Reduced-order shape optimization using offset surfaces

Abstract

constant inner o set empty: unstable lled: unstable optimized inner o set empty: stable lled: unstable optimized inner & outer o set empty: stable lled: stable original model © http://www.modelplusmodel.com Figure 1: We introduce a method for reduced-order shape optimization of 2-manifolds that uses offset surfaces to deform the shape. Left: a bottle model is generated using offset surfaces with constant offsets. The resulting object is unable to stand. Center: the offsets are optimized such that the bottle can stand if empty, however, if filled it is unstable. Right: the model is optimized to stand both empty and filled. In order to account for that, offset surfaces are added inside and outside of the original shape. AbstractGiven the 2-manifold surface of a 3d object, we propose a novel method for the computation of an offset surface with varying thickness such that the solid volume between the surface and its offset satisfies a set of prescribed constraints and at the same time minimizes a given objective functional. Since the constraints as well as the objective functional can easily be adjusted to specific application requirements, our method provides a flexible and powerful tool for shape optimization. We use manifold harmonics to derive a reduced-order formulation of the optimization problem, which guarantees a smooth offset surface and speeds up the computation independently from the input mesh resolution without affecting the quality of the result. The constrained optimization problem can be solved in a numerically robust manner with commodity solvers. Furthermore, the method allows simultaneously optimizing an inner and an outer offset in order to increase the degrees of freedom. We demonstrate our method in a number of examples where we control the physical mass properties of rigid objects for the purpose of 3d printing.

Cross section-based hollowing and structural enhancement

“…Some of them attempt to design mechanical toy and automata [45,4], articulated models [1,28], external supporting structures [25,7,30]. The other algorithms are proposed to improve printing efficiency [31,34] and quality [10,37], shape details enhancement [21], and dynamic stability [2,18,19,33]. In contrast, our work is proposed to reduce the material cost, fix the structural weak regions, and optimize static stability of the object.…”

“…Although the volume of the model is optimized in their method, they also do not consider the structural strength of the model. Musialski et al [18,19] propose shape optimization frameworks, which can achieve both static and dynamic stability. Although [19] takes into account structural strength in shape optimization, it is difficult for them to handle structural weak regions.…”

“…However, it is difficult for them to control the volume and maintain the strength of the model. Musialski et al [18] propose a shape optimization framework to meet different goals. For static stability, their goal is to minimize the distance between c ⊥g and c(CH).…”

“…But their algorithm cannot minimize the printing material cost. Moreover, [23] and [18] do not consider the structural strength of the model. In addition, they sometimes may even hollow the structural weak regions, because their methods cannot distinguish between structural weak and strong regions.…”

“…Fig. 9 and 10 show the comparison results with [23] and [18], respectively. To be fair, the projected mass centers are optimized to the same positions as that in [23] and [18].…”