An adaptive local maximum entropy point collocation method for linear elasticity  

Fan, L.; Coombs, W.M.; Augarde, C.E.

Abstract

Point collocation methods are strong form approaches that can be applied to continuum mechanics problems and possess attractive features over weak form-based methods due to the absence of a mesh. While various adaptive strategies have been proposed to improve the accuracy of weak form-based methods, such techniques have received little attention for strong form-based methods. In this paper, combined rh-adaptivity, in which r- and h-adaptivities are adopted iteratively, is applied to the local maximum entropy point collocation method for the first time to solve linear elasticity problems. Material force residuals act as driving forces in r-adaptivity to relocate collocation points, reducing the error associated with a given point distribution. Physical equilibrium residuals are used as the error estimator in h-adaptivity to determine the insertion locations for new points, diminishing the error caused by inadequate degrees of freedom. Issues arising in mesh-based methods, such as mesh distortion and hanging nodes, are entirely absent from the proposed method. The paper introduces the approach for the rst time and the study is therefore conned to 2D domains. Numerical examples are presented to demonstrate the performance of the proposed adaptive strategies, comparing convergence rates and computational costs using uniform renement, pure r-, h- and combined rh-adaptivities.

Citation

Fan, L., Coombs, W., & Augarde, C. (2021). An adaptive local maximum entropy point collocation method for linear elasticity  . Computers and Structures, 256, Article 106644. https://doi.org/10.1016/j.compstruc.2021.106644

• Journal Article Type: Article
• Acceptance Date: Jul 20, 2021
• Online Publication Date: Aug 10, 2021
• Publication Date: 2021-11
• Deposit Date: Jul 20, 2021
• Publicly Available Date: Aug 11, 2023
• Journal: Computers and Structures
• Print ISSN: 0045-7949
• Electronic ISSN: 1879-2243
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 256
• Article Number: 106644
• DOI: https://doi.org/10.1016/j.compstruc.2021.106644
• Public URL: https://durham-repository.worktribe.com/output/1239258