Structural optimisation of axisymmetric and prismatic shells and folded plates

Abstract

This paper deals with the development and application of reliable, creative and efficient computational tools for the structural optimisation of variable thickness axisymmetric and prismatic shells and folded plates using computer-aided analysis and design procedure. The problem of finding optimal forms and thickness variations for such structures is solved by integrating computer aided geometry modelling tools, automatic mesh generation, structural analysis, sensitivity evaluation and mathematical programming methods. The shape and thickness variation of the structures are defined using parametric cubic splines and the structural analysis is carried out with either finite element or finite strip methods in which Mindlin-Reissner assumptions are adopted. In static situations, the composition of the strain energy is monitored during the optimisation process to obtain insight into the energy distribution for the optimum structures. This allows us to demonstrate that, in the majority of cases, the optimum shells are membrane energy dominated as might be expected. For the vibrating structures, the mode shapes of the initial and optimum solutions are presented. A set of carefully defined, unambiguous benchmark examples is presented and studied with independent verification to test the various features of the structural optimisation process.