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.

在本文中，多孔材料的弹性减振分析是通过使用混合近似的无网格方法进行的。基于用于混合分析的混合变分原理和多孔材料的屈服函数，两种无网格方法适用于对离散的混合问题求解应力和速度场的混合近似值。这两种新方法分别称为混合移动最小二乘法和混合Shepard方法，用于求解一些数值示例。获得的数值结果与可用的解析解和通过有限元方法发表的结果显示出良好的一致性。所提出的混合方法可用于分析由多孔材料制成并承受可变载荷的结构和机械零件。