Mesh-free kinematic shakedown analysis of cohesive soils

A novel mesh-free solution is proposed for kinematic shakedown analysis of cohesive soils under repeating loads. For this purpose, the continuous velocity field in the mathematical expression of Koiter’s theorem is discretized by the Radial Point Interpolation Method (RPIM), as a mesh-free approach. The strain rate smoothing technique is implemented in conjunction with the RPIM to satisfy the admissibility conditions at the entire problem domain. Using the nodal integration and the discretized velocity field, the kinematic shakedown problem is expressed as a nonlinear optimization problem. The optimization problem is solved by separation of plastic and non-plastic/rigid zones using a repetitive algorithm. Eventually, the efficiency of the proposed approach is elucidated by solving examples of a strip footing resting on cohesive soil and a cohesive half space pavement under repeating loads.