含孔功能梯度压电材料板的力电耦合无网格伽辽金法  

Electromechanical element-free Galerkin method for functionally graded piezoelectric plate with circular hole

作　　者：孟广伟[1] 王晖[1] 周立明[1] 李锋[1] 李霄琳[1] 

机构地区：[1]吉林大学机械科学与工程学院,吉林长春130022

出　　处：《中南大学学报（自然科学版）》2015年第11期4015-4020,共6页Journal of Central South University:Science and Technology

基　　金：国家重大科学仪器开发专项(2012YQ030075);国家自然科学基金资助项目(51305157);吉林省科技厅基金资助项目(20130305006GX);吉林大学研究生创新基金资助项目(2015121)~~

摘　　要：为提高含孔功能梯度压电材料板的计算精度,基于变分原理和功能梯度压电材料的本构关系、几何关系、边界条件等,推导出功能梯度压电材料的无网格方程,提出含孔功能梯度压电材料板的力电耦合无网格伽辽金法。求解含孔功能梯度压电材料板的力学问题,研究孔边环向应力分布及力电集中问题,讨论材料参数按某一方向呈指数函数梯度变化时功能梯度压电材料的力学响应,与ANSYS计算结果进行比较,数值算例结果表明本方法正确可行且具有较高的精度,可求解任意梯度函数的功能梯度压电材料问题。For improving the calculation precision of functionally graded piezoelectric plate with a circular hole, the element-free method equations were deducted by using variation principle, constitutive relations, geometrical relations and the boundary conditions of functionally graded piezoelectric plate. Electromechanical-coupling element-free Galerkin method （EEFGM） for functionally graded piezoelectric plate with a circular hole was proposed. The mechanical issues of functionally graded piezoelectric material plate were solved. The problems of hoop stress distribution and electromechanical concentration were studied. The mechanical response of functionally graded piezoelectric material was discussed, with its material parameters changing exponentially in a certain direction. The numerical example results were compared with those of the finite element software ANSYS. Numerical example results show that this method is feasible. Any problem of fimctionally graded piezoelectric material can be solved.

关 键 词：功能梯度压电材料 无网格伽辽金法 力电耦合 

分 类 号：TB115[理学—数学]