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This study presents a novel numerical procedure for kinematic yield design of periodic heterogeneous microstructures. The fluctuating part of displacement field is approximated using stabilized radial point interpolation method (RPIM). Taking advantage of truly mesh-free approximation and second order cone programming (SOCP), the resulting optimization problem formulated on a representative volume element (RVE) can be efficiently solved. The macroscopic strength domains at limit state and failure mechanisms associated with different load cases are obtained. Several numerical examples are investigated to perform the computational aspect of proposed method.