A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics
A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics
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DOI：
10.1016/j.cma.2010.06.015
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发表时间：
2011
影响因子：
7.2
通讯作者：
R. Simpson;J. Trevelyan
中科院分区：
文献类型：
--
作者：
R. Simpson;J. Trevelyan
提出了一种新的富边界元法（BEM）和双边界元法（DBEM）方法来精确计算裂纹问题中的应力强度因子（SIFs）。该公式利用了统一划分法（PUM），使得从解空间的先验知识中获得的函数可以合并到元素公式中。描述了一种富集策略，其中在附加配置点形成的边界积分方程用于提供辅助方程，以容纳额外引入的未知数。此外，给出了求强奇异和超奇异富边界积分的一种有效的数值求积方法。最后，给出了混合模式裂纹问题的结果；这些表明，与传统的未浓缩DBEM相比，引入PUM浓缩提供了大约一个数量级的精度改进。
We introduce a novel enriched Boundary Element Method (BEM) and Dual Boundary Element Method (DBEM) approach for accurate evaluation of Stress Intensity Factors (SIFs) in crack problems. The formulation makes use of the Partition of Unity Method (PUM) such that functions obtained from a priori knowledge of the solution space can be incorporated in the element formulation. An enrichment strategy is described, in which boundary integral equations formed at additional collocation points are used to provide auxiliary equations in order to accommodate the extra introduced unknowns. In addition, an efficient numerical quadrature method is outlined for the evaluation of strongly singular and hypersingular enriched boundary integrals. Finally, results are shown for mixed mode crack problems; these illustrate that the introduction of PUM enrichment provides for an improvement in accuracy of approximately one order of magnitude in comparison to the conventional unenriched DBEM.