| 基于基面力概念的余能原理任意网格有限元方法 |
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| 引用本文： | 彭一江,金明.基于基面力概念的余能原理任意网格有限元方法[J].工程力学,2007,24(10):41-45,56. |
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| 作者姓名： | 彭一江 金明 |
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| 作者单位： | 1. 北京工业大学结构工程系,北京,100022
2. 北京交通大学工程力学研究所,北京,100044 |
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| 基金项目： | 国家自然科学基金
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高等学校博士学科点专项科研项目
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北京市教委科技发展计划项目
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北京市属市管高校人才强教计划 |
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| 摘 要： | 利用基面力概念,给出一种任意形状网格都可以使用的柔度矩阵表达式的具体形式,运用拉格朗日乘子法得到以基面力为基本未知量的余能原理有限元支配方程,提出计算节点位移的表达式,编制出相应的任意网格有限元计算程序。该文对不同形状的单元网格以及畸变网格进行了计算分析,并与理论解和传统的有限元进行了对比和讨论。结果表明:该方法可以适用于任意形状的有限元网格,对网格的畸变不敏感。
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| 关 键 词： | 有限元 余能 柔度矩阵 基面力 任意网格 |
| 文章编号： | 1000-4750（2007）10-0041-05 |
| 修稿时间： | 2006-02-282007-01-25 |
FINITE ELEMENT METHOD FOR ARBITRARY MESHES BASED ON COMPLEMENTARY ENERGY PRINCIPLE USING BASE FORCES |
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| PENG Yi-jiang,JIN Ming.FINITE ELEMENT METHOD FOR ARBITRARY MESHES BASED ON COMPLEMENTARY ENERGY PRINCIPLE USING BASE FORCES[J].Engineering Mechanics,2007,24(10):41-45,56. |
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| Authors: | PENG Yi-jiang JIN Ming |
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| Affiliation: | 1. Department of Structure Engineering, Beijing University of Technology, Beijing 100022, China; 2. Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, China |
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| Abstract: | An explicit expression of element compliance matrix of the finite element method for arbitrary meshes is derived using the base forces. The governing equations expressed by the base forces are obtained using Lagrangian multiplier method, and the displacements formulation of nodes is given. A program of the finite element method is developed. The method is used to solve several problems of arbitrary polygonal meshes and aberrant meshes, and the numerical results are compared with those of the theoretical solutions and traditional finite element method solutions. The results show that the method proposed is efficient to employ the arbitrary meshes and is free from mesh aberrant. |
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| Keywords: | finite element complementary energy compliance matrix base forces arbitrary meshes |
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