Solution for temperature shear stresses in a two-layer strip by the Saint-Venant – Picard – Banach method

Аuthors

Pykhtin A. V.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: pykhtin-av@yandex.ru

Abstract

Using the example of an unfixed two-layer strip temperature warping problem, the evolution of elements of the Saint-Venant – Picard – Banach (SVPB) method and an expanded presentation of some of its aspects are given. The formulation is concentrated on the problem of determining the shear stresses at the junction between layers, where the usually applied apparatus of the method leads to a trivial result. Variants of correcting the obtained form of the solution using a physical hypothesis, expanding the form of the initial approximation with the inclusion of the required factors, and an asymptotic statement of the boundary condition at the junction of the layers are considered. The solutions are constructed analytically; their comparison is carried out, including with the result of calculation using the finite element method. The ways of constructing solutions of differential and integro-differential equations, applying expressions of higher iterations and convergence are considered. A version of the method is proposed that does not rely on approximations of the unknown values, as well an approach to constructing a solution for it.

Keywords:

plane problem, layered material, temperature stresses, edge effect, iterations, Saint-Venant – Picard – Banach method

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