Keywords: large-span shallow dome, hybrid heuristic and metaheuristic optimisation, global and local stability constraints.

In this paper, an improved ANGEL algorithm is presented for minimal weight design of shallow dome structures with discrete and continuous design variables. The flexibility of the shallow dome structures might causes different type of structural instability. According to the nonlinear behaviour of the resulted lightweight space structures, a special treatment is required in order to tackle the stability constraints during the optimisation process.

The algorithm presented is an improved version of the ANGEL metaheuristic developed for truss design by Csébfalvi et al. [1]. The "exact" procedure, in each step, tries to decrease the weight of a feasible structure or increase the feasibility of an unfeasible structure subject to the current weight by choosing the best values from the current local catalogue spanned by the immediate predecessor and successor values and changing the shape variables simultaneously. In the approach presented, the feasibility is measured by the maximal feasible load intensity factor given by a higher-order nonlinear path-following method [2]. The local search procedure exploits the fact, that using a fast and effective solver a small MILP/MIQP problem can be solved within reasonable time.

In this study, in order to compare the effectiveness of the proposed method, a continuous and discrete sizing optimisation problem is presented for dome structures with many degrees of freedom requires great number of structural analyses.

1

A. Csébfalvi, G. Csébfalvi, "Optimum Design and Sensitivity Analysis of Shallow Space Structures using an Improved Meta-Heuristic Method", In B.H.V. Topping, (Editor), "Proceedings of the Fifteenth UK Conference of the Association of Computational Mechanics in Engineering", Civil-Comp Press, Strilingshire, UK, Paper 59, 2007. doi:10.4203/ccp.85.59

2

A. Csébfalvi, "A nonlinear path-following method for computing the equilibrium curve of structures", Annals of operations research, 81, 15-23, 1998.

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