Minimum material vault designs generated via adaptive layout optimization

Vaults are commonly used to form lightweight long-span roof structures, allowing flexible internal spaces with minimal associated embodied carbon. The precise shape of the vault should be chosen to reduce or eliminate bending effects, so as to promote more-efficient structures that work in pure compression. Many existing form-finding methods can identify bending-free designs; however, these are restricted to operate on predefined layouts and therefore cannot generally achieve optimal material-efficiency. This paper presents a new family of form-finding methods employing the numerical layout optimization method, which uses the ‘ground structure’ approach to simultaneously optimize a vault’s form and force flow topology. A conic programming problem is formulated, enabling the attainment of globally-optimal minimum-volume designs for any given nodal discretization. The formulation is newly presented from an accessible engineering perspective, building upon the standard truss layout optimization method to provide an explainable and flexible framework for future research within the community. To enhance computational efficiency, an adaptive ‘member adding’ technique is employed, enabling the solution of large-scale problems while also allowing rapid exploration of smaller-scale scenarios for more practical vault designs. The proposed method is applied to a range of examples, demonstrating the ability of the proposed procedure to generate more materially efficient vault designs, compared to traditional Force Density Method (FDM) designs.