An adaptive isogeometric analysis meshfree collocation method for elasticity and frictional contact problems
A collocation method has been recently developed as a powerful alternative to Galerkin's method in the context of isogeometric analysis, characterized by significantly reduced computational cost, but still guaranteeing higher‐order convergence rates. In this work, we propose a novel adaptive is...
| Main Authors: | , , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2019
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| Online Access: | https://hdl.handle.net/10356/103298 http://hdl.handle.net/10220/49967 |
| _version_ | 1811695245966966784 |
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| author | Nguyen‐Thanh, Nhon Li, Weidong Huang, Jiazhao Srikanth, Narasimalu Zhou, Kun |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Nguyen‐Thanh, Nhon Li, Weidong Huang, Jiazhao Srikanth, Narasimalu Zhou, Kun |
| author_sort | Nguyen‐Thanh, Nhon |
| collection | NTU |
| description | A collocation method has been recently developed as a powerful alternative to Galerkin's method in the context of isogeometric analysis, characterized by significantly reduced computational cost, but still guaranteeing higher‐order convergence rates. In this work, we propose a novel adaptive isogeometric analysis meshfree collocation (IGAM‐C) for the two‐dimensional (2D) elasticity and frictional contact problems. The concept of the IGAM‐C method is based upon the correspondence between the isogeometric collocation and reproducing kernel meshfree approach, which facilitates the robust mesh adaptivity in isogeometric collocation. The proposed method reconciles collocation at the Greville points via the discretization of the strong form of the equilibrium equations. The adaptive refinement in collocation is guided by the gradient‐based error estimator. Moreover, the resolution of the nonlinear equations governing the contact problem is derived from a strong form to avoid the disadvantages of numerical integration. Numerical examples are presented to demonstrate the effectiveness, robustness, and straightforward implementation of the present method for adaptive analysis. |
| first_indexed | 2024-10-01T07:20:25Z |
| format | Journal Article |
| id | ntu-10356/103298 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:20:25Z |
| publishDate | 2019 |
| record_format | dspace |
| spelling | ntu-10356/1032982021-01-05T06:50:56Z An adaptive isogeometric analysis meshfree collocation method for elasticity and frictional contact problems Nguyen‐Thanh, Nhon Li, Weidong Huang, Jiazhao Srikanth, Narasimalu Zhou, Kun School of Electrical and Electronic Engineering School of Mechanical and Aerospace Engineering Energy Research Institute @ NTU (ERI@N) Engineering::Electrical and electronic engineering Collocation Adaptive A collocation method has been recently developed as a powerful alternative to Galerkin's method in the context of isogeometric analysis, characterized by significantly reduced computational cost, but still guaranteeing higher‐order convergence rates. In this work, we propose a novel adaptive isogeometric analysis meshfree collocation (IGAM‐C) for the two‐dimensional (2D) elasticity and frictional contact problems. The concept of the IGAM‐C method is based upon the correspondence between the isogeometric collocation and reproducing kernel meshfree approach, which facilitates the robust mesh adaptivity in isogeometric collocation. The proposed method reconciles collocation at the Greville points via the discretization of the strong form of the equilibrium equations. The adaptive refinement in collocation is guided by the gradient‐based error estimator. Moreover, the resolution of the nonlinear equations governing the contact problem is derived from a strong form to avoid the disadvantages of numerical integration. Numerical examples are presented to demonstrate the effectiveness, robustness, and straightforward implementation of the present method for adaptive analysis. NRF (Natl Research Foundation, S’pore) Accepted version 2019-09-19T05:21:05Z 2019-12-06T21:09:24Z 2019-09-19T05:21:05Z 2019-12-06T21:09:24Z 2019 Journal Article Nguyen‐Thanh, N., Li, W., Huang, J., Srikanth, N., & Zhou, K. (2019). An adaptive isogeometric analysis meshfree collocation method for elasticity and frictional contact problems. International Journal for Numerical Methods in Engineering, 120(2), 209-230. doi;http://dx.doi.org/10.1002/nme.6132 0029-5981 https://hdl.handle.net/10356/103298 http://hdl.handle.net/10220/49967 10.1002/nme.6132 en International Journal for Numerical Methods in Engineering This is the peer reviewed version of the following article: Nguyen‐Thanh, N., Li, W., Huang, J., Srikanth, N., & Zhou, K. (2019). An adaptive isogeometric analysis meshfree collocation method for elasticity and frictional contact problems. International Journal for Numerical Methods in Engineering, 120(2), 209-230, which has been published in final form at http://dx.doi.org/10.1002/nme.6132. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. 25 p. application/pdf |
| spellingShingle | Engineering::Electrical and electronic engineering Collocation Adaptive Nguyen‐Thanh, Nhon Li, Weidong Huang, Jiazhao Srikanth, Narasimalu Zhou, Kun An adaptive isogeometric analysis meshfree collocation method for elasticity and frictional contact problems |
| title | An adaptive isogeometric analysis meshfree collocation method for elasticity and frictional contact problems |
| title_full | An adaptive isogeometric analysis meshfree collocation method for elasticity and frictional contact problems |
| title_fullStr | An adaptive isogeometric analysis meshfree collocation method for elasticity and frictional contact problems |
| title_full_unstemmed | An adaptive isogeometric analysis meshfree collocation method for elasticity and frictional contact problems |
| title_short | An adaptive isogeometric analysis meshfree collocation method for elasticity and frictional contact problems |
| title_sort | adaptive isogeometric analysis meshfree collocation method for elasticity and frictional contact problems |
| topic | Engineering::Electrical and electronic engineering Collocation Adaptive |
| url | https://hdl.handle.net/10356/103298 http://hdl.handle.net/10220/49967 |
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