Eurocode stability requirements in optimal shakedown truss design

Abstract

The buckling resistance of truss elements under compression is determined according to the requirements of standards such as the Eurocode (EC). The element loses its stability, which implies that the ultimate limit state is violated, when the design value of a compression force exceeds the resistance value of an element. When mathematical programming is used for optimal perfectly elastic-plastic truss design, the complementary slackness conditions of mathematical programming are written with the help of plastic multipliers [1]. These multipliers are used for evaluating the residual forces, therefore, their accurate determination makes the main stage of the solution of the problem. In this paper, new conditions, which complement the optimization problem and enhance the interpretation of the stability constraints in the shakedown process, are presented. Plastic deformations of the compression members after the loss of stability are not defined in the EC and, therefore, cannot be evaluated. Thus, the above-mentioned complementary slackness conditions are not adequate to ensure the correct evaluation of plastic deformations in the shakedown process. The proposed new formulation solves this problem by ensuring that plastic deformations (in the form of plastic multipliers) could only emerge as a result of the development of the tension yield stress or compression yield stress of very stocky elements. Slender elements under compression are checked for loss of stability and cannot reach the yield stress (and, therefore, cannot produce nonzero plastic multipliers).