This work aims to enable explicit dynamics in the method of finite spheres (MFS). We propose a method to apply a direct inverse mass matrix with the modified local mass matrix for explicit dynamics in the MFS. We show that the performance of the proposed method depends on the proper selection of the modification parameters and set of enriched functions; hence, solution accuracy can be improved by choosing them optimally. Furthermore, we analyze the effects of time integration schemes when the MFS with the proposed method is used; the results show that the proposed method with the Noh-Bathe explicit method is remarkably accurate, and its performance is comparable to that of the widely used -Bathe implicit method.

中文翻译：

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使用修正的直接逆质量矩阵的有限球方法的显式动力学

这项工作的目的是在有限球体方法（MFS）中实现显式动力学。我们提出了一种应用直接逆质量矩阵和修改后的局部质量矩阵的方法，以实现 MFS 中的显式动力学。我们表明，所提出方法的性能取决于修改参数和丰富函数集的正确选择；因此，通过优化选择它们可以提高解的精度。此外，我们还分析了使用所提出方法的 MFS 时时间积分方案的效果；结果表明，所提出的Noh-Bathe显式方法非常准确，其性能与广泛使用的-Bathe隐式方法相当。