【作者】 李家宇；

【导师】 卿光辉； 田秀云；

【作者基本信息】 中国民航大学 ， 飞行器设计， 2008， 硕士

【摘要】 基于弹性力学和传热学理论,结合状态空间法和对偶理论,研究了热弹性复合材料和压电材料层合板及壳问题。首先,分别推导了机-热耦合的热弹性复合材料和机-电-热耦合的热弹性压电材料的非齐次状态方程;再由对偶理论,将热传导方程并入到复合材料和压电材料的本构关系中,分别得到热弹性复合材料和压电材料的增维本构关系,由此增维本构关系,通过状态空间法,便可直接推导出热弹性复合材料机-热耦合和热弹性压电材料机-电-热耦合问题的齐次状态方程。齐次状态方程的导出,避免了非齐次状态方程求解时,必须先求解由热传导方程和热平衡方程导出的,关于温度的二阶微分方程,可大大简化求解过程,提高计算精度,并可直接进行有限元离散,为工程实践中,求解复杂边界条件下层合板及壳的半解析解提供了一种新方法。文中除了详细推导了热弹性复合材料层合板、开口圆柱壳和正交双曲壳,以及热弹性压电材料层合板和开口圆柱壳的非齐次状态方程和齐次状态方程外,以非齐次状态方程和齐次状态方程为求解对象,分析了简支边界条件下多种板壳结构的精确解。两种方法的求解结果完全吻合,从而验证了齐次状态方程的正确性。更多还原

【Abstract】 Based upon the theories of elastic mechanics and heat transfer, uniting the symplectic theory and state space method, the static mechanics problems of the laminated plates and laminated shells of thermoelastic composites and piezothermoelastic composites were studied.First, deduced the non-homogenous state equations of thermoelastic composites with mechanic-heat coupling effect and piezothermoelastic composites with mechanic-electric-heat coupling effect respectively. Secondly, according to the symplectic theory, a corresponding augment dimensions constitutive relationships was established by combining the heat exchange equations with the constitutive relationships of thermoelastic composite materials and piezothermoelastic composite materials. The homogenous state equations of thermoelastic composites with mechanic-heat coupling effect and piezothermoelastic composites with mechanic-electric-heat coupling effect, wer directly derived by the augment dimensions constitutive relationships and the state space method.The treatment avoided the solution of the second order differential equation on the thermal equilibrium equations and thermal gradient relationships, which was necessary performed to solving non-homogeneous state equations, greatly simplified the solution procedure of laminated structures, and improved numerical precision. Notably the homogenous state equations could be straightly discreted in finite element format, presented a new method for the semi-analytical solution of laminated plates and shells with complicated boundary condition in practice.In this paper, non-homogenous state equations and homogenous state equations were detailedly derived of thermoelastic composites laminated plates, cylindrical open shells, orthogonal generic shells, and piezothermoelastic composites laminated plates, cylindrical open shells, and respectively analyzed their exact solution with four simply supported, the results validated the correctness of the homogenous state equations.更多还原