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| Isogeometric refined quasi-convex meshfree method |
| Received:May 19, 2016 Revised:June 16, 2016 |
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| DOI：10.7511/jslx201604029 |
| KeyWord:meshfree method quasi-convex meshfree shape functions reproducing conditions relaxed reproducing conditions structural vibration |
| Author | Institution |
| 王东东 |
厦门大学 土木工程系, 厦门 |
| 张汉杰 |
厦门大学 土木工程系, 厦门 ;华北理工大学 建筑工程学院, 唐山 |
| 梁庆文 |
厦门大学 土木工程系, 厦门 |
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| Abstract: |
| 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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