Topology Design Optimization and Data-aided Analysis by Physics Informed Neural Networks for Additive Manufactured Structure

Abstract

This dissertation addresses methodologies for the design and analysis related to additive manufacturing. First, the design methodology is proposed to optimize the structural shape for stiffness maximization, and to generate the CAD file for its additive manufacturing. Specifically, open-source MATLAB code is developed for topology optimization of three-dimensional arbitrary design domains. In addition, the post-processing procedure is built to generate STL format file for the additive manufacturing of topology optimization result. The developed program enables the practical design process, which includes the loading of three-dimensional CAD file for setting the design domain, topology design optimization, and the additive manufacturing of design result. The effectiveness of the developed code is validated through various design examples, including a simply supported beam, a bridge, and an airplane bearing bracket. Subsequently, the data-aided analysis methodology is developed, which aims to reconcile the discrepancies between the analysis results by Computer-Aided Engineering (CAE), and the actual behavior of additive manufactured structures. Here, the discrepancies come from uncertainty in additive manufacturing processes. To overcome this problem, the distribution of material properties is included as the additional state variable, and the measured physical variables are added as the data. To treat material property as unknown variable and contain the data in the structural analysis, the physics-informed neural networks (PINNs) are utilized in this dissertation. For the stable analysis of additive manufactured structure with complex shapes, energy functional targeting loss function is proposed, and its effectiveness is validated by comparing with the result of existing PINN loss functions. In addition, the effect of data, i.e. data type among displacement and strain, and data domains, on the analysis result is investigated how to improve the accuracy of data-aided analysis results. The limitation of this work is as follows. The developed code for topology design optimization contains inaccuracies in geometry representation due to the use of an external, and discrepancies between the CAE model and the actual structure caused using isotropic properties of materials. The proposed data-aided analysis treats simplified two-dimensional geometries, and utilizes virtual data instead of the actual measured data of addictive manufactured structure.