Some Basic Problems of the Mathematical Theory of Elasticity

Rating:
Summary: A masterpiece
Review: For those who are involved in any way with the mathematical theory of 2-D elasticity, this book is really a must have. Though the first edition goes back to 1949 (English edition by Noordhoff Ltd in 1953), it still contains everything that is known in this field. It actually employs the theory of holomorphic functions, Cauchy integrals and conformal mapping in order to solve the various boundary value problems met in plane elasticity. It is almost self contained as far as it concerns its mathematical background. Its results can be used to treat numerous applications of practical interst, such as cracks, inclusions, holes, contact problems, etc. Its a pitty it is out of print (or in print-on-demand only). It can be used along with the same author's "Singular Integral Equations" (another masterpiece on the subject) and Gakhov's:"Boundary Value Problems". Basic knowledge of complex analysis is a prerequisite. It covers 700 pages, contents are: 1. Analysis of stress 2. Analysis of strain 3. Basic Equations 4. Basic eqns of the plane theory of elasticity 5. Stress function-Complex representation 6.Multi-valued displacements. Thermal stresses 7. Transformation of the basic formulae for conformal mapping 8.On Fourier series 9. Solutions for regions bounded by a circe 10.The circular ring 11. Application of conformal mapping 12.Fundamental properties of Cauchy integrals 13.Boundary values of holomorphic functions 14.General solution for the fundamental problems for regions bounded by one contour 15.solution of the fundamental problems for regions mapped onto a circle by rational functions 16.solution for the half-plane and for semi-infinite regions 17.some general methods for solution of bouundary value problems 18.The problem of linear relationship 19.Solution for the half-plane and the plane with straight cuts 20.solution of boundary problems for regions bounded by circle and the infinite plane cut along circular arcs 21.solution of the boundary problems for regions mapped onto a circle by rational functions 22.Torsion and bending of homogenous bars 23.Torsion of bars consisting of different materials 24.Extension and bending of bars consisting of different materials with uniform Poisson's ratio 25.Extension and bending for different Poisson's ratio. Appendix 1. On the concept of a tensor Appendix 2.On the determination of functions from their differentials in multiply connected regions. Appendix 3. Determination of a function of a complex variable from its real part. Indefinite integrals of holomorphic functions