Plastic Behaviour and Stability Constraints in the Reliability based Shakedown Analysis and Optimal Design of Skeletal Structures

摘要

The aim of this paper is to take into consideration the influence of the limited load carrying capacity of the connections on the plastic limit state of elasto-plastic steel (or composite) skeletal structures under multi-parameter static loading and probabilistically given conditions during the analysis and optimal design. In addition to the plastic shakedown analysis and optimal design to control the plastic behaviour of the structure, bound on the complementary strain energy of the residual forces is also applied. This bound has significant effect for the load parameter. The different behaviour of the beam elements in compression and tension is taken into consideration by the reduced load carrying capacity in compression. The calculation is based on the requirements of the Eurocode. If the design uncertainties (manufacturing, strength, geometrical) are expressed by the calculation of the complementary strain energy of the residual forces the reliability based extended shakedown analysis and optimal design problems can be formed. Numerical procedures are elaborated which are based on a direct integration technique and the uncertainties are assumed to follow Gaussian distribution. The formulations of the problems yield to nonlinear mathematical programming which are solved by the use of sequential quadratic algorithm. The nested optimization procedure is governed by the reliability index calculation.