A stabilized iRBF mesh-free method for quasi-lower bound shakedown analysis of structures. (February 2020) - Ho, Phuc L.H.; Le, Canh V.
Highlights: Integrated radial basis functions-based shape functions are the stabilized using stabilized conforming nodal integration (SCNI) technique. Optimization constraints are enforced at discretized nodes, keeping its size to be minimum. Load domains consisting of a large number of points can be approximated efficiently. The proposed approach is capable of capturing the stress fields at limit state. Abstract: This paper presents a quasi-static formulation, based on integrated radial basis functions (iRBF) and conic programming, for direct analysis of 2D and 3D structures. The iRBF shape functions are stabilized using stabilized conforming nodal integration (SCNI) technique. Equilibrium equations, boundary conditions and yield criterion associated with the residual stresses are directly enforced at scattered nodes without any special treatment. The safety load multipliers are determined by solving the conic optimization problems resulting from static shakedown theorem. The computation cost in terms of the number of variables and optimization CPU time is kept to a minimum. Various benchmark problems in two and three dimensions are investigated, showing the efficiency of the presented numerical approach.