Purpose

The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered.

Design/methodology/approach

Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results.

Findings

Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities.

Originality/value

This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies.

中文翻译：

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关于裂纹扩展问题的广义/扩展有限元方法分析中的数值积分

目的

本文的目的是评估在广义（G）/扩展有限元方法（XFEM）中使用的一些数值积分策略，以解决线性弹性断裂力学问题。这里分析了一系列参数，证明了当适当考虑这些示例的特殊性时，如何改善数值积分误差和计算效率。

设计/方法/方法

数值积分策略是在现有的计算环境中实施的，该环境提供了有限元方法和G / XFEM工具。考虑分析的主要参数，并将使用此类策略的性能与标准积分结果进行比较。

发现

研究并实现了适用于断裂力学分析的已知数值积分策略。呈现并讨论了来自不同裂纹构造的结果，突出了针对奇异和/或不连续性问题的替代集成技术的必要性。

创意/价值

这项研究提供了由G / XFEM解决的各种断裂力学示例，其中使用标准数值积分与高斯正交积分会导致精度降低。讨论了一系列网格和裂缝几何形状的元素细分行为和积分点策略映射，还介绍了扭曲元素以及这两种策略如何影响应变能和应力强度因子评估。