Analysis of thin plates by the element-free Galerkin method
Analysis of thin plates by the element-free Galerkin method
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DOI：
10.1007/bf00356476
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发表时间：
1995-12
影响因子：
4.1
通讯作者：
P. Krysl;T. Belytschko
中科院分区：
文献类型：
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作者：
P. Krysl;T. Belytschko
提出了一种用无网格伽辽金法分析任意Kirchhoff板的无网格方法。该方法是基于移动最小二乘逼近。该方法是无网格的，这意味着离散化是独立的几何细分成“有限元”。由于EFG只需要C1权，因此C1连续性要求很容易满足;因此，没有必要求助于Mindlin-Reissner理论或离散Kirchhoff理论等设备。一致性的要求是通过使用一个二次多项式的基础。一个类似于有限元的细分是用来提供一个背景网格的数值积分。本质边界条件由拉格朗日乘子施加。结果表明，高精度可以实现任意网格的几何形状，为固定和简支的边缘条件，并为规则和不规则的网格。数值研究表明，最佳的支持是约3.9节点间距，高阶求积是必需的。
A meshless approach to the analysis of arbitrary Kirchhoff plates by the Element-Free Galerkin (EFG) method is presented. The method is based on moving least squares approximant. The method is meshless, which means that the discretization is independent of the geometric subdivision into “finite elements”. The satisfaction of theC1continuity requirements are easily met by EFG since it requires onlyC1weights; therefore, it is not necessary to resort to Mindlin-Reissner theory or to devices such as discrete Kirchhoff theory. The requirements of consistency are met by the use of a quadratic polynomial basis. A subdivision similar to finite elements is used to provide a background mesh for numerical integration. The essential boundary conditions are enforced by Lagrange multipliers. It is shown, that high accuracy can be achieved for arbitrary grid geometries, for clamped and simply-supported edge conditions, and for regular and irregular grids. Numerical studies are presented which show that the optimal support is about 3.9 node spacings, and that high-order quadrature is required.