Multi-lattice Topology Optimization with Lattice Representation Learned by Generative Models
Multi-lattice Topology Optimization with Lattice Representation Learned by Generative Models
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This work was made possible by the prior works "Smooth Like Butter: Evaluating Multi-lattice Transitions in Property-Augmented Latent Spaces" and "Smoothing the Rough Edges: Evaluating Automatically Generated Multi-Lattice Transitions".
Abstract:
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, surpassing the advancements in computational methods for design optimization.
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.
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Smooth Like Butter: Evaluating Multi-lattice Transitions in Property-Augmented Latent Spaces
Smooth Like Butter: Evaluating Multi-lattice Transitions in Property-Augmented Latent Spaces
This work expands on the the analysis in "Smoothing the Rough Edges: Evaluating Automatically Generated Multi-Lattice Transitions".
Abstract:
Abstract:
Additive manufacturing has revolutionized structural optimization by enhancing component strength and reducing material requirements. One approach used to achieve these improvements is the application of multi-lattice structures, where the macro-scale performance relies on the detailed design of mesostructural lattice elements. Many current approaches to designing such structures use data-driven design to generate multi-lattice transition regions, making use of machine learning models that are informed solely by the geometry of the mesostructures. However, it remains unclear if the integration of mechanical properties into the dataset used to train such machine learning models would be beneficial beyond using geometric data alone. To address this issue, this work implements and evaluates a hybrid geometry/property Variational Autoencoder (VAE) for generating multi-lattice transition regions. In our study, we found that hybrid VAEs demonstrate enhanced performance in maintaining stiffness continuity through transition regions, indicating their suitability for design tasks requiring smooth mechanical properties.
Read the full work here.
Smoothing the Rough Edges: Evaluating Automatically Generated Multi-Lattice Transitions
Smoothing the Rough Edges: Evaluating Automatically Generated Multi-Lattice Transitions
This work expands on the the analysis in "A Data-Driven Approach for Multi-Topology Lattice Transitions".
Abstract:
Abstract:
Additive manufacturing is advantageous for producing lightweight components while addressing complex design requirements. This capability has been bolstered by the introduction of unit lattice cells and the gradation of those cells. In cases where loading varies throughout a part, it may be beneficial to use multiple, distinct lattice cell types, resulting in multi-lattice structures. In such structures, abrupt transitions between unit cell topologies may cause stress concentrations, making the boundary between unit cell types a primary failure point. Thus, these regions require careful design in order to ensure the overall functionality of the part. Although computational design approaches have been proposed, smooth transition regions are still difficult to achieve, especially between lattices of drastically different topologies. This work demonstrates and assesses a method for using variational autoencoders to automate the creation of transitional lattice cells, examining the factors that contribute to smooth transitions. Through computational experimentation, it was found that the smoothness of transition regions was strongly predicted by how closely the endpoints were in the latent space, whereas the number of transition intervals was not a sole predictor.
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AddLat2D the 2D Lattice Generator
AddLat2D the 2D Lattice Generator
Abstract:
Abstract:
This work addresses the challenges of acquiring additive manufacturing data, given the complexities and design possibilities of such structures. Researchers in additive manufacturing struggle with scarcity and unsuitability of 2D datasets which pose further difficulties. To overcome these concerns, this research presents an application, AddLat2D, for generating 2D lattice structure datasets tailored to user specifications. Building upon a previous version of the application (Baldwin et al., 2023, 2022), this work highlights our development and usage of AddLat2D to generate datasets that have custom image size and pixel intensity values.
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A Data-Driven Approach for Multi-Topology Lattice Transitions
A Data-Driven Approach for Multi-Topology Lattice Transitions
This work explores the relationships that exist in the latent space of a variational autoencoder trained on synthetic unit cells. The goal was to learn how traveling through the latent space affects the performance of the transition regions.
Through computational experimentation, it was found that the smoothness of transition regions was higher when the endpoints were located closer together in the latent space.
Abstract:
Abstract:
Additive manufacturing is advantageous for producing lightweight components while maintaining function and form. This ability has been bolstered by the introduction of unit lattice cells and the gradation of those cells. In cases where loading varies throughout a part, it may be necessary to use multiple lattice cell types, also known as multi-lattice structures. In such structures, abrupt transitions between geometries may cause stress concentrations, making the boundary a primary failure point; thus, transition regions should be created between each lattice cell type. Although computational approaches have been proposed, smooth transition regions are still difficult to intuit and design, especially between lattices of drastically different geometries. This work demonstrates and assesses a method for using variational autoencoders to automate the creation of transitional lattice cells. In particular, the work focuses on identifying the relationships that exist within the latent space produced by the variational autoencoder. Through computational experimentation, it was found that the smoothness of transition regions was higher when the endpoints were located closer together in the latent space.
Read the full work here.
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