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An engineering method for complex structural optimization involving both size and topology design variables
Author(s) -
Huang Hai,
An Haichao,
Ma Haibo,
Chen Shenyan
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5957
Subject(s) - topology optimization , mathematical optimization , continuous optimization , sizing , optimization problem , genetic algorithm , mathematics , topology (electrical circuits) , sequence (biology) , computer science , algorithm , finite element method , structural engineering , multi swarm optimization , engineering , art , combinatorics , biology , visual arts , genetics
Summary This work presents an engineering method for optimizing structures made of bars, beams, plates, or a combination of those components. Corresponding problems involve both continuous (size) and discrete (topology) variables. Using a branched multipoint approximate function, which involves such mixed variables, a series of sequential approximate problems are constructed to make the primal problem explicit. To solve the approximate problems, genetic algorithm (GA) is utilized to optimize discrete variables, and when calculating individual fitness values in GA, a second‐level approximate problem only involving retained continuous variables is built to optimize continuous variables. The solution to the second‐level approximate problem can be easily obtained with dual methods. Structural analyses are only needed before improving the branched approximate functions in the iteration cycles. The method aims at optimal design of discrete structures consisting of bars, beams, plates, or other components. Numerical examples are given to illustrate its effectiveness, including frame topology optimization, layout optimization of stiffeners modeled with beams or shells, concurrent layout optimization of beam and shell components, and an application in a microsatellite structure. Optimization results show that the number of structural analyses is dramatically decreased when compared with pure GA while even comparable to pure sizing optimization.