Shape Optimization of Cover Plates for Retractable Roof Structures

Department of Engineering, University of Cambridge Trumpington Street, Cambridge CB2 1PZ, U.K. Abstract The optimal shape of cover plates for circular, symmetric retractable roof structures based on a grid of multi-angulated rods connected by revolute joints is considered. It is assumed that these cover plates are co-planar, and hence they are not allowed to overlap in any configuration; they are also required to form a gap free surface in the closed configuration. Suitable shapes for the plates are found by formulating an optimization problem based on suitably defined overlap and gap area functions. The size of the hinges of the bar structure is considered in the optimization. To stabilize the optimization convergence various move limit strategies are tested and a min-max formulation is proposed. The optimization problems are solved by the method of moving asymptotes and the sensitivities are found by finite differences. A series of test cases are presented, whose results agree with previously known solutions, however the generality of the present method makes it suitable to develop structures of general shape. ∗Current address: Risø National Laboratory, Wind Energy Department, Building VEA-118, P.O. Box 49, Frederiksborgvej 399, DK-4000 Roskilde, Denmark. †Corresponding author: [email protected]