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Numerical simulation of arbitrary holes in orthotropic media by an efficient computational method based on adaptive XIGA

机译：基于自适应XIGA的正交各向异性介质中任意孔的数值模拟

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摘要

We present in this paper an efficient computational approach based on an adaptive extended isogeometric analysis (XIGA) for simulation of arbitrary holes in orthotropic materials. The interfaces of holes are described by multiple level set functions so that the developed XIGA can capture the hole geometry without considering its interfaces. The approach is further enhanced by using the locally refined (LR) B-spline basis functions, which dominate over B-spline or non-uniform rational B-spline functions (NURBS) due to the local refinement. This study only deals with the structured mesh strategy for local refinement. The implementation of the local refinement is guided by posteriori error estimator based on stress recovery. Accuracy study is performed for isotropic media due to the availability of analytical solutions. For numerical experiments, different types of holes in orthotropic media are studied, and the computed numerical results are compared with reference solutions derived from ABAQUS (FEM). We also compare the convergence rate obtained by our adaptive local refinement with that derived from uniform global refinement to indicate the greater advantage of the developed adaptive XIGA.
机译：我们在本文中介绍了一种基于自适应扩展等几何分析（XIGA）的高效计算方法，用于模拟正交各向异性材料中的任意孔。孔的界面由多个级别集功能描述，因此开发的XIGA无需考虑孔的界面即可捕获孔的几何形状。通过使用局部精炼（LR）B样条基函数进一步增强了该方法，由于局部精炼，该函数优于B样条或非均匀有理B样条函数（NURBS）。本研究仅涉及用于局部优化的结构化网格策略。局部细化的实现由基于应力恢复的后验误差估计器指导。由于分析溶液的可用性，对各向同性介质进行了精度研究。对于数值实验，研究了正交各向异性介质中不同类型的孔，并将计算出的数值结果与从ABAQUS（FEM）导出的参考溶液进行了比较。我们还比较了通过自适应局部细化获得的收敛速度与从统一全局细化得出的收敛速度，以表明已开发的自适应XIGA的更大优势。

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