Abstract

The present study is focused on the numerical investigation in time domain of the deformation in thermoelastic material with one relaxation time (Lord and Shulman theory) with voids under dependence of modulus of elasticity and thermal conductivity on reference temperature. For dependency on reference temperature, we have taken two cases: (i) linear case and (ii) quadratic case. For numerical investigation, the finite element method with eight-/nine-noded isoparametric finite elements has been used. The results demonstrate that finite element method can reliably predict the deformation of the medium. Finite element method has an advantage over Laplace/Fourier transformation as the equations are solved directly in the time domain, but in Laplace/Fourier transformation, numerical inversion is quite complicated with possible errors. The comparison of these two cases has been discussed in result and discussion section for the temperature distribution, the displacement component, volume fraction field and the stresses. A comparison of Newmark method and Galerkin’s method for time domain has been given though three-dimensional graphs. An appreciable effect of thermal relaxation times t₀ is observed from the various results.

摘要

本研究的重点是在弹性模量和热导率对参考温度的依赖下，具有一个弛豫时间（Lord 和 Shulman 理论）的热弹性材料变形的时域数值研究（Lord 和 Shulman 理论）。对于参考温度的依赖性，我们采用了两种情况：（i）线性情况和（ii）二次情况。对于数值研究，使用了具有八/九节点等参有限元的有限元方法。结果表明，有限元法能够可靠地预测介质的变形。有限元法优于拉普拉斯/傅立叶变换，因为方程直接在时域求解，但在拉普拉斯/傅立叶变换中，数值反演非常复杂，可能存在误差。这两种情况的比较已在结果和讨论部分讨论了温度分布、位移分量、体积分数场和应力。通过三维图给出了Newmark方法和Galerkin方法在时域上的比较。热弛豫时间的显着影响t ₀从各种结果中观察到。