Abstract We introduce a method to design lightweight shell objects that are structurally robust under the external forces they may experience during use. Given an input 3D model and a general description of the external forces, our algorithm generates a structurally‐sound minimum weight shell object. Our approach works by altering the local shell thickness repeatedly based on the stresses that develop inside the object. A key issue in shell design is that large thickness values might result in self‐intersections on the inner boundary creating a significant computational challenge during optimization. To address this, we propose a shape parametrization based on the solution to the Laplace's equation that guarantees smooth and intersection‐free shell boundaries. Combined with our gradient‐free optimization algorithm, our method provides a practical solution to the structural design of hollow objects with a single inner cavity. We demonstrate our method on a variety of problems with arbitrary 3D models under complex force configurations and validate its performance with physical experiments.

We introduce a lightweight structure optimization approach for problems in which there is uncertainty in the force locations. Such uncertainty may arise due to force contact locations that change during use or are simply unknown a priori. Given an input 3D model, regions on its boundary where arbitrary normal forces may make contact, and a total force-magnitude budget, our algorithm generates a minimum weight 3D structure that withstands any force configuration capped by the budget. Our approach works by repeatedly finding the most critical force configuration and altering the internal structure accordingly. A key issue, however, is that the critical force configuration changes as the structure evolves, resulting in a significant computational challenge. To address this, we propose an efficient critical instant analysis approach. Combined with a reduced order formulation, our method provides a practical solution to the structural optimization problem. We demonstrate our method on a variety of models and validate it with mechanical tests.