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Homogeneous solution theory of elasticity. Basis properties

Kleyn N.V., Kovalenko M.D.

#### Abstract:

This is a study of basic properties of a characteristic of homogeneous solutions of the theory of elasticity, which is obtained by solving the first fundamental boundary value problem of elasticity theory in a half-strip with the free longitudinal sides and set at the end of normal and shear stresses [1]. However, in contrast to the theory of elasticity [1], where we are talking about the same time (that is, with one set of coefficients) expansion of two functions defined at the end of the half-strip, is considered the expansion of only one function in a system of homogeneous solutions. Such expansions were studied for the first time, apparently, in the paper [2], which were called Lagrange expansion.

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