基于单元平滑有限元法与虚拟元法的等价性研究
On the equivalence between the cell-based smoothed finite element method and the virtual element method
AI总结：
本文探讨了基于单元平滑有限元法在四边形元素上的等价性，并扩展至任意多边形和多面体，提出了一种新的稳定化方法，通过基准问题验证了方法的精度和收敛性。
摘要：
我们重新审视了用于四边形元素的基于单元平滑有限元法（SFEM），并将其扩展到二维和三维中的任意多边形和多面体。我们强调了SFEM与虚拟元法（VEM）之间的相似性。基于VEM，我们提出了一种新的稳定化方法，用于处理任意多边形和多面体的SFEM。通过二维和三维线弹性基准问题研究了SFEM的精度和收敛性。随后，将SFEM与扩展边界有限元法结合，用于包含奇异性的线弹性断裂力学问题。
英文摘要：
We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element method (VEM). Based on the VEM, we propose a new stabilization approach to the SFEM when applied to arbitrary polygons and polyhedrons. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Later, the SFEM is combined with the scaled boundary finite element method to problems involving singularity within the framework of the linear elastic fracture mechanics in 2D.
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