Shakedown analysis of porous materials via mixed meshless methods

Abstract

In this paper, the elastic shakedown analysis of porous materials is performed by means of meshless methods using mixed approximations. Based on a mixed variational principle for shakedown analysis and using a yield function for porous materials, two meshless methods are adapted to perform mixed approximations of the stress and velocity fields for the solution of the discrete shakedown problem. These two new methods are named mixed moving least squares method and mixed Shepard's method and are used to solve some numerical examples. The numerical results obtained showed a good agreement with available analytical solutions and published results by the finite element method. The proposed mixed methods can be applied in the analysis of structural and machine parts made of porous materials and subjected to variable loads.