## Manual of the Theory of Elasticity – Rekach

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

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

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 