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Numerical implementation of the extended Finite Element Method for dynamic crack analysis

机译：动态裂纹分析扩展有限元法的数值实现

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摘要

A numerical implementation of the extended Finite Element Method (X-FEM) to analyze crack propagation in a structure under dynamic loading is presented in this paper. The arbitrary crack is treated by the X-FEM method without re-meshing but using an enrichment of the classical displacement-based finite element approximation in the framework of the partition of unity method. Several algorithms have been implemented, within an oriented object framework in C++, in the home made explicit FEM code. The hew module, called DynaCrack, included in the dynamic FEM code DynELA, evaluates the crack geometry, the propagation of the crack and allow the post-processing of the numerical results. The module solves the system of discrete equations using an explicit integration scheme. Some numerical examples illustrating the main features and the computational efficiency of the DynaCrack module for dynamic crack propagation are presented in the last section of the paper.
机译：本文提出了一种扩展有限元方法（X-FEM）的数值实现方法，用于分析结构在动态载荷下的裂纹扩展。通过X-FEM方法对任意裂纹进行处理，而无需重新网格化，而是在统一方法的划分框架内使用了基于经典位移的有限元逼近方法。在自制的显式FEM代码中，已在C ++的面向对象框架内实现了几种算法。动态FEM代码DynELA中包含的称为DynaCrack的软件模块评估裂纹的几何形状，裂纹的传播并允许对数值结果进行后处理。该模块使用显式积分方案求解离散方程组。本文的最后一部分提供了一些数值示例，这些示例说明了DynaCrack模块动态裂纹扩展的主要特征和计算效率。

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