摘要
首先以修正的H-R(Hellinger-Reissner)变分原理,先推导出热弹性材料的非齐次状态方程,再利用热平衡方程和热传导方程变量间的对偶关系,通过增加非齐次状态向量矩阵的维数,将非齐次状态方程转化为可以独立求解的齐次状态向量方程;根据对偶理论,将热传导方程并入材料的本构关系中,得到新的修正的H-R变分原理,从而可直接推导出热弹性材料的齐次状态向量方程。齐次状态向量方程的导出可大大简化热弹性体稳态温度问题的求解,最后以一算例验证文中方法的准确性和可靠性。
Firstly, by the modified mixed H-R（Hellinger-Reissner） variational principle, the non-homogeneous state-vector equation for thermoelastic materials is derived. And then the symplectic relationships of variables in the thermal equilibrium formulations and the gradient equations are considered, the non-homogeneous state-vector equation is transformed into homogeneous state-vector equation for solving independently the coupling problem of thermoelastic bodies by increasing the dimensions of the non-homogeneous state-vector equation. By extending the constitutive relation and establishing a new modified mixed H-R variational principle of thermoelastic materials, the homogeneous state-vector equation is derived straightway from the new variation theorem by performing the variational operations. The homogeneous state-vector equation can simplify greatly the solution procedure of the steady state temperature problem of thennoelastic bodies. A numerical example validates the veracity and reliability of the homogeneous state-vector equation.
出处
《机械强度》
CAS
CSCD
北大核心
2009年第4期638-644,共7页
Journal of Mechanical Strength
基金
天津市自然科学基金资助项目(07JCYBJC02100)~~
