热弹性正交双曲壳广义H-R变分原理和齐次向量方程

基于热弹性体基本方程,根据弹性体修正后的H-R变分原理,建立正交双曲坐标系下热弹性体在温度梯度下的广义H-R变分原理,并推导了相应的非齐次广义Hamilton正则方程。再根据对偶变量理论,通过增加方程的维数,导出了可独立求解的齐次向量方程。齐次向量方程的导出,大大简化了热弹性层合正交双曲壳的求解过程,提高了计算精度。实例分析验证了该文方法的正确性。

GENEALIZED H-R VARIATION PRINCIPLE AND HOMOGENEOUS VECTOR EQUATION OF THERMO-ELASTIC ORTHOGONAL HYPERBOLIC SHELL

By introducing the basic equations and the modified H-R (Hellinger-Reissner) variation principle of thermo-elastic body, a new generalized H-R variation principle, subjected to the orthogonal hyperbolic coordinate and the temperature gradient, is proposed. Meanwhile, the relevant nonhomogeneous generalized Hamilton canonical equation is deduced. According to the symplectic variable theory, the homogeneous vector equation, which could be solved independently, is obtained by increasing the dimension of the nonhomogeneous generalized Hamilton canonical equation. The homogeneous vector equation simplifies the solution procedure, and improves numerical precision of the thermo-elastic laminated orthogonal hyperbolic shell. Numerical examples are used to verify the method.