Novel Decomposition Methods for Reliability-Based Topology Optimization

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Topology optimization is a computational design framework to idealize materials distribution of complex engineering systems. Uncertainties, unavoidable in manufacturing process and operating environments, often plague those engineering systems, thus need be taken into account during the design process. Conventional deterministic design approaches typically lead to inefficient and overly conservative designs that overcompensate for uncertainties, or unknowingly risky designs due to the inherent uncertainties. This award supports fundamental research on topology optimization of complex engineering structures in the presence of uncertainty. Specifically, it will develop novel methods to determine the ideal material distribution of complex engineering systems with low probabilities of failure corresponding to some critical failure mechanisms. The methods and associated numerical tools will be applicable to a broad, multidisciplinary optimization methodology. The findings will promote growth in additive manufacturing, especially 3D-printing, which is able to manufacture products with complex topology and thus demands efficient topology design methods to bring out its full potential. Other engineering applications include durable design for energy harvest devices, fatigue-resistant design for civil and aerospace applications, and reliable design for green energy industry. The education impact consists of attracting, engaging, and training K-12 and undergraduate students through extensive dissemination and outreach programs. Technically, this research project aims to create new theoretical foundations and numerical algorithms for large-scale, robust topology optimization (RTO) and reliability-based topology optimization (RBTO) of complex engineering systems. Innovations include: (1) a new adaptive-sparse polynomial dimensional decomposition method designed for statistical moments and reliability analyses of ultra-high-dimensional, stochastic systems; (2) a new topology design sensitivity analysis for RTO and RBTO to enable concurrent evaluation of uncertainties and their design sensitivities; and (3) a new topology optimization algorithm integrating the level-set method for both fast convergence and clear geometry. In addition, proposed research will incorporate utility functions for developing new practical RBTO model for industrial applications. The project will deliver a novel, feasible paradigm-shifting advance toward solving large-scale topology optimization problems under uncertainty.