属性与温度相关材料的广义热弹性问题有限元分析

FINITE ELEMENT ANALYSIS OF GENERALIZED THERMOELASTIC PROBLEMS IN ELASTIC MEDIA WITH TEMPERATURE-DEPENDENT PROPERTIES

计及材料特性与温度的相关性,基于Lord和Shulman(L-S)广义热弹性理论,建立了此类问题的有限元控制方程.由于材料属性的温度相关性,温度控制方程具有非线性,积分变换求解方法难以采用,因而将有限元方程直接在时间域求解.利用所建立方法研究了材料特性与温度相关、带有孔洞的无限大体在热冲击和机械冲击作用下的广义热弹性问题.分析表明,在时间域直接求解材料属性与温度相关的广义热弹性问题是可行的,所得结果具有很高的精度,热的波动性得到充分的展现.同时发现,热冲击载荷作用时,材料属性与温度的相关性对结构的机械响应影响显著,对温度响应影响很小;机械载荷作用时,材料参数与温度的相关性对所有响应影响都很小.因此,研究热冲击载荷作用的机械响应时,必须考虑材料属性的温度相关性,而研究温度响应时,无论何种冲击载荷,都可以不考虑材料属性的温度相关性.

Finite element nonlinear equations based on Lord-Shulman （L-S） generalized thermoelasticity theory are derived for elastic media with temperature-dependent properties and solved directly in time domain. A case of an infinite medium with a cylindrical hole under thermal and mechanical shock is analyzed with the developed method. The numerical results with temperature-dependent properties show the fluctuation of heat conduction and the efficiency of the time domain method in solving generalized thermoelastic problems. Furthermore, it also shows that the influence of temperature-dependent properties are more pronounced on mechanical response of the media with the thermal shock loading, rather than the mechanical shock.