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A hybrid finite difference and moving least square method for elasticity problems

机译：弹性问题的混合有限差分和移动最小二乘方法

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In this paper, a novel hybrid finite difference and moving least square (MLS) technique is presented for the two-dimensional elasticity problems. A new approach for an indirect evaluation of second order and higher order derivatives of the MLS shape functions at field points is developed. As derivatives are obtained from a local approximation, the proposed method is computationally economical and efficient. The classical central finite difference formulas are used at domain collocation points with finite difference grids for regular boundaries and boundary conditions are represented using a moving least square approximation. For irregular shape problems, a point collocation method (PCM) is applied at points that are close to irregular boundaries. Neither the connectivity of mesh in the domain/ boundary or integrations with fundamental/particular solutions is required in this approach. The application of the hybrid method to two-dimensional elastostatic and elastodynamic problems is presented and comparisons are made with the boundary element method and analytical solutions.
机译：本文针对二维弹性问题提出了一种新的混合有限差分和移动最小二乘（MLS）技术。提出了一种间接评估场点处MLS形状函数的二阶和高阶导数的新方法。由于导数是从局部近似中获得的，因此所提出的方法在计算上既经济又有效。在具有规则规则边界的有限差分网格的域搭配点处使用经典的中心有限差分公式，并使用移动最小二乘近似表示边界条件。对于不规则形状的问题，在靠近不规则边界的点上应用点配置方法（PCM）。这种方法既不需要域/边界中的网格连通性，也不需要与基本/特定解决方案集成。介绍了混合方法在二维弹性静力学和弹性力学问题中的应用，并与边界元法和解析解进行了比较。

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