Abstract
This paper discusses a 1D one-dimensional mathematical model for the thermoelasticity problem in a two-layer plate. Basic equations in dimensionless form contain both temperature and displacement. General solutions of homogeneous equations (displacement and temperature equations) are assumed to be a linear combination of Trefftz functions. Particular solutions of these equations are then expressed with appropriately constructed sums of derivatives of general solutions. Next, the inverse operators to those appearing in homogeneous equations are defined and applied to the right-hand sides of inhomogeneous equations. Thus, two systems of functions are obtained, satisfying strictly a fully coupled system of equations. To determine the unknown coefficients of these linear combinations, a functional is constructed that describes the error of meeting the initial and boundary conditions by approximate solutions. The minimization of the functional leads to an approximate solution to the problem under consideration. The solutions for one layer and for a two-layer plate are graphically presented and analyzed, illustrating the possible application of the method. Our results show that increasing the number of Trefftz functions leads to the reduction of differences between successive approximations.
Highlights
The multilayered materials have several unique characteristics that are frequently required and essential in structural design problems
This approach has been extended to thermoelasticity problems
The behavior of thermoelastic waves at the interface of layered medium and distributions of these waves through the domain is examined by applying the direct finite element method by the authors of [8]
Summary
The multilayered materials have several unique characteristics that are frequently required and essential in structural design problems. Various approaches and methods have been presented in the literature for the stress analysis of a multilayered medium. The solution is obtained using the matrix similarity transformation and inverse Laplace transform. The behavior of thermoelastic waves at the interface of layered medium and distributions of these waves through the domain is examined by applying the direct finite element method by the authors of [8]. Using the semi-inverse method, a simple analytic solution is obtained for a thermoelastic problem of a nonhomogeneous plate with arbitrary contour. The authors of [14] study the mechanical behavior of two linear isotropic thermoelastic solids, bonded together by a thin layer, constituting a linear isotropic thermoelastic material, using an asymptotic analysis based on a finite element approach
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