Kinematic Shakedown Analysis for Strain-Hardening Plates with the C1 Nodal Natural Element Method

Abstract

This paper proposes a novel numerical solution approach for the kinematic shakedown analysis of strain-hardening thin plates using the C¹ nodal natural element method (C¹ nodal NEM). Based on Koiter’s theorem and the von Mises and two-surface yield criteria, a nonlinear mathematical programming formulation is constructed for the kinematic shakedown analysis of strain-hardening thin plates, and the C¹ nodal NEM is adopted for discretization. Additionally, König’s theory is used to deal with time integration by treating the generalized plastic strain increment at each load vertex. A direct iterative method is developed to linearize and solve this formulation by modifying the relevant objective function and equality constraints at each iteration. Kinematic shakedown load factors are directly calculated in a monotonically converging manner. Numerical examples validate the accuracy and convergence of the developed method and illustrate the influences of limited and unlimited strain-hardening models on the kinematic shakedown load factors of thin square and circular plates.