Open Access

ARTICLE

Investigation on a Two-dimensional Generalized Thermal Shock Problem with Temperature-dependent Properties

Tianhu He^1,2,3, Yongbin Ma^2,3, Shuanhu Shi³

1 Corresponding author. E-mail: heth@lut.cn
2 Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province, Lanzhou University of Technology, Lanzhou 730050, P.R. China.
3 School of Science, Lanzhou University of Technology, Lanzhou 730050, P.R. China.

Computers, Materials & Continua 2015, 47(1), 15-29. https://doi.org/10.3970/cmc.2015.047.015

Abstract

The dynamic response of a two-dimensional generalized thermoelastic problem with temperature-dependent properties is investigated in the context of generalized thermoelasticity proposed by Lord and Shulman. The governing equations are formulated, and due to the nonlinearity and complexity of the governing equations resulted from the temperature-dependent properties, a numerical method, i.e., finite element method is adopted to solve such problem. By means of virtual displacement principle, the nonlinear finite element equations are derived. To demonstrate the solution process, a thermoelastic half-space subjected to a thermal shock on its bounding surface is considered in detail. The nonlinear finite element equations for this problem are solved directly in time domain. The variations of the considered variables are obtained and illustrated graphically. The results show that the effect of the temperature-dependent properties on the considered variables is to reduce their magnitudes, and taking the temperature-dependence of material properties into consideration in the investigation of generalized thermoelastic problem has practical meaning in predicting the thermoelastic behaviors accurately. It can also be deduced that directly solving the nonlinear finite element equations in time domain is a powerful method to deal with the thermoelastic problems with temperature-dependent properties.

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