semistrip, boundary-value problem, Fadle-Papkovich functions, analytical solutions, antisymmetric boundary-value problem.

The problem of solving the biharmonic equation in a finite canonical domains with corner points of the boundary (biharmonic problem) exists almost 200 years (see the review [3]). In the theory of elasticity it is usually formulated as the problem of finding the solution of the biharmonic equation in rectangular half-strip, the longitudinal sides of which are not loaded, and at the end the normal and tangential stresses are set. If the decision to half-strip is built, the decision for a rectangle is not difficult already. In the series of publications, summarized the articles [13], the general theory was developed, the scheme of the solution of the problem in half-strip was given and various examples were considered (looked through). But it was done only for symmetric deformation of half-strip. In this work the examples of solutions the back-symmetric problem for half-stripare provided. The longitudinal sides of half-strip are free, and at the end the normal and shear stresses are set. The solution is appeared in the form of explicit expansions for FadlePapkovich functions which coefficients are defined as Fourier integrals given at the end of half-strip boundary functions. The work is based on the article [13] and the article [18], in which the ratio of biorthogonality and decomposition Lagrangian for backward symmetric tasks are given. 

Semenova, Irina Alexandrovna Postgraduate student, Departament of Mathematical Analysis, I. Yakovlev Chuvash State Pedagogical University, Cheboksary