The Generalized/eXtended Finite Element Method (G/XFEM) is applied as a very useful tool in the resolution of complex structural models using an effective approach to represent the existence of cracks and other micro-defects. This is an unconventional formulation of the Finite Element Method (FEM), in that there is an expansion of the approximate solution field from the use of enrichment functions associated with the nodes. Enrichment functions can be singular functions derived from analytic deductions, polynomial functions or even functions resulting from other solution processes, such as the global–local strategy. The Stable Generalized Finite Method (SGFEM) is a variation of the G/XFEM with a simple modification in its enrichment functions, reducing the condition number of the stiffness matrix as well as the approximate error in the so-called blending elements. Considering this under the global–local strategy, the solution quality and the conditioning of the stiffness matrix in 3D linear fracture problems are investigated here. The crack surface is described by the Heaviside discontinuous functions and singular/crack front functions on a local scale. The solution of the local problem is used to enrich the approximation in the global domain, which may cause bad conditioning of the resulting system of equations and poor approximation errors in the solution. In order to overcome this problem, its projection into the linear polynomial space, according to the SGFEM strategy, is subtracted from the enrichment. Numerical examples, with different load and crack configurations, of linear elastic fracture mechanics are employed. Differently from other works, the meshes of the two scales are kept constant. Only the number of nodes associated with the local enrichment functions is changing. The impact on the accuracy and conditioning of the analysis is assessed, and the importance of using the SGFEM strategy is highlighted.

通用/扩展有限元方法（G / XFEM）作为一种非常有用的工具，可以使用一种有效的方法来表示裂缝和其他微缺陷的存在，从而解决复杂的结构模型。这是有限元方法（FEM）的一种非常规表示形式，因为使用与节点关联的富集函数扩展了近似解字段。富集函数可以是从解析推论，多项式函数甚至是其他求解过程（例如全局-局部策略）产生的函数得出的奇异函数。稳定广义有限方法（SGFEM）是G / XFEM的一种变体，只是对其富集函数进行了简单的修改，减少刚度矩阵的条件数以及所谓的混合元素中的近似误差。考虑到这一点，在全局局部策略下，本文研究了3D线性断裂问题的解质量和刚度矩阵的条件。裂纹表面由局部局部的Heaviside不连续函数和奇异/裂纹前沿函数描述。局部问题的解决方案用于丰富全局域中的逼近，这可能会导致所得方程组的条件不好，并且解决方案中的逼近误差也较小。为了克服这个问题，根据SGFEM策略，将其投影到线性多项式空间中，并将其从富集中减去。数值示例，具有不同的载荷和裂纹配置，采用线性弹性断裂力学。与其他作品不同，两个比例尺的网格保持恒定。仅与本地扩展功能关联的节点数量正在更改。评估了对分析准确性和条件的影响，并强调了使用SGFEM策略的重要性。