M. Basheleishvili
abstract:
The paper is devoted to systematic application of the
potential method and the theory of integral equations to the two-dimensional
problems of statics of an anisotropic elastic body. Chapter I deals with the
Fredholm integral equations of second kind which are composed for all basic
boundary value problems (except the mixed ones). Theorems on the existence and
uniqueness of solution are proved. For the mixed problem, a singular
integral equation with discontinuous coefficients is obtained; its
investigation is carried out by the same method as in the isotropic case.
Chapter II is wholly concerned with applications of integral equations
constructed in Chapter I. Effective solutions of integral equations for
concrete regions are given. By means of these solutions, the solutions of
boundary value problems are presented by absolutely and uniformly convergent
series or in quadratures. Solutions of many specific problems which have not
been solved by other methods, are given here.
Mathematics Subject Classification: 73C02.
Key words and phrases: Anisotropic elastic body, two-dimensional problems, integral equation, potential method, effective solutions.