On error estimation and adaptive refinement for element free Galerkin method. Part II : adaptive refinement
In this paper, an adaptive refinement procedure using the element free Galerkin method (EFGM) for the solution of 2D linear elastostatic problems is suggested. Based on the numerical experiments done in Part I of the current study, in the proposed adaptive refinement scheme, the Zienkiewicz and Z...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2014
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/103287 http://hdl.handle.net/10220/19228 |
| _version_ | 1826124014864564224 |
|---|---|
| author | Lee, Chi King Zhou, C. E. |
| author2 | School of Civil and Environmental Engineering |
| author_facet | School of Civil and Environmental Engineering Lee, Chi King Zhou, C. E. |
| author_sort | Lee, Chi King |
| collection | NTU |
| description | In this paper, an adaptive refinement procedure using the element free Galerkin method
(EFGM) for the solution of 2D linear elastostatic problems is suggested. Based on the
numerical experiments done in Part I of the current study, in the proposed adaptive
refinement scheme, the Zienkiewicz and Zhu (Z-Z) error estimator using the TBelytschko
(TB) stress recovery scheme is employed for the a posteriori error
estimation of EFGM solution. By considering the a priori convergence rate of the
EFGM solution and the estimated error norm, an adaptive refinement strategy for the
determination of optimal node spacing is proposed. A simple point mesh generation
scheme using pre-defined templates to generate new nodes inside the integration cells
for adaptive refinement is also developed. The performance of the suggested refinement
procedure is tested by using it to solve several benchmark problems. Numerical results
obtained indicate that the suggested procedure can lead to the generation of nearly
optimal meshes and the effects of singular points inside the problem domain are largely
eliminated. The optimal convergence rate of the EFGM analysis is restored and the
effectivity indices of the Z-Z error estimator are converging towards the ideal value of
unity as the meshes are refined. |
| first_indexed | 2024-10-01T06:14:04Z |
| format | Journal Article |
| id | ntu-10356/103287 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:14:04Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | ntu-10356/1032872020-03-07T11:45:54Z On error estimation and adaptive refinement for element free Galerkin method. Part II : adaptive refinement Lee, Chi King Zhou, C. E. School of Civil and Environmental Engineering DRNTU::Engineering::Civil engineering::Structures and design In this paper, an adaptive refinement procedure using the element free Galerkin method (EFGM) for the solution of 2D linear elastostatic problems is suggested. Based on the numerical experiments done in Part I of the current study, in the proposed adaptive refinement scheme, the Zienkiewicz and Zhu (Z-Z) error estimator using the TBelytschko (TB) stress recovery scheme is employed for the a posteriori error estimation of EFGM solution. By considering the a priori convergence rate of the EFGM solution and the estimated error norm, an adaptive refinement strategy for the determination of optimal node spacing is proposed. A simple point mesh generation scheme using pre-defined templates to generate new nodes inside the integration cells for adaptive refinement is also developed. The performance of the suggested refinement procedure is tested by using it to solve several benchmark problems. Numerical results obtained indicate that the suggested procedure can lead to the generation of nearly optimal meshes and the effects of singular points inside the problem domain are largely eliminated. The optimal convergence rate of the EFGM analysis is restored and the effectivity indices of the Z-Z error estimator are converging towards the ideal value of unity as the meshes are refined. Accepted version 2014-04-10T06:11:41Z 2019-12-06T21:09:08Z 2014-04-10T06:11:41Z 2019-12-06T21:09:08Z 2003 2003 Journal Article Lee, C. K., & Zhou, C. E. (2004). On error estimation and adaptive refinement for element free Galerkin method. Computers & Structures, 82(4-5), 429-443. 0045-7949 https://hdl.handle.net/10356/103287 http://hdl.handle.net/10220/19228 10.1016/j.compstruc.2003.10.017 en Computers & structures © 2003 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by Computers & Structures, Elsevier. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [Article DOI: http://dx.doi.org/10.1016/j.compstruc.2003.10.017]. application/pdf |
| spellingShingle | DRNTU::Engineering::Civil engineering::Structures and design Lee, Chi King Zhou, C. E. On error estimation and adaptive refinement for element free Galerkin method. Part II : adaptive refinement |
| title | On error estimation and adaptive refinement for element free Galerkin method. Part II : adaptive refinement |
| title_full | On error estimation and adaptive refinement for element free Galerkin method. Part II : adaptive refinement |
| title_fullStr | On error estimation and adaptive refinement for element free Galerkin method. Part II : adaptive refinement |
| title_full_unstemmed | On error estimation and adaptive refinement for element free Galerkin method. Part II : adaptive refinement |
| title_short | On error estimation and adaptive refinement for element free Galerkin method. Part II : adaptive refinement |
| title_sort | on error estimation and adaptive refinement for element free galerkin method part ii adaptive refinement |
| topic | DRNTU::Engineering::Civil engineering::Structures and design |
| url | https://hdl.handle.net/10356/103287 http://hdl.handle.net/10220/19228 |
| work_keys_str_mv | AT leechiking onerrorestimationandadaptiverefinementforelementfreegalerkinmethodpartiiadaptiverefinement AT zhouce onerrorestimationandadaptiverefinementforelementfreegalerkinmethodpartiiadaptiverefinement |