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Homogeneous solution theory of elasticity. biorthogonal expansions

Kleyn N.V., Kovalenko M.D.

#### Abstract:

The article gives a general scheme for solving the first fundamental boundary value problem of plane elasticity theory in a half-strip (rectangle) in the form of explicit expansions in homogeneous solutions, the coefficients of which are expressed in terms of Fourier integrals on the boundary functions given at the end of the half-strip (as in the decisions of Filon-Ribiere). Moreover, they are practically determined in the same manner as in the decisions of the Filon-Ribiere. Therefore, by analogy with the expansions Filon-Ribiere, these solutions give exact analytical solutions (as opposed to the approximate solutions using homogeneous solutions in which the problem of determining the unknown coefficients of expansions, one way or another, amounts to an approximate solution of the infinite, indecomposable system of algebraic equations) . The paper is a direct continuation of [1] and is entirely based on it.

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