Combined shape and topology optimisation of shell structures using FE-based parameterisations

Studies that optimise both the shape and topology of shell structures typically utilise CAD parametrisations to describe the geometry of the shell and density-based methods to characterise its material layout. Relying on CAD-based approaches has the advantage that only a few design variables, usually the control points of the surface, are included in the shape optimisation problem, thereby resulting in fast optimal shell geometries. This approach, however, requires a CAD description of the shell surface that must be updated continuously and, depending on the number of shape parameters, the set of possible designs is in many cases very small. To combine the optimisation of the shell topology and shape, in this work we integrate a density-based method to find the optimal topology with a node-based method to find the optimal shape. Because of a larger design space, a node-based approach offers much greater freedom in realisable geometries. Further, since both the density-based and node-based methods exclusively rely on information from the finite element models, the proposed approach is easy to integrate into existing finite element software. We find that when comparing sequential workflows—where the shape and topology optimisation problems are performed in independent, consecutive steps—to a concurrent scheme where the shape and the topology are optimised simultaneously, the lowest cost function is generally achieved by the concurrent workflow. Moreover, because node-based shape optimisation involves highly non-convex cost functions, we observe that the different workflows converge to notably different geometries and topologies.