Topology optimisation method applied to fabrication of developable ship hulls

Abstract

The topology optimisation methodology is extended to problems that find the optimal load distribution for the fabrication of developable ship hulls, using the same methodology with different design variables of load distribution, to obtain the desired deformed shapes. The ship hulls made of fibreglass reinforced plastic (FRP) can be fabricated by assembling the planar patches that are most suitable for three-dimensional geometry of the ship hulls. To reduce the difference between the assembly and the real geometry, appropriate loads are applied during the fabrication process. The objective of this paper is to find minimal loading area and magnitude to make the assembly as close to the real geometry as possible. For the linear elastic systems, based on the principle of superposition, there are many ways of applying the loads to obtain the desired deformed shape. The topology optimisation method provides a very good tool to find an optimal load distribution that has a minimal loading area and magnitude, yielding the desired deformed shape. A continuum-based design sensitivity analysis (DSA) method for non-shape problems is developed for linearly elastic structural systems. The non-shape problem is characterised by the design variables that are not associated with the domain of the system like sizing, material property, loading, and so on. The first-order variations of energy form, load form, and structural responses with respect to the non-shape design variables are derived. The adjoint variable method is used for more efficient computation than the direct differentiation method. The Mindlin plate element is selected to discretise the structural domain. For numerical implementation, the finite element analysis method, the developed design sensitivity analysis method, and a gradient-based optimisation method are integrated into a unified and automated framework. Several numerical examples show very good agreement with intuitive designs.