Global minimum cost design of a welded square stiffened plate supported at four corners

This paper presents the application of a refined version of the original Snyman–Fatti (SF) global continuous optimization algorithm (Snyman and Fatti, J Optimiz Theory Appl 54:121–141, 1987) to the optimal design of welded square stiffened plates. In particular we investigate square plates of square symmetry subjected to uniformly distributed normal static loads, supported at four corners, and stiffened by a square symmetrical orthogonal grid of ribs. Halved rolled I-section stiffeners are used welded to the base plate by double fillet welds. Profiles of different size are used for internal and edge stiffeners. A cost calculation method, developed by the first two authors and mainly used for welded structures (Farkas and Jármai 2003), allows for the computation of cost for different proposed designs of the welded stiffened plates. The cost function includes material, welding as well as painting costs, and is formulated according to the fabrication sequence. Design variables include base plate thickness as well as the dimensions of the edge and internal stiffeners. Constraints on stress in the base plate and in stiffeners, as well as on deflection of edge stiffeners and of internal stiffeners are considered. For this purpose the Snyman–Fatti (SF) global unconstrained trajectory method is adapted to handle constraints of this type. For control purposes a particle swarm optimization (PSO) algorithm is also applied to confirm the results given by the SF algorithm. Since the torsional stiffness of open section stiffeners is very small, the stiffened plates are modelled as a torsionless gridwork. We present an algorithm for calculating the moments and deflections for torsionless gridworks with different number of internal stiffeners, using the force method.