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Biorthogonal systems of functions and the lagrange expansions on the fadl-papkovich functions, to the boundary value problem of the semistrip bending with longitudinal stiffeners

Menshova I.V., Semenova I. A.

#### Abstract:

The peculiarities of functions construction, which biorthogonal to the Fadle-Papkovich functions, are considered. The problem arises in the solution of the boundary value problem to the semi-strip bending in the case of the antisymmetric deformation. The longitudinal sides of which are reinforced by ribs. The ribs work in bending only. The exact analytical solution of this problem , as much as the authors know, has not been constructed. The method on the Fadle-Papkovich Function expansions [1,2] allows to find the solution. Unlike Fadle-Papkovich systems of functions, which was discussed earlier, for example, in papers [1-4], here it is necessary, an additional, biorthogonal functions to a summands of polynomial type (which can be considered as solutions of the beam bending theory) to construct. If there are two or more polynomial summands, we called the corresponding biorthogonal functions as biorthogonal functions of the zero index of the first, second, etc. orders. We show the conditions to expansion function when the polynomial summands in the Lagrange expansions of these functions will be missing. The Lagrange expansions for to be in tension semi-strip, with bending longitudinal stiffeners in the case of symmetric deformation of the semistrip, was given in the article [5].

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