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论文:2017,Vol:35,Issue(1):7-12 |
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引用本文： |
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谢伟, 贺旭东, 吴建国, 刘轶军. 二维光滑边域有限元法在弹性力学中的应用研究[J]. 西北工业大学学报 |
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Xie Wei, He Xudong, Wu Jianguo, Liu Yijun. An Edge-Based Smoothed Finite Element Method for 2D Mechanics Problems[J]. Northwestern polytechnical university |
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| 二维光滑边域有限元法在弹性力学中的应用研究 |
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| 谢伟1, 贺旭东1, 吴建国2, 刘轶军1 |
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1. 西北工业大学 航空学院, 陕西 西安 710072;
2. 北京强度环境研究所可靠性与环境工程技术重点实验室, 北京 100076 |
| 摘要: |
| 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。 |
| 关键词:
弹性力学
光滑有限元法
光滑边域有限元法
C++
应用
应变能
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| An Edge-Based Smoothed Finite Element Method for 2D Mechanics Problems |
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| Xie Wei1, He Xudong1, Wu Jianguo2, Liu Yijun1 |
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1. School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China;
2. Science and Technology on Reliability and Environment Engineering Laboratory, Beijing Institute of Structure and Environment Engineering, Beijing 100076, China |
| Abstract: |
| 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 calculated. The results of ES-FEM will be compared with those of the standard FEM using triangular and quadrilateral elements (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 results and generally higher convergence rate compared with original FEM. |
| Key words:
mechanics
smoothed finite element method
edge-based smoothed finite element method
C++
application
strain energy
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| 收稿日期: 2016-09-28
修回日期:
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| DOI: |
| 基金项目: 国家自然科学基金（11672238，11472218）和中国航天科技集团公司航天科技创新基金资助 |
| 通讯作者:
Email： |
| 作者简介: 谢伟(1978-),西北工业大学副教授,主要从事计算固体力学、材料/结构疲劳断裂与可靠性分析研究。
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参考文献: |
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