四边简支压电热弹性层合正交双曲壳的精确解  

EXACT SOLUTION FOR LAMINATED PIEZOTHERMOELASTIC GENERIC SHELLS WITH FOUR SIMPLY SUPPORTED EDGES

作　　者：李家宇[1] 程秀全[1] 卿光辉[2] 

机构地区：[1]广州民航职业技术学院机务工程系,广州510403 [2]中国民航大学航空工程学院,天津300300

出　　处：《工程力学》2010年第8期83-89,共7页Engineering Mechanics

基　　金：天津市自然基金项目(07JCYBJC02100)

摘　　要：正交双曲坐标系下,对考虑温度梯度的压电热弹性材料,首先基于基本方程,结合对偶变量理论,将热传导关系并入到压电材料的本构关系中,得到压电热弹性材料包含温度的增维本构关系;由此增维本构关系,利用状态空间法消去曲面内的应力分量,便可直接推导出可独立求解的压电热弹性材料的齐次状态方程。齐次状态方程的导出,将大大简化层合正交双曲壳的求解过程,提高计算精度,且齐次状态方程可以直接进行有限元离散,为工程实践中复杂边界条件下层合双曲结构的分析求解提供一种新方法。In generic coordinates, firstly, by the basic equations and the theory of symplectic variable, an augmented dimension constitutive relationship was obtained by combining the heat exchange equations into the constitutive equations of piezoelectric materials. Utilizing the state space method and the augmented dimension constitutive relationships, the homogeneous state equation which can be solely solved is educed by eliminating the stress in the shell surface. The homogeneous state equation can simplify greatly the solution procedure of the laminated generic shell, improve numerical precision, and be straightly discreted in finite element format, as well as presents a new method for the semi-analytical solution of laminated structures with complicated boundary condition in practice.

关 键 词：压电热弹性材料 层合正交双曲壳 精确解 状态空间法 齐次状态方程 

分 类 号：O343.6[理学—固体力学]