Optimization of the Structures at Shakedown and Rosen’s Optimality Criterion
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University of Zielona Gora, Institute of Civil Engineering, Szafrana sjr 1, 65-516 Zielona Góra, tel.+48683282322, Poland
Vilnius Gediminas Technical University, Department of Structural Mechanics, Saulétekio ave 11, 10223 Vilnius, tel-37052745216, Lithuania
Online publication date: 2016-10-21
Publication date: 2016-09-01
Civil and Environmental Engineering Reports 2016;22(3):5–24
Paper focuses on the problems of application of extreme energy principles and nonlinear mathematical programing in the theory of structural shakedown. By means of energy principles, which describes the true stress-strain state conditions of the structure, the dual mathematical models of analysis problems are formed (static and kinematic formulations). It is shown how common mathematical model of the structures optimization at shakedown with safety and serviceability constraints (according to the ultimate limit state (ULS) and serviceability limit state (SLS) requirements) on the basis of previously mentioned mathematical models is formed. The possibilities of optimization problem solution in the context of physical interpretation of optimality criterion of Rosen’s algorithm are analyzed.
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