Application of generalized "method of lines", for solving problems of thermoelasticity of thick plates

Abstract

In this paper, a new combined method of reducing dimensions of spatial thermoelasticity problems was proposed; based on the “method of lines”, combined with Bubnov-Galerkin-Petrov`s projection method which significantly expands its capabilities. The generalized “method of lines” can be used for plates of variable thickness, in problems of dynamics and thermoelasticity. The basic idea is to reduce the dimension of the spatial coordinates using the projection method, with a system of basis functions. This article is the first part of the work. It shows the reduced differential equations and proposes a new way of modeling boundary conditions.