Some Basic Problems of the Mathematical Theory of Elasticity, Issue 1

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Springer Science & Business Media, Apr 30, 1977 - Technology & Engineering - 732 pages
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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.
 

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Contents

Fundamental equations of the mechanics of an elastic body
1
ANALYSIS OF STRESS
5
ANALYSIS OF STRAIN
28
THE FUNDAMENTAL LAW OF THE THEORY OF ELASTICITY THE BASIC EQUATIONS
52
General formulae of the plane theory of elasticity
85
BASIC EQUATIONS OF THE PLANE THEORY OF ELASTICITY
89
STRESS FUNCTION COMPLEX REPRESENTATION OF THE GENERAL SOLUTION OF THE EQUATIONS OF THE PLANE THEORY OF ELA...
105
MULTIVALUED DISPLACEMENTS THERMAL STRESSES
167
Application of Cauchy integrals to the solution of boundary problems of plane elasticity
315
GENERAL SOLUTION OF THE FUNDAMENTAL PROBLEMS FOR REGIONS BOUNDED BY ONE CONTOUR
317
SOLUTION OF THE FUNDAMENTAL PROBLEMS FOR REGIONS MAPPED ON TO A CIRCLE BY RATIONAL FUNCTIONS EXTENSION TO ...
334
SOLUTION OF THE FUNDAMENTAL PROBLEMS FOR THE HALFPLANE AND FOR SEMIINFINITE REGIONS
391
SOME GENERAL METHODS OF SOLUTION OF BOUNDARY VALUE PROBLEMS GENERALIZATIONS
414
SOLUTION OF THE BOUNDARY PROBLEMS OF THE PLANE THEORY OF ELASTICITY BY REDUCTION TO THE PROBLEM OF LINEAR ...
445
THE PROBLEM OF LINEAR RELATIONSHIP
447
SOLUTION OF THE FUNDAMENTAL PROBLEMS FOR THE HALFPLANE AND FOR THE PLANE WITH STRAIGHT CUTS
471

TRANSFORMATION OF THE BASIC FORMULAE FOR CONFORMAL MAPPING
176
Solution of several problems of the plane theory of elasticity by means of power series
197
ON FOURIER SERIES
199
SOLUTION FOR REGIONS BOUNDED BY A CIRCLE
204
THE CIRCULAR RING
230
APPLICATION OF CONFORMAL MAPPING
250
On Cauchy integrals
265
FUNDAMENTAL PROPERTIES OF CAUCHY INTEGRALS
267
BOUNDARY VALUES OF HOLOMORPHIC FUNCTIONS
298
SOLUTION OF BOUNDARY PROBLEMS FOR REGIONS BOUNDED BY CIRCLES AND FOR THE INFINITE PLANE CUT ALONG CIRCULAR ...
525
SOLUTION OF THE BOUNDARY PROBLEMS FOR REGIONS MAPPED ON TO THE CIRCLE BY RATIONAL FUNCTIONS
546
Extension torsion and bending of homogeneous and compound bars
579
TORSION AND BENDING OF HOMOGENEOUS BARS PROBLEM OF SAINTVENANT
583
TORSION OF BARS CONSISTING OF DIFFERENT MATERIALS
621
EXTENSION AND BENDING OF BARS CONSISTING OF DIFFERENT MATERIALS WITH UNIFORM POISSONS RATIO
640
EXTENSION AND BENDING FOR DIFFERENT POISSONS RATIOS
650
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