A stable and efficient meshfree Galerkin method with consistent integration schemes for strain gradient thin beams and plates
© 2020 Elsevier Ltd The strain gradient (SG) theory, incorporating with thin beam and plate models, can effectively describe size effects of micro- and nano-structures. However, since these models are determined by a sixth-order partial differential equation that requires the C2 continuity of de...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Language: | English |
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ELSEVIER SCI LTD
2020
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/80195 |
| _version_ | 1848764178469224448 |
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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 | © 2020 Elsevier Ltd
The strain gradient (SG) theory, incorporating with thin beam and plate models, can effectively describe size effects of micro- and nano-structures. However, since these models are determined by a sixth-order partial differential equation that requires the C2 continuity of deflection in a Galerkin weak form, it is difficult to make stable and efficient numerical analysis. In this paper, a meshfree Galerkin method is presented for SG thin beams and plates. To satisfy the continuity and convergence requirement, moving least square or reproducing kernel shape functions are employed with cubic approximation bases. To pass the patch test, integration constraints are derived and consistent integration schemes are proposed with nodal smoothed derivatives instead of standard ones on evaluating points. Numerical results show that consistent integration is superior to the standard Gauss integration in convergence, accuracy and efficiency. |
| first_indexed | 2025-11-14T11:15:14Z |
| format | Journal Article |
| id | curtin-20.500.11937-80195 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:15:14Z |
| publishDate | 2020 |
| publisher | ELSEVIER SCI LTD |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-801952020-08-14T01:10:18Z A stable and efficient meshfree Galerkin method with consistent integration schemes for strain gradient thin beams and plates Wang, B.B. Lu, Chunsheng Fan, C.Y. Zhao, M.H. Science & Technology Technology Engineering, Civil Engineering, Mechanical Mechanics Engineering Strain gradient Thin beam and plate Meshfree Integration constraint Smoothed derivative POINT INTERPOLATION METHOD QUADRATIC EXACTNESS NONLINEAR VIBRATION NODAL INTEGRATION ELEMENT FORMULATION ELASTICITY DEFORMATION PLASTICITY SURFACE © 2020 Elsevier Ltd The strain gradient (SG) theory, incorporating with thin beam and plate models, can effectively describe size effects of micro- and nano-structures. However, since these models are determined by a sixth-order partial differential equation that requires the C2 continuity of deflection in a Galerkin weak form, it is difficult to make stable and efficient numerical analysis. In this paper, a meshfree Galerkin method is presented for SG thin beams and plates. To satisfy the continuity and convergence requirement, moving least square or reproducing kernel shape functions are employed with cubic approximation bases. To pass the patch test, integration constraints are derived and consistent integration schemes are proposed with nodal smoothed derivatives instead of standard ones on evaluating points. Numerical results show that consistent integration is superior to the standard Gauss integration in convergence, accuracy and efficiency. 2020 Journal Article http://hdl.handle.net/20.500.11937/80195 10.1016/j.tws.2020.106791 English ELSEVIER SCI LTD restricted |
| spellingShingle | Science & Technology Technology Engineering, Civil Engineering, Mechanical Mechanics Engineering Strain gradient Thin beam and plate Meshfree Integration constraint Smoothed derivative POINT INTERPOLATION METHOD QUADRATIC EXACTNESS NONLINEAR VIBRATION NODAL INTEGRATION ELEMENT FORMULATION ELASTICITY DEFORMATION PLASTICITY SURFACE Wang, B.B. Lu, Chunsheng Fan, C.Y. Zhao, M.H. A stable and efficient meshfree Galerkin method with consistent integration schemes for strain gradient thin beams and plates |
| title | A stable and efficient meshfree Galerkin method with consistent integration schemes for strain gradient thin beams and plates |
| title_full | A stable and efficient meshfree Galerkin method with consistent integration schemes for strain gradient thin beams and plates |
| title_fullStr | A stable and efficient meshfree Galerkin method with consistent integration schemes for strain gradient thin beams and plates |
| title_full_unstemmed | A stable and efficient meshfree Galerkin method with consistent integration schemes for strain gradient thin beams and plates |
| title_short | A stable and efficient meshfree Galerkin method with consistent integration schemes for strain gradient thin beams and plates |
| title_sort | stable and efficient meshfree galerkin method with consistent integration schemes for strain gradient thin beams and plates |
| topic | Science & Technology Technology Engineering, Civil Engineering, Mechanical Mechanics Engineering Strain gradient Thin beam and plate Meshfree Integration constraint Smoothed derivative POINT INTERPOLATION METHOD QUADRATIC EXACTNESS NONLINEAR VIBRATION NODAL INTEGRATION ELEMENT FORMULATION ELASTICITY DEFORMATION PLASTICITY SURFACE |
| url | http://hdl.handle.net/20.500.11937/80195 |