Limit state analysis of reinforced concrete slabs using an integrated radial basis function based mesh-free method

Ho, Phuc L. H. and Le, Canh V. and Tran-Cong, T. (2018) Limit state analysis of reinforced concrete slabs using an integrated radial basis function based mesh-free method. Applied Mathematical Modelling, 53. pp. 1-11. ISSN 0307-904X


Abstract

Limit analysis, a general and powerful method to predict the collapse load of reinforced concrete slabs, combines the limit theorems of classical plasticity with numerical methods, and results in an optimization problem. The number of variables in the corresponding optimization problem depends on the number of degrees of freedom used per node. In this paper, a rotation-free meshfree method based on integrated radial basis functions (iRBF) is developed. There is no rotational degree of freedom involved in the approximation, and hence the size of the resultant optimization problem is kept to a minimum. Moreover, the iRBF based shape functions hold the Kronecker delta property, ensuring that there is no need for any special treatment when enforcing essential boundary conditions. The obtained discrete kinematic formulation is handled using available highly efficient solvers. Various Nielsen’s reinforced concrete slabs of arbitrary geometries are examined, showing that the proposed numerical procedure is capable of providing accurate collapse load multipliers and automatically identifying yield-patterns in terms of plastic dissipation distribution.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Files associated with this item cannot be displayed due to copyright restrictions.
Faculty/School / Institute/Centre: Historic - Computational Engineering and Science Research Centre (CESRC) (1 Jul 2013 - 31 Jul 2018)
Faculty/School / Institute/Centre: Historic - Computational Engineering and Science Research Centre (CESRC) (1 Jul 2013 - 31 Jul 2018)
Date Deposited: 17 Jun 2022 00:35
Last Modified: 20 Jun 2022 00:15
Uncontrolled Keywords: Limit analysis, Yield design, Integrated radial basis function, Mesh-free method, Second order cone programming
Fields of Research (2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010399 Numerical and Computational Mathematics not elsewhere classified
01 Mathematical Sciences > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490302 Numerical analysis
49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490399 Numerical and computational mathematics not elsewhere classified
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490199 Applied mathematics not elsewhere classified
Identification Number or DOI: https://doi.org/10.1016/j.apm.2017.08.006
URI: http://eprints.usq.edu.au/id/eprint/49113

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