Multi-objective topology and geometry optimization of statically determinate beams

Agata Kozikowska

Abstract

he paper concerns topology and geometry optimization of statically determinate beams with arbitrary number of supports. The optimization problem is treated as a bi-criteria one, with the objectives of minimizing the absolute maximum bending moment and the maximum deflection for a uniform gravity load. The problem is formulated and solved using the Pareto optimality concept and the lexicographic ordering of the objectives. The non-dominated sorting genetic algorithm NSGA-II and the local search method are used for the optimization in the Pareto sense, whereas the genetic algorithm and the exhaustive search method for the lexicographic optimization. Trade-offs between objectives are examined and sets of Pareto-optimal solutions are provided for different topologies. Lexicographically optimal beams are found assuming that the maximum moment is a more important criterion. Exact formulas for locations and values of the maximum deflection are given for all lexicographically optimal beams of any topology and any number of supports. Topologies with lexicographically optimal geometries are classified into equivalence classes, and specific features of these classes are discussed. A qualitative principle of the division of topologies equivalent in terms of the maximum moment into topologies better and worse in terms of the maximum deflection is found.
Author Agata Kozikowska (FA / DAD)
Agata Kozikowska,,
- Department of Architectural Design
Journal seriesStructural Engineering and Mechanics, ISSN 1225-4568, (N/A 70 pkt)
Issue year2019
Vol70
No3
Pages 367-380
Publication size in sheets0.65
Keywords in EnglishPareto optimality, lexicographic ordering, beams, topology and geometry optimization, bending moment, deflection
ASJC Classification2205 Civil and Structural Engineering; 2210 Mechanical Engineering; 2211 Mechanics of Materials; 2215 Building and Construction
DOIDOI:10.12989/sem.2019.70.3.367
Internal identifierROC 19-20
Languageen angielski
Score (nominal)70
Score sourcejournalList
ScoreMinisterial score = 70.0, 04-03-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2017 = 0.899; WoS Impact Factor: 2018 = 2.804 (2) - 2018=2.264 (5)
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