IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures
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by
Jun Wang, Wei Wayne Chen, Daicong Da, Mark Fuge, Rahul Rai
2022
Abstract
Variable-density cellular structures can overcome connectivity and
manufacturability issues of topologically optimized structures, particularly
those represented as discrete density maps. However, the optimization of such
cellular structures is challenging due to the multiscale design problem. Past
work addressing this problem generally either only optimizes the volume
fraction of single-type unit cells but ignoring the effects of unit cell
geometry on properties, or considers the geometry-property relation but builds
this relation via heuristics. In contrast, we propose a simple yet more
principled way to accurately model the property to geometry mapping using a
conditional deep generative model, named Inverse Homogenization Generative
Adversarial Network (IH-GAN). It learns the conditional distribution of unit
cell geometries given properties and can realize the one-to-many mapping from
geometry to properties. We further reduce the complexity of IH-GAN by using the
implicit function parameterization to represent unit cell geometries. Results
show that our method can 1) generate various unit cells that satisfy given
material properties with high accuracy (relative error <5%) and 2) improve the
optimized structural performance over the conventional topology-optimized
variable-density structure. Specifically, in the minimum compliance example,
our IH-GAN generated structure achieves an 84.4% reduction in concentrated
stress and an extra 7% reduction in displacement. In the target deformation
examples, our IH-GAN generated structure reduces the target matching error by
24.2% and 44.4% for two test cases, respectively. We also demonstrated that the
connectivity issue for multi-type unit cells can be solved by transition layer
blending.
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