Simultaneous sizing, shape, and layout optimization and automatic member grouping of dome structures

Abstract

This paper presents both discrete and continuous sizing, shape, and layout structural optimization problems concerning the weight minimization of dome structures and considering displacements, stresses, natural frequencies of vibration, and global stability as constraints. The layout optimization searches for the best structural configuration through the maintenance of the bars’ grouping by introducing a new design variable. This variable refers to the number of standard modules used to generate the structural configuration of optimized domes. It can be attractive to use a reduced number of distinct cross-sectional areas, minimizing the costs of fabrication, transportation, storing, checking, and welding, providing labor saving measures. To obtain an automatic member grouping of the bars of the trusses analyzed in this paper, a specific encoding using cardinality constraints is considered. As result, trade-off curves are provided, showing the optimized weights in comparison with the number of distinct cross-sectional areas used in the solutions. Differential Evolution is the search algorithm adopted in this paper. The structural optimization problems showed better solutions when compared with those presented in the literature.