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The self-stress condition in a strip

Menshova I.V.

#### Abstract:

The analytical solutions of a boundary value problem of the elasticity in а canonical region with angular points of border (in particular, the solutions of the first boundary value problems of the elasticity theory in a rectangle or in a semi-strip), look like the expansions on the Fadle-Papkovich functions. The coefficients of the expansions are Fourier-integrals of a given boundary functions. The Fadle-Papkovich functions do not form basis on a segment, but they form basis on Riemannian logarithm surface. Therefore the series expansions on them are not unique and there are not trivial solutions in the semi-strip with zero boundary conditions. The stresses that correspond to these solutions are self-stresses. The existence of such solutions has been predicted by E.I. Shemyakin. We construct the analytical solutions for the self-stress condition in the strip. In article the formulas for a symmetric self-stress field in infinite strip and also formulas for corresponding displacements in the right (left) semi-strip are given.

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