A LINEARLY CONFORMING POINT INTERPOLATION METHOD (LC-PIM) FOR 2D SOLID MECHANICS PROBLEMS
A LINEARLY CONFORMING POINT INTERPOLATION METHOD (LC-PIM) FOR 2D SOLID MECHANICS PROBLEMS
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DOI：
10.1142/s0219876205000661
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发表时间：
2005-12
影响因子：
1.7
通讯作者：
Guirong Liu;Guiyong Zhang;K. Y. Dai;Y. Y. Wang-Y.;Z. Zhong;G. Y. Li;Xu Han
中科院分区：
文献类型：
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作者：
Guirong Liu;Guiyong Zhang;K. Y. Dai;Y. Y. Wang-Y.;Z. Zhong;G. Y. Li;Xu Han
提出了一种求解二维实体问题的线性协调点插值方法。该方法利用多项式基函数生成形状函数，并提出了一种基于背景单元的局部支撑节点选择方案，只要不存在重合节点，就能保证矩阵可逆。采用Galerkin弱形式建立离散化的系统方程，并采用带应变光滑操作的节点积分法进行数值积分。本文提出的LC-PIM算法能够保证数值解的线性精确性和单调收敛性。数值例子被用来检查本方法的精度，收敛性和效率。与采用线性三角形单元的有限元法和采用高斯积分的径向点插值法相比，LC-PIM具有更快的收敛速度和更好的计算效率。
A linearly conforming point interpolation method (LC-PIM) is developed for 2D solid problems. In this method, shape functions are generated using the polynomial basis functions and a scheme for the selection of local supporting nodes based on background cells is suggested, which can always ensure the moment matrix is invertible as long as there are no coincide nodes. Galerkin weak form is adopted for creating discretized system equations, and a nodal integration scheme with strain smoothing operation is used to perform the numerical integration. The present LC-PIM can guarantee linear exactness and monotonic convergence for the numerical results. Numerical examples are used to examine the present method in terms of accuracy, convergence, and efficiency. Compared with the finite element method (FEM) using linear triangle elements and the radial point interpolation method (RPIM) using Gauss integration, the LC-PIM can achieve higher convergence rate and better efficiency.