A gradient smoothing method (GSM) based on strong form governing equation for adaptive analysis of solid mechanics problems

Authors:
Jian Zhang;G. R. Liu;K. Y. Lam;Hua Li;G. Xu
Affiliations:
Department of Civil Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore 117576, Singapore;Centre for ACES, Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore and Singapore-MIT Alliance (SMA), E4-04-10, 4 Engineeri ...;School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore;School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore;Institute of High Performance Computing, 1 Science Park Road, #01-01 The Capricorn Singapore Science Park II, Singapore 117528, Singapore
Venue:
Finite Elements in Analysis and Design
Year:
2008

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Abstract

A gradient smoothing method (GSM) based on strong form of governing equations for solid mechanics problems is proposed in this paper, in which gradient smoothing technique is used successively over the relevant gradient smoothing domains to develop the first- and second-order derivative approximations by calculating weights for a set of field nodes surrounding a node of interest. The GSM is found very stable and can be easily applied to arbitrarily irregular triangular meshes for complex geometry. Unlike other strong form methods, the present method has excellent stability that is crucial for adaptive analysis. An effective and robust residual based error indicator and simple refinement procedure using Delaunay diagram are then implemented in our GSM for adaptive analyses. The reliability and performance of the proposed GSM for adaptive procedure are demonstrated in several solid mechanics problems including problems with singularities and concentrated loading, compared with the well-known finite element method (FEM).