Some basic problems of the mathematical theory of elasticity : fundamental equations, plane theory of elasticity, torsion and bending

TO THE FIRST ENGLISH EDITION. In preparing this translation, I have taken the liberty of including footnotes in the main text or inserting them in small type at the appropriate places. I have also corrected minor misprints without special mention .. The Chapters and Sections of the original text have been called Parts and Chapters respectively, where the latter have been numbered consecutively. The subject index was not contained in the Russian original and the authors' index represents an extension of the original list of references. In this way the reader should be able to find quickly the pages on which anyone reference is discussed. The transliteration problem has been overcome by printing the names of Russian authors and journals also in Russian type. While preparing this translation in the first place for my own informa­ tion, the knowledge that it would also become accessible to a large circle of readers has made the effort doubly worthwhile. I feel sure that the reader will share with me in my admiration for the simplicity and lucidity of presentation. Front Matter....Pages I-XXXI Front Matter....Pages 1-3 Analysis of Stress....Pages 5-27 Analysis of Strain....Pages 28-51 The Fundamental Law of the Theory of Elasticity. The Basic Equations....Pages 52-84 Front Matter....Pages 85-88 Basic Equations of the Plane Theory of Elasticity....Pages 89-104 Stress Function. Complex Representation of the General Solution of the Equations of the Plane Theory of Elasticity....Pages 105-166 Multi-Valued Displacements. Thermal Stresses....Pages 167-175 Transformation of the Basic Formulae for Conformal Mapping....Pages 176-195 Front Matter....Pages 197-197 On Fourier Series....Pages 199-203 Solution for Regions, Bounded by a Circle....Pages 204-229 The Circular Ring....Pages 230-249 Application of Conformal Mapping....Pages 250-263 Front Matter....Pages 265-265 Fundamental Properties of Cauchy Integrals....Pages 267-297 Boundary Values of Holomorphic Functions....Pages 298-314 Front Matter....Pages 315-315 General Solution of the Fundamental Problems for Regions Bounded by One Contour....Pages 317-333 Solution of the Fundamental Problems for Regions Mapped on to a Circle by Rational Functions. Extension to Approximate Solution for Regions of General Shape....Pages 334-390 Solution of the Fundamental Problems for the Half-Plane and for Semi-Infinite Regions....Pages 391-413 Some General Methods of Solution of Boundary Value Problems. Generalizations....Pages 414-443 Front Matter....Pages 445-445 The Problem of Linear Relationship....Pages 447-470 Solution of the Fundamental Problems for the Half-Plane and for the Plane with Straight Cuts....Pages 471-524 Solution of Boundary Problems for Regions, Bounded by Circles, and for the Infinite Plane, Cut Along Circular Arcs....Pages 525-545 Front Matter....Pages 445-445 Solution of the Boundary Problems for Regions, Mapped on to the Circle by Rational Functions....Pages 546-577 Front Matter....Pages 579-581 Torsion and Bending of Homogeneous Bars (Problem of Saint-Venant)....Pages 583-620 Torsion of Bars Consisting of Different Materials....Pages 621-639 Extension and Bending of Bars, Consisting of Different Materials with Uniform Poisson’s Ratio....Pages 640-649 Extension and Bending for Different Poisson’s Ratios....Pages 650-681 Back Matter....Pages 682-732 TO THE FIRST ENGLISH EDITION. In preparing this translation, I have taken the liberty of including footnotes in the main text or inserting them in small type at the appropriate places. I have also corrected minor misprints without special mention . The Chapters and Sections of the original text have been called Parts and Chapters respectively, where the latter have been numbered consecutively. The subject index was not contained in the Russian original and the authors' index represents an extension of the original list of references. In this way the reader should be able to find quickly the pages on which anyone reference is discussed. The transliteration problem has been overcome by printing the names of Russian authors and journals also in Russian type. While preparing this translation in the first place for my own informaƯ tion, the knowledge that it would also become accessible to a large circle of readers has made the effort doubly worthwhile. I feel sure that the reader will share with me in my admiration for the simplicity and lucidity of presentation