Consistent integration schemes for meshfree analysis of strain gradient elasticity
Integration schemes with nodal smoothed derivatives, which meet integration constraint conditions, are robust and efficient for use in meshfree Galerkin methods, however, most of them are focussed on the classical elasticity determined by a second-order partial differential equation. In this paper,...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
ELSEVIER SCIENCE SA
2019
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/78291 |
| _version_ | 1848763953701715968 |
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| author | Wang, B.B. Lu, Chunsheng Fan, C.Y. Zhao, M.H. |
| author_facet | Wang, B.B. Lu, Chunsheng Fan, C.Y. Zhao, M.H. |
| author_sort | Wang, B.B. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Integration schemes with nodal smoothed derivatives, which meet integration constraint conditions, are robust and efficient for use in meshfree Galerkin methods, however, most of them are focussed on the classical elasticity determined by a second-order partial differential equation. In this paper, arbitrary-order integration constraint conditions are derived for strain gradient elasticity in a fourth-order partial differential equation. These integration constraint conditions provide the discrete forms of nodal shape functions and their first- and second-order derivatives. Furthermore, to meet the integration constraint conditions, consistent integration schemes are designed with nodal smoothed (but not standard) derivatives at evaluating points. It is shown that such nodal smoothed derivatives are able to satisfy the differentiation of approximation consistency. Finally, several case studies are given and the results demonstrate that, based on convergence, accuracy and efficiency, the numerical performance of consistent integration in meshfree analysis of strain gradient elasticity is superior to the standard Gaussian one. |
| first_indexed | 2025-11-14T11:11:39Z |
| format | Journal Article |
| id | curtin-20.500.11937-78291 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:11:39Z |
| publishDate | 2019 |
| publisher | ELSEVIER SCIENCE SA |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-782912020-06-09T07:46:05Z Consistent integration schemes for meshfree analysis of strain gradient elasticity Wang, B.B. Lu, Chunsheng Fan, C.Y. Zhao, M.H. Science & Technology Technology Physical Sciences Engineering, Multidisciplinary Mathematics, Interdisciplinary Applications Mechanics Engineering Mathematics Meshfree Numerical integration Integration constraint Smoothed derivatives Strain gradient Consistency CONFORMING NODAL INTEGRATION FINITE-ELEMENT FORMULATIONS BOUNDARY-VALUE-PROBLEMS QUADRATIC EXACTNESS LEAST-SQUARES APPROXIMATION DYNAMICS STATICS Integration schemes with nodal smoothed derivatives, which meet integration constraint conditions, are robust and efficient for use in meshfree Galerkin methods, however, most of them are focussed on the classical elasticity determined by a second-order partial differential equation. In this paper, arbitrary-order integration constraint conditions are derived for strain gradient elasticity in a fourth-order partial differential equation. These integration constraint conditions provide the discrete forms of nodal shape functions and their first- and second-order derivatives. Furthermore, to meet the integration constraint conditions, consistent integration schemes are designed with nodal smoothed (but not standard) derivatives at evaluating points. It is shown that such nodal smoothed derivatives are able to satisfy the differentiation of approximation consistency. Finally, several case studies are given and the results demonstrate that, based on convergence, accuracy and efficiency, the numerical performance of consistent integration in meshfree analysis of strain gradient elasticity is superior to the standard Gaussian one. 2019 Journal Article http://hdl.handle.net/20.500.11937/78291 10.1016/j.cma.2019.112601 English ELSEVIER SCIENCE SA restricted |
| spellingShingle | Science & Technology Technology Physical Sciences Engineering, Multidisciplinary Mathematics, Interdisciplinary Applications Mechanics Engineering Mathematics Meshfree Numerical integration Integration constraint Smoothed derivatives Strain gradient Consistency CONFORMING NODAL INTEGRATION FINITE-ELEMENT FORMULATIONS BOUNDARY-VALUE-PROBLEMS QUADRATIC EXACTNESS LEAST-SQUARES APPROXIMATION DYNAMICS STATICS Wang, B.B. Lu, Chunsheng Fan, C.Y. Zhao, M.H. Consistent integration schemes for meshfree analysis of strain gradient elasticity |
| title | Consistent integration schemes for meshfree analysis of strain gradient elasticity |
| title_full | Consistent integration schemes for meshfree analysis of strain gradient elasticity |
| title_fullStr | Consistent integration schemes for meshfree analysis of strain gradient elasticity |
| title_full_unstemmed | Consistent integration schemes for meshfree analysis of strain gradient elasticity |
| title_short | Consistent integration schemes for meshfree analysis of strain gradient elasticity |
| title_sort | consistent integration schemes for meshfree analysis of strain gradient elasticity |
| topic | Science & Technology Technology Physical Sciences Engineering, Multidisciplinary Mathematics, Interdisciplinary Applications Mechanics Engineering Mathematics Meshfree Numerical integration Integration constraint Smoothed derivatives Strain gradient Consistency CONFORMING NODAL INTEGRATION FINITE-ELEMENT FORMULATIONS BOUNDARY-VALUE-PROBLEMS QUADRATIC EXACTNESS LEAST-SQUARES APPROXIMATION DYNAMICS STATICS |
| url | http://hdl.handle.net/20.500.11937/78291 |