Optimal archgrids: a variational setting

Radosław Tomasz Czubacki , Tomasz Denis Lewiński

Abstract

The paper deals with the variational setting of the optimal archgrid construction. The archgrids, discovered by William Prager and George Rozvany in 1970s, are viewed here as tension-free and bending-free, uniformly stressed grid-shells forming vaults unevenly supported along the closed contour of the basis domain. The optimal archgrids are characterized by the least volume. The optimization problem of volume minimization is reduced to the pair of two auxiliary mutually dual problems, having mathematical structure similar to that known from the theory of optimal layout: the integrand of the auxiliary minimization problem is of linear growth, while the auxiliary maximization problem involves test functions subjected to mean-square slope conditions. The noted features of the variational setting governs the main properties of the archgrid shapes: they are vaults over a subregion of the basis domain being the effective domain of the minimizer of the auxiliary problem. Thus, the method is capable of cutting out the material domain from the design domain; this process is built in within the theory. Moreover, the present paper puts forward new methods of numerical construction of optimal archgrids and discusses their applicability ranges.
Author Radosław Tomasz Czubacki (FCE / ICE)
Radosław Tomasz Czubacki,,
- The Institute of Civil Engineering
, Tomasz Denis Lewiński (FCE / ICE)
Tomasz Denis Lewiński,,
- The Institute of Civil Engineering
Journal seriesStructural and Multidisciplinary Optimization, ISSN 1615-147X, e-ISSN 1615-1488
Issue year2020
Pages1371-1393
Keywords in EnglishPrager-Rozvany archgrids, Michell structures, Least-volume design
ASJC Classification1704 Computer Graphics and Computer-Aided Design; 1706 Computer Science Applications; 1712 Software; 2207 Control and Systems Engineering; 2606 Control and Optimization
DOIDOI:10.1007/s00158-020-02562-y
URL https://link.springer.com/article/10.1007%2Fs00158-020-02562-y
Languageen angielski
File
Czubacki-Lewiński2020.pdf 6.28 MB
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 28-08-2020, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 1.76; WoS Impact Factor: 2018 = 3.925 (2) - 2018=4.105 (5)
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