FINITE ELEMENT ANALYSIS OF LORD-SHULMAN THERMOELASTICITY TIME-DEPENDENT PROBLEM

Vitalii Stelmashchuk, Roman Petryshyn, Heorhiy Shynkarenko

Анотація


The initial boundary value problem for Lord-Shulman thermoelasticity is considered. It is then transformed into the corresponding variational one. Using Galerkin semidiscretization by spatial variables with finite element basis functions the variational problem is reduced to matrix Cauchy problem. For time discretization of the Cauchy problem we adopt a hybrid time integration scheme (based on Newmark scheme and generalized trapezoidal rule) that was initially developed for Lord-Shulman thermopiezoelectricity problem. In numerical experiments we consider a ramp-type heating of the edge of a solid bar. The solutions obtained by the proposed numerical scheme are then compared with the ones for the corresponding Lord-Shulman thermopiezoelectricity problem which are available in the literature. In particular, it is shown that piezoeffect and pyroeffect make a noticeable influence of the behaviour of the stress wave in the solid bar. Besides, the numerical results are in accordance with the ones obtained by other researchers via other solution techniques.

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DOI: http://dx.doi.org/10.30970/vam.2024.33.12374

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