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Sizing and topology optimization are the two main structural optimization tools in a wide range of applications in aerospace, mechanical, and design. An iterative process solves the sizing optimization using classical gradient-based methods, usually carried out with an integrated process including a full-scale finite element analysis (FEA) to evaluate the design performance and a gradient search step at each iteration. With a complex real-world model, the optimization process is extremely cumbersome, time-consuming, and with no guarantee for an optimal solution or design. Alternatively, global population-based methods, such as genetic algorithm and particle swarm, can achieve the global optimal design with many simulations for every iteration to evaluate different designs for searching for the best candidates. This tremendous computational effort for simulations at each iteration prevents the global method from optimizing with complex physics simulation models. As for topology optimization, state-of-the-art methods, such as the Solid Isotropic Material with Penalty (SIMP) method, uses hand-coded gradient functions for optimization and must be run repeatedly for different boundary and loading conditions. Several practical and efficient machine-learning-based data-driven approaches have been proposed to optimize structures instantaneously using the generative adversarial network. Nevertheless, a complex machine learning model is costly because of the large amount of data and long training time.This dissertation presents several new, rapid, and accurate optimal design approaches for improving current structural sizing and topology optimization methods. First, for sizing optimization, to reduce the optimization time while preserving global optimality, a new optimization framework with response surface method and global sensitivity method is presented to approximate the simulation model with high accuracy while using a minimum number of simulations. The response surface approximates the original physics model using a mathematical basis, which reduces the time for function evaluation significantly. Global sensitivity analysis is conducted to reduce the model dimension and further reduce the number of function evaluations. A novel vehicle subframe compliance optimization framework is proposed using a response surface. The response surfaces approximate vehicle dynamic performance from multi-body dynamic simulation and subframe structure compliance from finite element analysis. It is shown that the mass of the subframe is reduced without violating the vehicle performance constraints. A physics-informed deep neural network for the structural topology optimization process is proposed in the second part of the dissertation. The deep neural network is trained with a built-in finite element model. The finite element model is made to be fully differentiable, and with the help of automatic differentiation, the gradient of the finite element model can be backpropagated to adjust the weights of the neural network. It is shown that the neural network can quickly learn the optimized structure without using much training data. Furthermore, no hand-code adjoint/gradient equations are required since the neural network can be trained to generate optimal structures based on the gradient information directly from the finite element model via automatic differentiation. The benefits of this physics-informed deep learning approach provide a data-efficient training process to construct a generator neural network to learn optimized topology under different design target conditions. |
