计算力学学报2016，Vol.33Issue(4)：605-612,8.DOI:10.7511/jslx201604029
等几何修正准凸无网格法
Isogeometric refined quasi-convex meshfree method
摘要
Abstract
An isogeometric refined quasi-convex meshfree method is proposed.The present quasi-convexi-ty 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 func-tions 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 pre-vious 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 condi-tions with analytical nodal relaxed coefficients,and consequently there is no need for any factitious ad-j ustment.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.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Key words
meshfree method/quasi-convex meshfree shape functions/reproducing conditions/relaxed reproducing conditions/structural vibration分类
数理科学引用本文复制引用
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):605-612,8.基金项目
国家自然科学基金(11472233,11222221) （11472233,11222221）
福建省自然科学基金(2014J06001)资助项目 （2014J06001）
