横观各向同性层合压电矩形板稳定问题的三维精确分析  

EXACT THREE DIMENSIONAL ANAL YSISOF THE STABILITY OF LAMINATED TRANSVERSEL Y ISOTROPIC PIEZOEL ECTRIC RECTANGULAR PLATES

作　　者：蔡金标[1] 叶贵如[1] 陈伟球[1] 丁皓江[1] 

机构地区：[1]浙江大学土木系,杭州310027

出　　处：《复合材料学报》2002年第1期69-73,共5页Acta Materiae Compositae Sinica

基　　金：国家自然科学基金项目 ( 10 0 0 2 0 16 )

摘　　要：从横观各向同性压电弹性力学的三维基本方程出发 ,通过引入位移函数和应力函数 ,构造了两类相互独立的状态空间方程 ,使原方程解耦成两个低阶方程 ,有利于具体问题的求解。对于四边简支压电层合矩形板面内双向均匀受压的稳定问题 ,建立了层合板上下表面状态变量间的关系式 ,利用边界条件进一步导出特征方程。发现存在两类彼此无关的稳定形式 :第一类对应板的纯面内稳定 ,而第二类则是一般意义上的板的弯曲稳定。给出了数值结果 。By introducing two displacement functions and two stress functions, two independent state space equations are constructed based on three-dimensional piezoelasticity equations for transverse isotropy. The original differential equation is thus decoupled into two low-order equations, which facilitates the solutions for various problems. For the simply supported rectangular plate subjected to bi-axial uniform pressures, two relations between the state variables at the top surface and the bottom surface are established. In particular, it is found that there exist two independent classes of stabilities. The first class corresponds to the purely in-plane stability while the second corresponds to the general flexural stability. Numerical examples are finally presented, and the effects of some parameters are discussed.

关 键 词：横观各向同性 层合压电矩形板 状态空间法 稳定问题 压电弹性力学 三维基本方程 

分 类 号：O343.2[理学—固体力学]