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A Combined Boundary Integral Method for Analysis of Crack Problems in Multilayered Elastic Media

机译:多层弹性介质中裂纹问题的组合边界积分法

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摘要

An efficient and accurate elastic analysis based on boundary integral methods is presented for crack problems in inhomogeneous elastic media consisting of a set of individually uniform strata. The method combines the direct boundary integral method (DM) and the displacement discontinuity method (DDM) so that it shares both the efficiency of the DDM and the broad applicability of the DM. The DDM is implemented to construct the stiffness matrix in each layer, while the DM is used to characterize the effects of the interfaces. All the variables on the interfaces can then be eliminated through the continuity conditions, leading to the final system of equations consisting of variables on crack surfaces only. The concept of the crack tip element is also adopted for a better treatment of the crack tip singularity. The examples demonstrate that the combined method has comparable accuracy of DM but is more efficient, especially for the scaled thin layers in the application of practical hydraulic fracturing simulations.
机译:针对边界不均匀的弹性介质中的裂纹问题,提出了一种基于边界积分法的高效,准确的弹性分析方法,该介质由一组单独均匀的地层组成。该方法结合了直接边界积分法(DM)和位移不连续法(DDM),因此它既具有DDM的效率,又具有DM的广泛适用性。 DDM用于构造每一层的刚度矩阵,而DM用于表征界面的影响。然后可以通过连续性条件消除界面上的所有变量,从而导致最终方程组仅由裂纹表面的变量组成。还采用了裂纹尖端元素的概念,以更好地处理裂纹尖端的奇异性。实例表明,该组合方法具有与DM相当的精度,但效率更高,尤其是对于实际水力压裂模拟应用中的按比例缩放的薄层。

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