| 工程计算力学中的正交基无网格方法 |
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| 引用本文： | 苗雨,蒋和洋,王元汉.工程计算力学中的正交基无网格方法[J].岩土力学,2004,25(Z2):126-129. |
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| 作者姓名： | 苗雨 蒋和洋 王元汉 |
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| 作者单位： | 1. 华中科技大学,土木工程与力学学院,湖北,武汉,430074
2. 北京工业大学,建筑工程学院,北京,100022 |
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| 基金项目： | 北京市自然科学基金资助项目(No.3033012)和中国科学院岩土力学重点实验室资助项目(No.Z110202). |
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| 摘 要： | 发现并研究了无网格伽辽金法(EFGM)节点不良分布以及采用一般高次多项式基构造形函数时产生数值解振荡的问题.提出工程计算力学的正交基无网格伽辽金法(MLMBOB),并以罚函数法引入强加边界条件,离散化得到偏微分方程的数值解.该方法保留了无网格伽辽金法所拥有的优秀品质,去除了其中的一些缺陷,使得用高次正交基作逼近时有高计算精度,它适合于工程计算中诸多计算问题.并用算例及其误差分析证实了该方法的优越性.
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| 关 键 词： | 无网格 正交基 数值振荡 罚函数法 误差分析 |
| 文章编号： | 1000-7598-(2004)增-0126-04 |
| 修稿时间： | 2004年4月30日 |
Meshless method based on orthogonal basis for engineering computational mechanics |
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| MIAO Yu ,JIANG He-yang ,WANG Yuan-han.Meshless method based on orthogonal basis for engineering computational mechanics[J].Rock and Soil Mechanics,2004,25(Z2):126-129. |
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| Authors: | MIAO Yu JIANG He-yang WANG Yuan-han |
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| Institution: | MIAO Yu 1,JIANG He-yang 2,WANG Yuan-han 1 |
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| Abstract: | The oscillation problems of numerical solution in elemeat-free Galerkin morhod element-free GalerRin method are discovered and researched by using high order polynomial basis. Meshless method based on orthogonal basis (MLMBOB) is presented,in which the penalty function method is applied to the essential boundary conditions. Then the numerical solution of the PDES is got by discretization. This method holds nearly all qualities of EFGM and removes many drawbacks of it. The method has high accuracy by using high order orthogonal basis. It is fit for many problems in engineering computational mechanics. Examples and error analysis are carried out to prove the excellent features of the present method. |
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| Keywords: | meshless orthogonal basis numerical oscillation penalty method error analysis |
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