Structurally optimized shells

Abstract

Shells, i.e., objects made of a thin layer of material following a surface, are among the most common structures in use. They are highly efficient, in terms of material required to maintain strength, but also prone to deformation and failure. We introduce an efficient method for reinforcing shells, that is, adding material to the shell to increase its resilience to external loads. Our goal is to produce a reinforcement structure of minimal weight. It has been demonstrated that optimal reinforcement structures may be qualitatively different, depending on external loads and surface shape. In some cases, it naturally consists of discrete protruding ribs; in other cases, a smooth shell thickness variation allows to save more material. Most previously proposed solutions, starting from classical Michell trusses, are not able to handle a full range of shells (e.g., are restricted to self-supporting structures) or are unable to reproduce this range of behaviors, resulting in suboptimal structures. We propose a new method that works for any input surface with any load configurations, taking into account both in-plane (tensile/compression) and out-of-plane (bending) forces. By using a more precise volume model, we are capable of producing optimized structures with the full range of qualitative behaviors. Our method includes new algorithms for determining the layout of reinforcement structure elements, and an efficient algorithm to optimize their shape, minimizing a non-linear non-convex functional at a fraction of the cost and with better optimality compared to standard solvers. We demonstrate the optimization results for a variety of shapes, and the improvements it yields in the strength of 3D-printed objects.