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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method
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Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method

机译：扩展有限元方法中不连续性和裂纹奇异性的广义高斯正交规则

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摘要

New Gaussian integration schemes are presented for the efficient and accurate evaluation of weak form integrals in the extended finite element method. For discontinuous functions, we construct Gauss-like quadrature rules over arbitrarily-shaped elements in two dimensions without the need for partitioning the finite element. A point elimination algorithm is used in the construction of the quadratures, which ensures that the final quadratures have minimal number of Gauss points. For weakly singular integrands, we apply a polar transformation that eliminates the singularity so that the integration can be performed efficiently and accurately. Numerical examples in elastic fracture using the extended finite element method are presented to illustrate the performance of the new integration techniques.
机译：提出了新的高斯积分方案，用于在扩展有限元方法中有效，准确地评估弱形式积分。对于不连续的函数，我们在二维上对任意形状的元素构造了类似高斯的正交规则，而无需划分有限元素。在积分的构造中使用了点消除算法，该算法可确保最终的积分具有最少数量的高斯点。对于弱奇异积分对象，我们应用了消除奇异性的极性变换，以便可以高效而准确地执行积分。给出了使用扩展有限元方法进行弹性断裂的数值实例，以说明新型集成技术的性能。

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