Optimal shakedown design of steel framed structures according to standards

Abstract

The paper considers the relationships between the optimization of perfectly elastic–plastic structures under repeated variable load and the valid structural design standards. The physical and geometrical properties of a structure are known in advance. The quasi-static cyclic loading is characterized by time-independent upper and lower bounds. The mathematical model for determining the optimal internal limiting force distribution of a structure at shakedown with strength, stiffness and stability constraints according to EC3 standard is presented. The model takes into account the ultimate and serviceability limit states of EC3 with corresponding reliability levels. The evaluation of the stability of the elements under compression takes into account plastic deformations in the shakedown process. The proposed methodology allows a more precise interpretation of the stability constraints in continuous optimization problems of mathematical programming. The results are valid for the assumption of small displacements. Numerical examples of the optimization of a portal and three storey steel frames are presented.