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| A superconvergent isogeometric meshfree collocation method |
| Received:October 25, 2023 Revised:March 12, 2024 |
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| DOI：10.7511/jslx20231025001 |
| KeyWord:meshfree method isogeometric collocation analysis reproduced gradient recursive gradient superconvergence |
| Author | Institution |
| 齐栋梁 |
河北水利电力学院 土木工程系, 沧州 |
| 刘建秀 |
河北水利电力学院 土木工程系, 沧州 |
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| Abstract: |
| Both meshfree methods and isogeometric analysis enjoy the highly smooth shape functions or basis functions.However the basis degree discrepancy issue is observed for the meshfree and isogeometric collocation analysis.This study presents a superconvergent isogeometric meshfree collocation method,which is based upon the consistent conditions of isogeometric basis functions and meshfree gradient reproducing theory.In the proposed method,a mixed gradient reproducing basis vector is defined in accordance with the reproducing kernel meshfree formulation of isogeometric basis functions.Subsequently,a meshfree framework is developed to construct the gradients of isogeometric basis functions in a meshfree fashion,which avoids the costly gradient computation of isogeometric basis functions,which is trivial for numerical implementation.Meanwhile,the second order recursive gradients of the transformed isogeometric meshfree shape functions are established by introducing the basis transformation technique and the recursive gradient formulation.It is noted that the proposed recursive transformed gradients meet extra one-order higher reproducing conditions,which provides an important safeguard for superconvergent collocation analysis.Finally,a series of typical numerical examples are used to systematically verify the convergence and accuracy of the proposed method.Numerical results well demonstrate that the proposed methodology exhibits superior computational accuracy in contrast to the conventional isogeometric collocation,and a superconvergence with two additional orders of accuracy is realized by the proposed approach. |
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