Stochastic structural analysis for context-aware design and fabrication

Abstract

In this paper we propose failure probabilities as a semantically and mechanically meaningful measure of object fragility. We present a stochastic finite element method which exploits fast rigid body simulation and reduced-space approaches to compute spatially varying failure probabilities. We use an explicit rigid body simulation to emulate the real-world loading conditions an object might experience, including persistent and transient frictional contact, while allowing us to combine several such scenarios together. Thus, our estimates better reflect real-world failure modes than previous methods. We validate our results using a series of real-world tests. Finally, we show how to embed failure probabilities into a stress constrained topology optimization which we use to design objects such as weight bearing brackets and robust 3D printable objects.

Design and Optimization of Conforming Lattice Structures

“…Stava et al proposed a method to detect and correct structural defects [23]. Recent efforts include worst-case structural analysis [24], [25], and stochastic structural analysis [26]. Chen et al proposed a solver for inverse elastic shape design [27].…”

Structural Design Using Laplacian Shells

“…Langlois et al . [LSD*16] present a stochastic finite element model to predict the failure probabilities of objects under scenarios where the loading is stochastic in nature (such as dropping and collisions). For problems with uncertainties in load direction and location spanning a small subspace, Schumacher et al .…”

“…As additively manufactured (AM) parts find their way into industrial applications as functional components, lightweighting and structural optimization methods have become prevalent in shape design [WWY*13; LSZ*14; CBN*15; LSD*16; ZKWG16]. In many such methods, the resulting shape usually contains complex internal structures, even for very simple loading configurations.…”

Efficient Load Sampling for Worst-Case Structural Analysis Under Force Location Uncertainty

“…However, it is limited to simple geometries, making it unsuitable for our purposes. For complex geometries, Langlois et al [8] use contact force samples generated by rigid body simulations to predict failure modes of objects in real world use. However, their method is applicable to scenarios where loading is stochastic in nature (such as dropping and collisions) and it is not practical for deterministic scenarios where possible force configurations are known and no failure is tolerated for any of them.…”