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Branch and Bound mixed nonlinear optimization for the GRP structure of Galápagos interisland small craft

Abstract:

The interisland transportation of passengers in Galápagos Archipelago is mainly carried out using high speed boats manufactured using Fiberglass Reinforced Plastic (GRP). The design of these small boats does not commonly follow advised construction standards and therefore it is possible that their structures are oversized. In addition, these boats navigate at high speeds and therefore it is advisable to investigate ways to reduce their weight. In this work, the structure of the central module of a 12-meter-long small interisland GRP craft traveling at 25 knots is optimized. Mixed Integer Nonlinear Programming (MINLP) is used for the optimization process, since the structural design contains both integer and real variables. These mixed problems can be solved applying the Branching and Bounding algorithm (BB). Due to the combination of variables, the Gekko optimization library, capable of solving MINLP problems through Python programming language, is used. The process is divided into two phases: the first phase optimizes the number of stiffeners and the laminate of the plates, and the second optimizes the dimensions and laminate of the stiffeners. The constraints of this structural optimization correspond to the requirements of the ISO 12215 standard for small craft: flexural strength of plates and stiffeners, inter-laminar resistance of plates, stiffness of stiffeners, and resistance to buckling of the web and flange of reinforcements. As a result of this structural optimization, the structural weight of the module is reduced by 20%. Finally, the results of the optimization process are evaluated using the finite element method, to compare the current and the optimized hull module. The structure is modelled with plane elements of composite laminated type material; end cross sections are considered as clamped. The load is applied with a half-wave distribution in the transversal direction, centered on the quarter of the beam, and at centreline of the bottom. It is verified that in the current design modules are oversized and that, in the case of the optimized section, stress levels do not exceed the permissible values.