Generative model of three-dimensional shapes incorporating structural mechanics

Abstract

We propose a deep generative model for 3D shapes that incorporates structural mechanics parameters, and a dataset of 6667 shapes created by topology optimization. Our model is based on DeepSDF, a decoder-type neural network that implicitly represents shapes as signed distance functions (SDFs). We extend DeepSDF to condition the shape generation on structural mechanics parameters, such as strain energy, load direction, volume, and dimension. We also introduce positional encoding to improve the spatial resolution of the model. Our dataset consists of various 3D shapes computed by a linear topology optimization method using the Building-Cube method. We use the strain energy as a quantitative indicator of the structural performance of the shapes. We train our model on the dataset and evaluate its ability to generate 3D shapes reflecting structural mechanics parameters. Our results indicate that our model can produce 3D shapes with high fidelity and diversity, and achieve an average reconstruction accuracy of 88.8% for the test shapes. Our model and dataset open up new possibilities for 3D shape generation and structural design using deep learning.