: There may be warping in some pages.

CONTENTS

Notation

Chapter 1 Theory of Stress 9

I. Static and Dynamic Equilibrium Equations. 9

II. Surface Conditions. 12

III. State of Stress at a Point Problems. 13

III. Cylindrical Co-ordinates. 15

IV. Spherical Co-ordinates.

Problems. 15

Chapter 2 Theory of Strain 24

I. Strain Equations in Orthogonal Co-ordinates 24

II. State of Strain at a Point 28

III. Cesaro’s Formulas 29

Problems 30

Chapter 3 Basic Equations of the Theory of Elasticity and Their Solution or Special Cases 40

I. Orthogonal Curvilinear Co-ordinates 40

II. Rectangular Co-ordinates 41

III. Cylindrical Co-ordinates 43

IV. Spherical Co-ordinates 44

Problems 46

Chapter 4 General Solutions of the Basic Equations of the Theory of Elasticity. Solution or Three-dimensional Problems 66

I. Harmonic Equation (Laplace’s ) 66

II. Biharmonic Equation 66

III. Boundary Value Problems for the Harmonic and Biharmonic Equations 72

IV. Various Forms of the General Solutions of Lame’s Equations 79

Problems 83

Chapter 5 Plane Problem in Rectangular Co-ordinates 106

I. Plane Stress 106

II. Plane Strain 108

III. Solutions of Basic Equations 109

Problems 119

Chapter 6 Plane Problem in Polar Co-ordinates. 151

I. Plane Stress 153

II. Plane Strain 153

III. Solution of Basic Equations 153

Problems 158

Chapter 7 Torsion of Prismatic and Cylindrical Bars 184

I. Pure Torsion of Bars of Constant Section 184

II. Pure Torsion of Circular Bars (Shafts) of Variable Section 187

Problems 194

Chapter 8 Thermal Problem 210

I. Steady-state Thermal Process 210

II. Transient Thermal Process 216

Problems 217

Chapter 9 Contact Problem. 236

I. The action of punches on an Elastic Half-plane 236

II. The Action of Punches on an Elastic Half-space 239

III. Contact Between Two Elastic Bodies 240

Problems 240

Chapter 10 Dynamic Problem. 267

I. Simple Harmonic Motion 267

II. Propagation of Volume Waves in an Elastic Isotropic Medium 269

III. Wave propagation over the surface of an elastic isotropic body 272

IV. Excitation of Elastic Waves by Body Forces 275

VI. Deformation of solids Under Centrifugal Forces 276

VI. Plane Dynamic Problems 277

VII. Thermodynamic Problem 281

Problems 283

References 302

Author Index 308

Subject Index 310