Minimum Mass Cast Glass Structures Under Performance and Manufacturability Constraints

Abstract

This work develops a computational method that produces algorithmically generated design forms, able to overcome inherent challenges related to the use of cast glass for the creation of monolithic structural components with light permeability. Structural Topology Optimization (TO) has a novel applicability potential, as decreased mass is associated with shorter annealing times and, thus, considerably improved manufacturability in terms of time, energy, and cost efficiency. However, realistic TO in such structures is currently hindered by existing mathematical formulations and commercial software capabilities. Incorporating annealing constraints into the optimization problem is an essential feature that needs to be accommodated, whereas the brittle nature of glass invokes asymmetric stress failure criteria that cannot be captured by conventional ductile plasticity surfaces or uniform stress constraints. This paper addresses the approximation problems in the evaluation of principal stresses while concurrently incorporating annealing-related manufacturing constraints into a unified TO formulation. A mass minimization objective is articulated, as this is the most critical factor for cast glass structures. To ensure the structural integrity and manufacturability of the component, the applied constraints refer both to the glass material/structural properties and to criteria that ensue from the annealing and fabrication processes. The developed code is based on the penalized artificial density interpolation scheme and the optimization problem is solved with the interior-point method. The proposed formulation is applied in a planar design domain to explore how different glass compositions and structural design strategies affect the final shape. Upon extraction of the optimized shape, the structural performance of the respective 3D structures is validated with respect to performance constraint violations using the Ansys software. Finally, brief guidelines on the practical aspects of the manufacturing process are provided.