Analysis and shape optimisation of variable thickness prismatic folded plates and curved shells — Part 2: Shape optimisation

This paper deals with the development of computational tools for structural shape optimisation of shells and folded plates in which the strain energy or the weight of the structure is minimised subject to certain constraints. Both thickness and shape variables defining the cross-section of the structure are considered. The analysis is carried out using curved, variable thickness finite strips formulated and tested in Part 1 of this paper. Optimal shapes are presented for several shells and folded plates of variable thickness including plates on elastic foundation. The changes in the relative contributions of the bending, membrane and shear strain energies are monitored during the whole process of optimisation. The tools developed in the present work can be used as an aid to structural engineers in designing novel forms for shells and folded plates and provide valuable insight into the structural behaviour. It is concluded that the finite strip method offers an accurate and inexpensive tool for the optimisation of a wide class of structures having regular prismatic-type geometry with diaphragm ends.