Open AccessThe Structure of the Optimal Control in the Problems of Strength Optimization of Steel Girders
Author(s) -
Leszek Mikulski
Publication year - 2019
Publication title -
archives of civil engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.208
H-Index - 15
eISSN - 2300-3103
pISSN - 1230-2945
DOI - 10.2478/ace-2019-0060
Subject(s) - correctness , optimal control , mathematical optimization , dimension (graph theory) , boundary value problem , optimization problem , control (management) , control variable , mathematics , computer science , algorithm , mathematical analysis , statistics , artificial intelligence , pure mathematics
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.