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The Structure of the Optimal Control in the Problems of Strength Optimization of Steel Girders

Authors
  • Mikulski, Leszek1
  • 1 Cracow University of Technology, 31-155 , (Poland)
Type
Published Article
Journal
Archives of Civil Engineering
Publisher
Sciendo
Publication Date
Dec 01, 2019
Volume
65
Issue
4
Pages
277–293
Identifiers
DOI: 10.2478/ace-2019-0060
Source
De Gruyter
Keywords
License
Green

Abstract

The paper concerns a strength optimization of continuous beams with variable cross-section. The continuous beams are subjected to a dead weight and a useful load, the six (seven) combinations of loads were analyzed. Optimal design problems in structural mechanics can by mathematically formulated as optimal control tasks. To solve the above formulated optimization problems, the minimum principle was applied. The paper is an introductory and survey paper of the treatment of realistically modelled optimal control problems from application in the structural mechanics. Especially those problems are considered, which include different types of constraints. The optimization problem is reduced to the solution of multipoint boundary value problems (MPBVP) composed of differential equations. Dimension of MPBVP is usually a large number, what produces numerical difficulties. Optimal control theory does not give much information about the control structure. The correctness of the assumed control structure can be checked after obtaining the solution of the boundary problem.

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