Multi-Lattice Topology Optimization With Lattice Representation Learned by Generative Models

Abstract Additive manufacturing (AM) technologies are often capable of fabricating geometries that are more complex than traditional manufacturing methods. A notable innovation enabled by AM is the fabrication of multi-lattice structures, an advanced design concept featuring an array of heterogeneous lattices in the mesoscale that are arranged to achieve a diverse distribution of material properties at the macroscale. Compared to uniform lattice structures, multi-lattice structures permit greater design freedom and a larger design space, which makes it possible to achieve superior structure performance. However, the expanded design space introduces a substantial increase in the complexity of multi-lattice structure design. There is still lack of an optimization framework that can maximize the physical properties of the macro-structures through fully exploiting lattice diversity while ensuring lattice connectivity. To solve these challenges, this paper introduces a multi-scale topology optimization (TO) framework for multi-lattice structures which simultaneously optimizes the structure topology at macroscale and the lattice heterogeneity at mesoscale. The distribution of the pseudo-densities and lattice parameters are represented by neural networks (NNs) whose weights and biases are the design variables. The spatial gradients of NN over the physical domain reflect the dissimilarity of adjacent lattices. So, the connection between the lattices can be implicitly constrained by restricting the spatial gradients of NNs. The diversity of the lattices is guaranteed through a generative lattice model which is trained over a large lattice dataset and is embedded into the optimization framework. The performances of various NN types are compared, and we found that Fourier Neural Operators (FNOs) have the best flexibility in balancing the lattice diversity and local connectivity. In the design problems of structural compliance minimization under complex loading conditions, our results show that the multi-lattice TO structures achieve a higher stiffness-to-weight ratio than normal TO structures.