Stress-strain state of symmetric rectangular plates with variable thickness under temperature impact


Аuthors

Firsanov V. V.*, Doan Q. H.**

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

*e-mail: k906@mai.ru
**e-mail: dqhieu57@gmail.com

Abstract

The article presents the results of construction of the refined theory of isotropic plates symmetric with respect to median plane, and of random thickness in longitudinal direction with regard to the temperature impact. Fidelity increasing of the computational techniques of the stress-strained state of the plates not only under mechanical loads, but also by accounting for temperature impact seems to be a topical issue. The plate state equations are described by the 3D theory of elasticity. The desired plate displacements are being expanded by normal to medial surface of the plate coordinate into polynomials two degrees higher, than those in the classical theory of Kirchhoff-Love type. The system of basic equations of the refined theory and corresponding boundary conditions were obtained with Lagrange variation principle. One of the distinctive features of the proposed refined theory consists in the fact, that while determining lateral normal and tangential stresses, direct integration of equilibrium equations of the 3D theory of elasticity is being used. For an isotropic rectangular plate of variable thickness, a system of differential equations of equilibrium in displacements with variable coefficients containing additional terms that accounted for the effect of thickness changing on the plate stress-strained state under temperature impact was obtained by Levy method. To solve the thermo-elasticity problems of anisotropic rectangular plates of variable thickness, an effective method of numerical solution of a system of differential equations with variable coefficients was used. Finite differences method is used in combination with double-sweep method, which has certain advantages while solving such types of problems. Firstly, it allows solving a system of differential equations with variable coefficients, and, secondly, a fairly small dividing of a plate in its marginal zone allows accounting for additional stress-strained states of a «boundary layer» type. As an example, the article considers stress-strained state computing of a rectangular isotropic plate of variable thickness under the impact of distributed loading and temperature. Comparison of the results of the plate stress-strained state computing by the refined theory for several variants of temperature impact is presented. It was established that with the modest temperature changing, the plate stress-strained state changes proportionally to the temperature.

Keywords:

rectangular plate, variable thickness, temperature, thermo-elasticity, Lagrange variation principle, finite difference method.

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