General Analytical Shakedown Analysis of a Structure Subjected to Combined Loading with Constant and Cyclic Loads

Abstract

The shakedown behavior of structures subjected to a combined loading of constant and cyclic loads has been well researched. For some specified problems, shakedown limit loads have been obtained. However, the general effect of combined loading on the structural shakedown has not yet been presented. The general analytic solution of the elastic shakedown limit load is thus derived for a structure subjected to combined loading. Polizzotto's extended static shakedown theorem for combined loading is applied. The stress field in equilibrium with the external constant load required in Polizzotto's extended theorem is constructed by subtracting the reference elastic stress field of the peak cyclic load from the elastic-plastic stress field of the combined constant load and peak cyclic load. The shakedown condition of the stress field is then derived according to the extended theorem. Through the analytical analysis of the shakedown condition, the structural shakedown behavior under combined loading is investigated. A general solution of the shakedown limit load is then derived, and the effects of the combined loading on the shakedown behavior are proposed. The obtained general analytical result is applied to a hollow tension specimen under constant tension and alternating torsion and a plate with a central hole under constant and cyclic tension. The results are consistent with the solutions reported in the literature.