Upper bound limit analysis of plates utilizing the C1 natural element method

Abstract

In this article, a novel numerical solution procedure is proposed to evaluate the upper bound limit load multipliers for thin plate problems, which incorporates the C1 natural element method (C1NEM) with a direct iteration algorithm. Due to its remarkable interpolation property to the nodal function and the nodal gradient values, the C1NEM with the C1- continuous trial function is used here to deal with the upper bound limit analysis problem of perfectly rigid-plastic plates. The relevant discrete mathematical programming formulation is established based on the kinematic theorem of plastic limit analysis, and a direct iteration algorithm with the advantages of simple solution formula and easy procedure implementation is presented to solve it. Several representative examples governed by the von Mises yield criterion are investigated. The numerical solutions obtained in this paper are reasonable and satisfactory, and are in good agreement with the previously reported results.