Upper bound limit analysis using radial point interpolation meshless method and nonlinear programming

This paper presents a numerical upper bound limit analysis using radial point interpolation method (RPIM) and a direct iterative method with nonlinear programming. By expressing the internal plastic dissipation power with a kinematically admissible velocity field obtained through RPIM interpolation, the upper bound problem is formulated mathematically as a nonlinear programming subjected to single equality constraint which is solved by a direct iterative method. To evaluate the integration of internal power dissipation rate without any background integral cell, a new meshless integration technique based on Cartesian Transformation Method (CTM) is employed to transform the domain integration first as boundary integration and then one-dimensional integration. The effectiveness and accuracy of the proposed approach are demonstrated by two classical limit analysis problems. Further discussion is devoted to optimal selection of relevant parameters for the computation.

Research highlights
► We present an upper bound limit analysis based on the RPIM mesh-free method.
► We employ a RPIM shape function to construct the kinematically admissible velocity field.
► The method offers a high accuracy and enables direct enforcement of essential boundary conditions.
► A Cartesian transformation integration method is developed to compute the internal dissipation.
► The RPIM-based optimization problem is solved by an iterative method with nonlinear programming.