近日，马来西亚多媒体大学的Kok Chee Kuang及其研究小组取得一项新进展。经过不懈努力，他们提出固体力学问题的一种新的基于应变的五边形薄膜有限元。相关研究成果已于2024年2月6日在国际知名学术期刊《理论与应用力学快报》上发表。

多边形有限元在有限元分析中仍然是一个有吸引力的选择，因为与三角形相比，多边形有限元在建模任意形状方面具有灵活性。在本研究中，研究人员首次用应变法建立了一个五边形膜单元。该单元具有不变性，并通过修正系数将平衡约束应用于假定的应变场。研究人员受前沿推进技术的启发，生成了一个五边形网格，并用拉普拉斯平滑法提高了网格质量。

研究人员对所开发的五边形单元的性能进行了数值试验，结果表明其适合于模拟梁的弯曲。他们发现采用五边形单元沿边界进行网格过渡，平滑曲面边缘，捕获分布载荷，提高了数值结果。

此外，研究人员采用五边形单元沿边界进行网格过渡，平滑曲面边缘，捕获分布载荷，发现数值结果得到了增强。

附：英文原文

Title: A New Strain-Based Pentagonal Membrane Finite Element for Solid Mechanics Problems

Author: Koh Wei Hao, Logah Perumal, Kok Chee Kuang

Issue&Volume: 2024-02-06

Abstract: Polygonal finite elements remain an attractive option in finite element analysis due to their flexibility in modeling arbitrary shapes compared to triangles. In this study, a pentagonal membrane element was developed with the strain approach for the first time. The element possesses invariance, and the equilibrium constraint was applied to the assumed strain field using corrective coefficients. Inspired by the advancing front technique, a pentagonal mesh was generated, and the mesh quality was enhanced with Laplacian smoothing. The performance of the developed pentagonal element was assessed in a few numerical tests, and the results revealed its suitability in modeling the bending of beams. Besides, the numerical results are enhanced when pentagonal elements are used in mesh transitions along boundaries to smoothen curved edges and capture distributed loads.

DOI: 10.1016/j.taml.2024.100499

Source: http://taml.cstam.org.cn/article/doi/10.1016/j.taml.2024.100499