ASPECTS OF ANALYSIS AND OPTIMIZATION OF STRUCTURES UNDER PROPORTIONAL AND VARIABLE LOADINGS

Abstract

The paper presents the basic principles, the method and numerical results of a computer program for processing both analysis and design of frame structures under proportional loadings (limit analysis and limit design) and variable loadings (shakedown analysis and shakedown design). The automatic search of independent mechanisms and the dual aspects of different formulations are examined. For example in the case of limit analysis, the kinematical formulation with rotation rates as variables is used but by considering the duality of the linear programming method the distribution of the moments of all sections are obtained directly from primal calculations. In the case of limit design the statical formulation with moments as variables is adopted but the duality the Foulkes’ mechanism is obtained directly from the primal calculation. The program CEPAO considers also the discrete variables corresponding to practical available profiles. It tries to verify all stability criteria proposed by the European Recommendations for Steel Constructions in such a way that the designed structures of minimum weight are satisfactory from the point of view of ultimate limit state. For shakedown analysis and design, linear programming formulations are adopted in such a way that all necessary information such as residual stresses and plastic deformations are obtained in a simple calculation. The method and its numerical efficiency.are illustrated by examples.