| 王东东,张汉杰,梁庆文.等几何修正准凸无网格法[J].计算力学学报,2016,33(4):605~612 |
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| 等几何修正准凸无网格法 |
| Isogeometric refined quasi-convex meshfree method |
| 投稿时间：2016-05-19 修订日期：2016-06-16 |
| DOI：10.7511/jslx201604029 |
| 中文关键词: 无网格法 准凸形函数 多项式再生条件 松弛多项式再生条件 结构振动 |
| 英文关键词:meshfree method quasi-convex meshfree shape functions reproducing conditions relaxed reproducing conditions structural vibration |
| 基金项目:国家自然科学基金（11472233，11222221）；福建省自然科学基金（2014J06001）资助项目. |
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| 摘要点击次数: 2086 |
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| 中文摘要: |
| 采用等几何B样条基函数的多项式再生条件对无网格形函数的多项式再生条件进行了修正，使得无网格形函数的负值部分明显减少，在域内趋于非负函数，即等几何修正准凸无网格形函数。该准凸无网格形函数仍然具有与传统再生核无网格形函数相似的构造形式，数值实现比较便捷，同时该准凸无网格形函数的多项式再生条件具有准确的修正系数，无需引入额外的人工节点松弛参数。更重要的是，等几何修正准凸无网格形函数可在确保形函数高阶光滑的前提下减小相对支持域，提高计算效率。最后，基于等几何修正准凸无网格形函数对杆梁和膜板结构进行了伽辽金无网格振动分析。结果表明，与标准再生核无网格法相比，等几何修正准凸无网格法具有更优的计算精度。 |
| 英文摘要: |
| An isogeometric refined quasi-convex meshfree method is proposed.The present quasi-convexity of meshfree approximation is obtained through refining the consistency or reproducing conditions of meshfree shape functions by their counterparts in the convex isogeometric B-spline basis functions.The derived meshfree shape functions are thus called isogeometric refined quasi-convex meshfree shape functions which are almost positive.These shape functions still belong to the general reproducing kernel meshfree framework and their numerical implementation is quite straightforward.In contrast to the previous quasi-convex meshfree approximants that are related to artificial nodal relaxed parameters,the present quasi-convex meshfree shape functions are built upon the isogeometric refined reproducing conditions with analytical nodal relaxed coefficients,and consequently there is no need for any factitious adjustment.More importantly,compared with the standard meshfree shape functions,a unique feature of the present isogeometric refined quasi-convex meshfree shape functions is that they require much smaller support size to ensure smoothing shape functions,which is very desirable from the computational point of view.The accuracy of the proposed approach is demonstrated by performing Galerkin meshfree analysis of free vibration of rods,membranes and thin plates.The dispersion analysis results also consistently support the superiority of the proposed method. |
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