Lightweight structure design under force location uncertainty

Abstract

Fig. 1. We present a method for lightweight structure design for scenarios where external forces may contact an object at a multitude of locations that are unknown a priori. For a given surface mesh (grey), we design the interior material distribution such that the final object can withstand all external force combinations capped by a budget. The red volume represents the carved out material, while the remaining solid is shown in clear. Notice the dark material concentration on the fragile regions of the optimum result in the backlit image. The cut-out shows the corresponding interior structure of the 3D printed optimum.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 con guration capped by the budget. Our approach works by repeatedly nding the most critical force con guration and altering the internal structure accordingly. A key issue, however, is that the critical force con guration changes as the structure evolves, resulting in a signi cant computational challenge. To address this, we propose an e cient 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.

Structural Design Using Laplacian Shells

“…Comparison of structures generated by Lu et al [LSZ*14], Ulu et al [UMK17] and our method. Our optimization approach produces a lighter structure that has only one connected cavity inside while sustaining any possible force applied on the boundary.…”

“…For scenarios where uncertainty in force contact location is large and cannot be described parametrically, Ulu et al . [UMK17] present a data‐driven technique to predict the stress distribution for each possible force configuration and determine the one that creates the highest stress within the shape. Wang et al .…”

“…For problems with force location uncertainties, we adopt a similar approach to [UMK17] in estimating the maximum stress distribution σ ∈ ℝ nv and σ cr . We perform FEAs for only a small number of force configurations and use them to construct a mapping between the nodal forces and the resulting stress distributions and estimate the stress distributions for the remaining force configurations.…”

“…Note that computed σ here is only an approximation of the actual values, thus cannot be used directly to obtain σ cr . We adopt the hierarchical search approach described in [UMK17] to compute σ cr accurately and guarantee the structural soundness of the resulting shell under prescribed force location uncertainties.…”

“…This capability enables each step of the shape optimization to perform FEAs without requiring costly resmeshing operations. Our approach addresses classical structural design problems with fixed and known external forces [ACS*11] as well as the more general class of problems ranging from multiple external force cases [JHM09] to force location uncertainties [UMK17]. Driven by a gradient‐free optimization algorithm, our method provides a practical solution for designing robust hollow structures with a single inner cavity while preserving the appearance of the input model.…”