双压电材料反平面断裂分析中的辛方法  

ANALYSIS OF ANTI-PLANE FRACTURE BEHAVIORS IN PIEZOELECTRIC BIMORPH BY SYMPLECTIC METHOD

作　　者：周震寰[1] 徐新生[1] 徐成辉[1] 李澄[1] 

机构地区：[1]大连理工大学工程力学系工业装备结构分析国家重点实验室,大连116024

出　　处：《固体力学学报》2013年第S1期105-111,共7页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(11302042);辽宁省博士启动基金(20121017)资助项目

摘　　要：本文将一种全新的辛求解方法引入到双压电材料断裂问题分析中,并利用该方法推导其解析解.在辛空间中,反平面位移和剪应力、面内电势和电位移分别互为对偶变量.通过引入对偶变量,问题归结为一个可以分离变量的一阶哈密顿方程组,其本征解在辛空间中张成完备的解空间.所有的对偶变量都可以通过辛本征解的展开形式表示,其待定系数由裂纹条件和几何模型的外边界条件共同确定.结果表明,力、电强度因子与本征值为1/2的本征解直接相关.数值算例展示了不同裂纹条件下强度因子的变化曲线,并且分析了界面裂纹的断裂行为.In this paper,an exact symplectic method was introduced to analyze the fracture problems of apiezoelectric bimorph and derive its explicit forms analytically.In symplectic space,the anti-plane displacements and shear stresses,in-plane electric potentials and electric displacements were proved to be dual variables respectively.By introducing the dual variables,the problem was reduced to a separable variable set of first-order Hamiltonian equations whose eigenvalue solutions were symplectic spanning over the solution space to cover all possible boundary conditions.All of the dual variables can be expanded in series in terms of the symplectic eigenvalue solutions.The coefficients of the series were determined from crack conditions and outer boundary conditions along the geometric domain.The result indicated that the value of stress and electric intensity factors directly depend on the coefficient of 1/2eigenvalue solutions.In numerical examples,the variations of intensity factors for different boundary conditions were shown in graphic curves and fracture behaviors of the interface crack were investigated.

关 键 词：辛方法 强度因子 界面裂纹 双压电材料 

分 类 号：O346.1[理学—固体力学]