Fast integration and weight function blending in the extended finite element method
Fast integration and weight function blending in the extended finite element method
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DOI：
10.1002/nme.2387
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发表时间：
2009
影响因子：
2.9
通讯作者：
G. Ventura;R. Gracie;T. Belytschko
中科院分区：
文献类型：
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作者：
G. Ventura;R. Gracie;T. Belytschko
讨论了扩展有限元法（XFEM）中的两个问题：当富集函数自平衡时弱形式的有效数值积分和富集函数的混合。积分的基础是将弱形式的域积分转化为等价的围道积分。结果表明，轮廓形式是计算效率比域的形式，特别是当富集功能是奇异和/或不连续的。研究了减小混合元素误差的方法。在这种方法中，富集函数被预乘以具有紧支持的光滑权重函数，以允许富集和非富集子域之间的完全平滑过渡。本文提出了一种混合阶跃函数富集和奇异富集的方法。同时还表明，如果富集度没有适当地移动，加权富集度与标准富集度是等价的。刃位错和裂纹问题被用来基准的技术，参数化的权重函数的变量的影响进行了分析。所得到的方法显示出提高的精度和最佳收敛速度，很容易实现到现有的XFEM代码。版权所有© 2008约翰威利父子有限公司.
Two issues in the extended finite element method (XFEM) are addressed: efficient numerical integration of the weak form when the enrichment function is self‐equilibrating and blending of the enrichment. The integration is based on transforming the domain integrals in the weak form into equivalent contour integrals. It is shown that the contour form is computationally more efficient than the domain form, especially when the enrichment function is singular and/or discontinuous. A method for alleviating the errors in the blending elements is also studied. In this method, the enrichment function is pre‐multiplied by a smooth weight function with compact support to allow for a completely smooth transition between enriched and unenriched subdomains. A method for blending step function enrichment with singular enrichments is described. It is also shown that if the enrichment is not shifted properly, the weighted enrichment is equivalent to the standard enrichment. An edge dislocation and a crack problem are used to benchmark the technique; the influence of the variables that parameterize the weight function is analyzed. The resulting method shows both improved accuracy and optimum convergence rates and is easily implemented into existing XFEM codes. Copyright © 2008 John Wiley & Sons, Ltd.