Complex Variable Methods in Elasticity

By: A. H. ENGLAND

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Paperback | 17 October 2003

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197 Pages

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The plane strain and generalized plane stress boundary value problems of linear elasticity are the focus of this graduate-level text, which formulates and solves these problems by employing complex variable theory. The text presents detailed descriptions of the three basic methods that rely on series representation, Cauchy integral representation, and the solution via continuation. Its five-part treatment covers functions of a complex variable, the basic equations of two-dimensional elasticity, plane and half-plane problems, regions with circular boundaries, and regions with curvilinear boundaries. Worked examples and sets of problems appear throughout the text. 1971 edition. 26 figures.

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Introduction	p. ix
Functions of a Complex Variable	p. 1
Basic definitions	p. 1
Complex functions	p. 2
Properties of holomorphic functions	p. 3
Multiple-valued functions	p. 5
Cauchy integrals	p. 9
The Hilbert problem	p. 11
Evaluation of the Plemelj functions	p. 17
Evaluation of line integrals	p. 18
The Basic Equations of Two-Dimensional Elasticity	p. 21
Basic equations of elasticity	p. 21
Plane strain	p. 23
Boundary conditions	p. 24
Generalized plane stress	p. 25
Complex variable formulation	p. 28
The body force potential	p. 32
Resultant force over an arc	p. 33
Arbitrariness of the complex potentials	p. 34
Restrictions on the complex potentials	p. 35
Conditions at infinity	p. 36
Boundary conditions for the complex potentials	p. 40
Stresses in curvilinear coordinates	p. 42
Appendix	p. 44
Examples	p. 46
Plane and Half-Plane Problems	p. 50
Infinite plane	p. 50
Point forces and moments	p. 51
Continuation of the complex potentials	p. 52
Stress boundary value problem for a half-plane	p. 55
Point forces and moments in a half-plane	p. 57
Displacement boundary value problem for a half-plane	p. 58
Mixed boundary value problems for a half-plane	p. 59
Frictionless punch problems	p. 66
A sliding punch with friction	p. 71
Crack problems	p. 77
Alternative methods of solution	p. 81
Examples	p. 83
Regions with Circular Boundaries	p. 87
Introduction	p. 87
Stress and displacement boundary value problems	p. 87
Series method of solution	p. 90
Direct method of solution	p. 97
Stress and displacement continuations	p. 101
Solutions to the stress and displacement problems by continuation	p. 104
The mixed boundary value problem	p. 111
An infinite medium with cracks along arcs of a circle	p. 114
Frictionless boundary conditions	p. 118
Examples	p. 125
Regions with Curvilinear Boundaries	p. 129
Introduction	p. 129
Conformal transformations	p. 129
Basic formulae	p. 137
Direct method of solution	p. 141
Stress and displacement continuations	p. 149
Stress and displacement problems	p. 152
The mixed boundary value problem	p. 158
Frictionless boundary conditions	p. 161
Concluding remarks	p. 169
Examples	p. 170
Bibliography	p. 174
Summary of Formulae	p. 177
Answers to the Examples	p. 178
Index	p. 193
Table of Contents provided by Ingram. All Rights Reserved.

Complex Variable Methods in Elasticity

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