FINITE ELEMENT ANALYSIS OF GREEN-LINDSAY THERMOPIEZOELECTRICITY TIME-DEPENDENT PROBLEM

Roman Drebotiy, Vitalii Stelmashchuk, Heorhiy Shynkarenko

Анотація


On the basis of Green-Lindsay thermopiezoelectricity model with so-called "relaxation time"-parameters, which influence on the way of interaction between mechanical, electrical and thermal fields in pyroelectric materials, we formulate initial boundary value problem and the corresponding variational problem in terms of vector of elastic displacements, electrical potential, and temperature increment. We derive the respective energy balance law and perform energy estimates of the solutions of the variational problem. Using the latter the well-posedness of the variational problem is proved. Based on finite element method and Newmark scheme the numerical scheme is developed for approximate solution of this problem. The unconditional stability of the constructed time integration scheme is proved. Finally we show the results of the numerical experiment which demonstrates the influence of the values of "time relaxation" parameters of Green-Lindsay model on the obtained solution.


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DOI: http://dx.doi.org/10.30970/vam.2023.31.11966

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