7. Optimal Design of Dome-Shaped Trusses

Domes are one of the oldest and well-established structural forms and have been used in architecture since the earliest times. These structures are of special interest to engineers as they enclose large spaces with small surfaces and have proven to be very economical in terms of consumption of constructional materials. The main aim of this chapter is frequency constraint optimization of dome truss structures; however, all the domes are also optimized considering strength, stability, and displacement constraints. Structural optimization considering natural frequency constraints is believed to represent nonlinear and non-convex search spaces with several local optima. In this class of problems, large generalized eigenproblems should be solved in order to find the natural frequencies of the structure. The size of the structure affects the dimensions of the matrices involved and thus the required computational time and effort. On the other hand, as the number of optimization variables increases, more and more structural analyses are needed to be performed in order to reach a near-optimal solution.