压电裂纹的插值型无单元伽辽金比例边界法分析*
网络出版日期: 2017-03-20
基金资助
* 国家自然科学基金(11462006，21466012)和江西省高校科技落地计划(KJLD14041)资助项目; 20161017收到初稿，20161216收到修改稿;
Analysis of Interpolating Element-free Galerkin Scaled Boundary Method for Piezoelectric Cracks
Online published: 2017-03-20
为了获得更为精确高效的压电裂纹分析方法，基于改进的插值型移动最小二乘法，提出压电材料断裂分析的插值型无单元伽辽金比例边界法，这种方法可以直接根据定义求得应力强度因子和电位移强度因子。该方法只需要在求解域的边界上采用无单元伽辽金法进行数值离散，减少了一个空间维数，并且不需要边界元法所需要的基本解。在没有离散的径向采用解析的方法求解，从而具有较高的计算精度。在改进的插值型移动最小二乘法中，不仅形函数满足Kronecker delta函数性质，而且权函数是非奇异的。此外，改进的插值型移动最小二乘法计算形函数时待定系数比传统的移动最小二乘法少一个。给出数值算例，并验证了所提方法的有效性和正确性。
陈莘莘 , 王娟 . 压电裂纹的插值型无单元伽辽金比例边界法分析*[J]. 机械工程学报, 2017 , 53(6) : 53 -59 . DOI: 10.3901/JME.2017.06.053
In order to obtain a more effective and accurate method to study the fracture behavior of the piezoelectric materials,an interpolating element-free Galerkin scaled boundary method (IEFG-SBM) is proposed for two-dimensional fracture analysis of piezoelectric material based on the improved interpolating moving least-squares (IIMLS) method. This method allows the stress and electric displacement intensity factors to be calculated directly from their definitions. Only the boundary of the computational domain requires to be discretized by the element-free Galerkin (EFG) method and thus the spatial dimension is reduced by one. However,in contrast to the boundary element method,no fundamental solution is required. The solution in the radial direction is analytical,therefore the simulation precision of this method is relatively high. In the IIMLS method,the shape functions satisfy Kronecker delta property and the weight function involved is nonsingular. Moreover,the number of unknown coefficients in the trial function of the IIMLS method is less than that of the conventional moving least-squares (MLS) approximation. At last,numerical examples are presented to demonstrate the effectiveness and correctness of the proposed method for fracture analysis of piezoelectric material.
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