
Structural Optimization of Lattice Structures Using Neural Networks for Geometry Representation
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Lattice structures consist of repeated, similarly shaped unit cells and are commonly found in modern engineering applications such as crash structures, acoustic components, or energy-efficient thermal applications. However, the design, analysis and optimization of such structures is still subject of current research. In this presentation we want to show how neural networks can be used to represent the geometry of the individual cells and how this enables an efficient optimization of spatially graded lattice structures. Unlike other lattice structure optimization methods, we neither assume a large separation of scale nor periodicity. Instead, we perform a full-scale finite element analysis (FEA) at each optimization step, which requires a large number of elements. Traditional topology optimization methods, such as SIMP, are not suitable because the large number of design parameters requires too many costly forward simulations. One approach to reduce the number of design parameters is to rely on shape optimization and define a parametrized unit cell using explicit geometrical representations, e.g. [1]. However, only a comparatively small set of geometries can be represented and finding a parametrization for complex geometries is not straight forward, especially if topological changes are desired. Instead, in our optimization approach, we employ the DeepSDF [2] method, where a continuous and low-dimensional latent space is introduced to encode the geometric information. Since each single unit cell is characterized by a different latent vector, a spatially graded lattice structure can subsequently be created by continuously varying the latent vector over the structure. A differentiable extension of the dual contouring algorithm [3] is used to transform the implicit representation to a computational mesh, which enables gradient based optimization. [1] Zwar, J., Elber, G. & Elgeti, S. Shape Optimization for Temperature Regulation in Extrusion Dies Using Microstructures. Journal of Mechanical Design 145, (2022). [2] Park, J. J., Florence, P., Straub, J., Newcombe, R. & Lovegrove, S. DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition 165–174 (2019). [3] Shen, T. et al. Flexible Isosurface Extraction for Gradient-Based Mesh Optimization. ACM Trans. Graph. 42, 1–16 (2023).