Elasto‐plasticity revisited: numerical analysis via reproducing kernel particle method and parametric quadratic programming

Abstract

SUMMARYAiming to simplify the solution process of elasto-plastic problems, this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto-plasticity. The parametric quadratic programming theory is useful and e ective for the assessment of certain features of structural elasto-plastic behaviour and can also be exploited for numerical iteration. Examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the exibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method.

An Elasto-Plastic Analysis of Solids by the Local Meshless Method Based on MLS

“…This value is called the critical failure load, and it is F=55.5 MN for this problem. Comparing with the FEM and other method results 10,12 , it can be seen that the results obtained by the present method are in good agreement with those obtained by other methods. It should be mentioned that the present method needs much less iteration steps than FEM.…”

A spline strip kernel particle method and its application to two‐dimensional elasticity problems

“…The coe cient functions, b i (y), i = 1; 2; 3; : : : ; N , are determined from the reproducing conditions [15][16][17][18] such that the reproducing Equation (2) exactly reproduces the monomial terms of a polynomial of required order. Equation (2) is a continuous form of reproducing kernel approximation.…”

“…The kernel particle shape function approximation, q a (y), of a function q(y) in a one-dimensional domain, y , is expressed as [15][16][17][18]:…”

“…In this study, we introduce a spline strip kernel particle method (SSKPM) for solving a class of 2D elasticity problem. The B 3 -spline functions are used in the longitudinal direction, while in the transverse direction, the kernel particle shape functions [15][16][17][18] are employed for the assuming displacement ÿeld. In this study, several numerical test examples considering di erent boundary conditions and load cases are presented to demonstrate the potential of the proposed method.…”

Reproducing Kernel Particle Method for Radiative Heat Transfer in 1D Participating Media

“…So the RKPM can work well over the whole domain. It has wide application in many engineering fields, such as, rolling plane strain problem [13], bucking analysis of thin plates [14], large deformation nonlinear elastic problems [15][16][17][18], metal forming problem [19][20][21][22], elastic-plastic problems [23,24], convection-diffusion problem [25][26][27], heat conduction problems [28][29][30], and fragment-impact problem [31,32]. But up to now, to the best of our knowledge, there is still lack of literature on the application of RKPM for radiative heat transfer.…”