A NURBS-based generalized finite element scheme for 3D simulation of heterogeneous materials
A NURBS-based generalized finite element scheme for 3D simulation of heterogeneous materials
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DOI：
10.1016/j.jcp.2016.05.004
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发表时间：
2016-08
期刊：
影响因子：
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通讯作者：
Masoud Safdari;A. Najafi;N. Sottos;P. Geubelle
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文献类型：
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作者：
Masoud Safdari;A. Najafi;N. Sottos;P. Geubelle
针对非均质材料分析中观察到的复杂不连续梯度场问题，提出了一种基于三维NURBS的界面丰富的广义有限元方法。该方法使用简单的六面体单元结构网格，不一定符合非均匀材料中的材料界面。通过避免在常规有限元中使用的协调网格的创建，NIGFE显著简化了网格生成过程。为了获得与材料界面相交的单元的精确解，NIGFE使用非均匀有理B-Splines(NURBS)来丰富局部解场。通过对一个基准问题的求解，验证了该算法的精度和收敛速度。我们观察到，NIGFE保持了最优的收敛速度，并提供了额外的优势，包括准确地捕捉材料界面附近的解场，以及内置的分层网格细化能力。最后，讨论了NIGFE在非均质材料计算分析中的应用。
A 3D NURBS-based interface-enriched generalized finite element method (NIGFEM) is introduced to solve problems with complex discontinuous gradient fields observed in the analysis of heterogeneous materials. The method utilizes simple structured meshes of hexahedral elements that do not necessarily conform to the material interfaces in heterogeneous materials. By avoiding the creation of conforming meshes used in conventional FEM, the NIGFEM leads to significant simplification of the mesh generation process. To achieve an accurate solution in elements that are crossed by material interfaces, the NIGFEM utilizes Non-Uniform Rational B-Splines (NURBS) to enrich the solution field locally. The accuracy and convergence of the NIGFEM are tested by solving a benchmark problem. We observe that the NIGFEM preserves an optimal rate of convergence, and provides additional advantages including the accurate capture of the solution fields in the vicinity of material interfaces and the built-in capability for hierarchical mesh refinement. Finally, the use of the NIGFEM in the computational analysis of heterogeneous materials is discussed.