The optimal design of an arch girder of variable curvature and stiffness by means of control theory
type: Item
instance of: scholarly article
title: The optimal design of an arch girder of variable curvature and stiffness by means of control theory
zbMATH Open document ID: 1427.74086
DOI: 10.1155/2018/8239464
author: Dorota Jasińska
author: Dorota Kropiowska
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The problem of optimal design of the statically indeterminate arch girder which constitutes the primary structural system of the arch bridge is presented. The task is to determine the optimal shape of the axis of the arch girder, as well as the optimal distribution of the cross section height, ensuring the minimum arch volume as well as fulfillment of the standard requirements. This optimisation task, with numerous control functions and constraints, is formulated as a control theory problem with maintaining the formal structure of the minimum principle and then transformed to the multipoint boundary value problem and solved by means of numerical methods. The numerical results are obtained with optimal control methods, using the Dircol software. Since the changes in the shape and cross-section of the arch affect the distribution of the dead and moving loads transferred on the girder from the bridge deck, the optimisation procedure is combined with the finite element method analysis, which together with the complexity of the multidecision arch optimisation problem accounts for the novelty of the proposed approach. The numerical analysis reveals that the optimal girder shape is the frame-arched structure, with considerable lengths of straight sections and only short arch elements, in the areas of the application of concentrated forces and moments. The presented method can be successfully extended to optimisation of structures with different static schemes and load categories taken into account.
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 49Q12
zbMATH DE Number: 7019574
describes a project that uses: DIRCOL
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8239464
OpenAlex ID: W2906553430
cites work: Q5184508
cites work: Q3721994
cites work: Optimal arch shape solution under static vertical loads
cites work: Optimal arches shape for single-point-supported deck bridges
cites work: How the Gateway Arch got its shape
cites work: Direct approach to the minimization of the maximal stress over an arch structure
cites work: Q5297916
cites work: Q3285814
cites work: Q5697127
cites work: Q4718779
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description: scientific article; zbMATH DE number 7019574