无单元伽辽金弱形式积分方法的研究  

STUDY ON THE NUMERICAL INTEGRATION OF ELEMENT FREE GALERKIN METHOD

作　　者：王立鹏[1] 王欣彦[2] 战洪仁[1] 曾祥福[1] 张先珍[1] 王翠华[1] 

机构地区：[1]沈阳化工学院机械工程学院,沈阳110142 [2]沈阳化工学院数理系,沈阳110142

出　　处：《机械强度》2011年第3期368-372,共5页Journal of Mechanical Strength

摘　　要：针对无单元伽辽金弱形式矩形域数值积分精度不高的问题进行研究,提出弓形域数值积分方法。首先,采用圆形支撑域构造背景网格,对支撑域交叠的部分利用对称性原则进行简化运算,简化成弓形区域;然后用高斯数值积分方法对该区域进行积分,依据高斯积分公式,导出弓形域高斯积分参数随节点距离变化的曲线方程,并给出弓形域数值积分法的具体步骤。用它可很方便地进行数值积分,并可提高求解精度,通过数值试验与实例证明该方法结果的精确性及适用性。In order to solve the low accuracy problem on rectangular domain numerical integration of element-free Galerkin method,the circular segment integration method was put forward.At first,the circular support domains were used to construct background cells,the overlapping areas of the supporting domains were simplified to circular segments according as symmetrical rules,and then Gauss numerical integration method was used to the domains.Based on the Gaussian integral formula,the curve equations between Gaussian integral parameter and the changing of node distance were derived,and the basic process of circular segment integration method was present.It could be used conveniently to numerical integration,which increased the accuracy of numerical solutions.The method＇s accuracy and applicability of the results were proved by the numerical test and examples.

关 键 词：无单元法 数值积分 背景网格 弓形域 支撑域 

分 类 号：O241[理学—计算数学]