| 无网格伽辽金法在二维结构问题中的应用研究 |
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| 引用本文： | 刘加光,陈义保,罗震.无网格伽辽金法在二维结构问题中的应用研究[J].山东理工大学学报,2006,20(3):25-30. |
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| 作者姓名： | 刘加光 陈义保 罗震 |
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| 作者单位： | 烟台大学机电汽车工程学院 山东烟台264005(刘加光，陈义保)，华中科技大学机械工程学院 武汉430074(罗震) |
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| 摘 要： | 无网格伽辽金法(EFGM)是一种新型的求解偏微分方程的数值计算方法,不需对结构进行有限元网格的离散化,只需节点信息而不需将节点连成单元.本文论述和研究了EF-GM的基本原理与实现过程,主要包括用移动最小二乘法(MLS)构造形函数、用变分原理推导控制方程、用拉格朗日乘子法增强本征边界条件和域的高斯积分4个主要过程.基于MAT-LAB平台,实现了二维弹性结构的EFGM算法,并将典型算例的EFGM求解结果与有限元近似解、解析解结果进行了比较,结果表明了EFGM算法的正确性和有效性.
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| 关 键 词： | 偏微分方程 计算方法 有限元法 无网格伽辽金法 移动最小二乘近似 |
| 文章编号： | 1672-6197(2006)03-0025-06 |
| 收稿时间： | 03 27 2006 12:00AM |
| 修稿时间： | 2006年3月27日 |
Application research on two dimensional structure problem based on element-free galerkin methods |
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| LIU Jia-guang,CHEN Yi-bao,LUO Zhen.Application research on two dimensional structure problem based on element-free galerkin methods[J].Journal of Shandong University of Technology:Science and Technology,2006,20(3):25-30. |
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| Authors: | LIU Jia-guang CHEN Yi-bao LUO Zhen |
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| Institution: | 1. School of Electromeehanieal Automobile Engineering, Yantai University, Yantai 264005, China; 2. School of Mechanical Engineering, Huazhong University of Science and Technology, Wuhan 430074, China |
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| Abstract: | Element free Galerkin method(EFGM) is a new computational method for solving partial differential equation,in which there is no need to generate finite element(FE) meshes and only the information of nodes not the connective information is needed.This work is mainly concerned with four problems,such as constructing moving least square(MLS) approximation to construct the shape function,developing control equation with the weak variational form,enforcing the essential boundary condition and integrating the design domain using Gauss method,where the shape function derived from MLS method generally can't meet Kronecker condition around the essential boundary and it can be settled by employing Lagrange multiplies.A typical example is performed to substantiate the validity of EFGM accompanied with the comparison of analytical result and FE approximation. |
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| Keywords: | partial differential equations computational methods finite element methods element-free galerkin methods moving least square approximation |
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