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Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

机译:三维静态断裂和疲劳裂纹扩展的等几何边界元方法

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摘要

We present a novel numerical method to simulate crack growth in 3D, directly from the Computer-Aided Design (CAD) geometry of the component, without any mesh generation. The method is an isogeometric boundary element method (IGABEM) based on non-uniform rational B-splines (NURBS). NURBS basis functions are used for the domain and crack representation as well as to approximate the physical quantities involved in the simulations. A stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted elements. Convergence studies in the crack opening displacement is performed for a penny-shaped crack and an elliptical crack. Two approaches to extract stress intensity factors (SIFs): the contour M integral and the virtual crack closure integral are compared using dual integral equations. The results show remarkable accuracy in the computed SIFs, leading to smooth crack paths and reliable fatigue lives, without requiring the generation of any mesh from the CAD model of the component under consideration.
机译:我们提出了一种新颖的数值方法,可以直接从组件的计算机辅助设计(CAD)几何图形模拟3D中的裂纹扩展,而无需生成任何网格。该方法是基于非均匀有理B样条(NURBS)的等几何边界元方法(IGABEM)。 NURBS基本函数用于域和裂纹表示,以及近似模拟中涉及的物理量。提出了一种用于奇异积分的稳定正交方案,以提高该方法在处理高度失真元素时的鲁棒性。对一个便士形的裂纹和一个椭圆形的裂纹进行裂纹扩展位移的收敛研究。提取应力强度因子(SIF)的两种方法:使用对偶积分方程比较轮廓M积分和虚拟裂纹闭合积分。结果表明,在计算出的SIF中具有非凡的准确性,从而导致平滑的裂纹路径和可靠的疲劳寿命,而无需从所考虑组件的CAD模型中生成任何网格。

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