Complex Variable Methods in Plane Elasticity

By: Lu Jian-Ke

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Hardcover | 1 December 1994

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240 Pages

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This text deals systematically with the mathematical theory of plane elasto-statics by using complex variable methods, together with many results originated by the author. The problems considered are reduced to integral equations, Fredholem or singular, which are proved to be uniquely solvable. Particular attention is paid to the subjects of crack problems in the quite general case, especially those of composite media, which are solved by a unified method. The methods used in this book are constructive so that they may be used in practice.

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Basic Concepts and Formulas	p. 1
Stress Functions	p. 5
The Stresses and Displacements under Transformation of Coordinate System	p. 12
Complex Expressions for Certain Mechanical Quantities	p. 15
Boundary Conditions of Fundamental Problems: The Case of Bounded and Simply Connected Regions	p. 19
The Case of Bounded and Multi-connected Regions	p. 24
The Case of Unbounded Regions	p. 29
Modified Second Fundamental Problems under General Relative Displacements	p. 35
First Fundamental Problems for Bounded and Simply Connected Regions	p. 41
First Fundamental Problems for the Infinite Plane with a Hole	p. 46
First Fundamental Problems for Multi-connected Regions	p. 49
The General Method of Solution for Second Fundamental Problems	p. 54
The Method of Solution for Modified Second Fundamental Problems	p. 62
The Case of Circular Region	p. 67
The Case of Infinite Plane with a Circular Hole	p. 73
The Case of Circular Ring Region	p. 81
Applications of Conformal Mapping	p. 91
The Case of Half-plane	p. 97
The Case of Cyclic Symmetry	p. 105
The Methods of Solution for Cyclically Symmetric Problems	p. 110
Mixed Boundary Problems	p. 123
First Fundamental Problems of Welding	p. 127
Second Fundamental Problems of Welding	p. 135
Welding in the Whole Plane, Some Examples	p. 140
General Expressions of Complex Stress Functions	p. 151
First Fundamental Problems for the Infinite Plane with Cracks	p. 154
Second Fundamental Problems for the Infinite Plane with Cracks	p. 159
Collinear or Co-circular Cracks in the Infinite Plane	p. 162
Crack Problems for Bounded Regions	p. 173
Simplification of the Method of Solution for First Fundamental Problems	p. 182
Fundamental Crack Problems of Composite Materials in the Infinite Plane	p. 191
The Welding Problem for a Circular Plate with a Straight Crack	p. 195
The Welding Problem for Two Half-planes with Cracks	p. 203
Fundamental Crack Problems of Composite Materials for a Bounded Region	p. 209
Appendix. On the Uniqueness Theorems for Fundamental Problems	p. 217
Bibliography	p. 227
Index	p. 229
Table of Contents provided by Blackwell. All Rights Reserved.

Complex Variable Methods in Plane Elasticity

At a Glance

Hardcover

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Defective items

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