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Unstructured grid method for stress wave propagation in elastic media

机译：弹性介质中应力波传播的非结构网格方法

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A new numerical method, named unstructured grid method, is presented to calculate two-dimensional stress wave propagation problems in elastic media. This method is based on the dynamic equilibrium equations of the investigated lumps that are formed among the auxiliary unstructured grids. The approach to the solution is obtained by calculating the node displacements and the central point stresses of the spatial grids alternately. The stability criterion of the method is given and tested numerically. Analysis of dispersion for numerical phase velocity is studied. The rule is provided to determine the spatial step size of discretization mesh so as to ensure the numerical accuracy of the unstructured grid method. Numerical results are compared with the available exact solutions and with the solutions of central difference method for demonstrating the good accuracy of the new method. The unstructured grid method possesses higher calculating speed than the central difference method. Finally, the dynamic behavior of a square plate with a hole under an impact loading is researched.
机译：提出了一种新的数值方法，称为非结构网格方法，用于计算二维应力波在弹性介质中的传播问题。该方法基于在非结构化辅助网格中形成的研究块的动态平衡方程。通过交替计算空间网格的节点位移和中心点应力来获得解决方案。给出了该方法的稳定性判据并进行了数值测试。研究了数值相速度的色散分析。提供规则以确定离散化网格的空间步长，以确保非结构化网格方法的数值准确性。将数值结果与可用的精确解和中心差分法的解进行比较，以证明新方法的良好准确性。非结构网格方法比中心差分方法具有更高的计算速度。最后，研究了带孔方形板在冲击载荷作用下的动力学行为。

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