二维光滑边域有限元法在弹性力学中的应用研究

An Edge-Based Smoothed Finite Element Method for 2D Mechanics Problems

在深入理解光滑有限元法基本理论的基础上,重点研究了光滑边域有限元法边域的形成方式,光滑应变矩阵的求解方法以及光滑有限元形函数的计算方法。利用C++语言编制了光滑边域有限元计算程序,针对具有解析解的二维悬臂梁模型和带孔板模型计算了位移场、应力场、位移误差和应变能误差,并与常规T3和Q4有限元法、CS-FEM光滑有限元解比较。通过研究发现相对于常规有限元法,光滑边域有限元法在解的精确性和收敛性方面具有显著优势。

We focus on the formation of the edge-based smoothed cells and the formulation of smoothed strain matrix and shape functions based on the deep understanding of theoretical aspects of the smoothed finite element method. The computational program of the edge-based smoothed finite element method （ES-FEM） which is made by C ＋ ＋ language is used to solve 2D elastic problems which are so-called cantilever beam and infinite plate with a circular hole in this work. The displacement field, strain/stress field and errors of displacement and strain energy are calcu- lated. The results of ES-FEM will be compared with those of the standard FEM using triangular and quadrilateral el- ements （FEM-T3, FEM-Q4）, cell-based smoothed finite element method （CS-FEM）, as well as the analytical solutions. It shows that the ES-FEM achieves more accurate with original FEM. results and generally higher convergence rate compared