<p dir="ltr">Multiscale topology optimization is a numerical method that enables the synthesis of hierarchical structures, offering greater design flexibility than single-scale topology optimization. However, this increased flexibility also incurs higher computational costs. Recent advancements have integrated machine learning models into MSTO methods to address this issue. Unfortunately, existing machine learning-based multiscale topology optimization (ML-MSTO) approaches underutilize the potential of machine learning models to surrogate the inner optimization, analysis, and numerical homogenization of arbitrary non-periodic microstructures. This dissertation presents an ML-MSTO method featuring displacement-driven topology-optimized microstructures (TOMs). The proposed method solves an outer optimization problem to design a homogenized macroscale structure and multiple inner optimization problems to obtain spatially distributed, non-periodic TOMs. The inner problem formulation employs the macroscale element densities and nodal displacements to define constraints and boundary conditions for microscale density-based topology optimization problems. Each problem yields a free-form TOM. To reduce computational costs, artificial neural networks (ANNs) are trained to predict their homogenized constitutive tensor. The ANNs also enable sensitivity coefficients to be approximated through a variety of standard derivative methods. The effect of the neural network-based derivative methods on topology optimization results is evaluated in a comparative study. An explicit dehomogenization approach is proposed, leveraging the TOMs of the ML-MSTO method. The explicit approach also features two post-processing schemes to improve the connectivity and clean the final multiscale structure. A 2D and a 3D case study are designed with the ML-MSTO method and dehomogenized with the explicit approach. The resulting multiscale structures are non-periodic with free-form microstructures. In addition, a second implicit dehomogenization approach is developed in this dissertation that allows the projection of homogenized mechanical property fields onto a discrete lattice structure of arbitrary shape. The implicit approach is capable of dehomogenizing any homogenized design. This is done by incorporating an optimization algorithm to find the lattice thickness distribution that minimizes the difference between a local target homogenized property and a corresponding lattice homogenized stiffness tensor. The result is a well-connected, functionally graded lattice structure, that enables control over the length scale, orientation, and complexity of the final microstructured design.</p>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/24723783 |
| Date | 05 December 2023 |
| Creators | Joel Christian Najmon (17548431) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Machine_Learning-based_Multiscale_Topology_Optimization/24723783 |
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