Shakedown Analysis of Framed Structures: Strong Duality and Primal-dual Analysis

The paper is aimed to illustrate the strong duality between the lower and upper bound formulations of shakedown analysis in a novel way. By the lower or upper bound theorem, shakedown analysis is a well-known direct method to evaluate the load carrying capacity of a structure subjected to cyclic loads. In the paper, the Hölder inequality is uniquely utilized to establish the upper bound formulation from the lower bound formulation. Accordingly, the strong duality between them is revealed by duality theorems. Following that, shakedown analysis is performed by the primal-dual algorithm provided by the computing tool MATLAB. Moreover, elastic-plastic analysis is also conducted for comparisons and validations using the commercial finite-element code ABAQUS. Finally, comparisons with good agreement validate the numerical results presented in the paper.