(Advisor: Prof. Graeme J. Kennedy)
"A Scalable GPU-accelerated Structural Topology Optimization Framework for Nonlinear Multiphysics"
Monday, September 26
Montgomery Knight Building 317
Established in 1988, structural topology optimization has become a promising research area in both academia and industry with fruitful applications such as in aerospace, mechanical, construction, and automotive. Prospects of structural topology optimization come along with the potential to design efficient and performant material layouts for systems governed by complex physics with inherent nonlinearity, for which designing desirable configurations with engineering intuition is not enough. Another thrust of structural topology optimization research comes from the maturity of additive manufacturing, which makes it possible to fabricate novel structural configurations that are not fabricable with conventional manufacturing techniques.
Structural topology optimization, on the other hand, can hardly be considered maturely practical for the following reasons. First, a great amount of the current studies has focused on linearized problems, e.g. linear elasticity, under the strong assumption of small-deformation which may fail in multiple circumstances. For example, nonlinearity must be taken into account if material and structure are under extreme loading conditions, or if crashworthiness and energy absorption need to be considered. Moreover, for aerospace applications where slender, lightweight structures are ubiquitous, buckling failure remains a critical design consideration, for which the linear analysis would lead to over-simplified and inappropriate results. Second, apart from the appropriate disciplinary modeling, computation serves as another major challenge. As for now, the largest structural topology optimization result in literature is an optimized inner structure of the wing of a Boeing-777-like aircraft with 1.1 billion finite elements computed on 8000 CPUs for up to 5 days. However, even for such a refined mesh, the relative resolution still does not reach the resolution capability of current metallic additive manufacturing techniques. Lastly, the effectiveness and robustness of optimization algorithms remain crucial. Within the community, the Method of Moving Asymptotes (MMA) has become the de facto optimizer for solving structural optimization problems. Recent benchmark studies, however, report that other nonlinear programming techniques such as Sequential Quadratic Programming (SQP) methods can outperform MMA for various topology optimization problems, demonstrating the potential of such methods as well as other nonlinear programming algorithms well-established in other domains. This opens the questions such as how optimization algorithms should be selected for different problem formulations, and more importantly, whether can one further improve the optimization performance by utilizing special structures for specific problem formulations.
Based on the observations above, this dissertation aims to contribute to both topology-specific optimization algorithms and high-fidelity physical simulation implementations. For the first part, A quasi-Newton correction technique is proposed that is compatible with second-order optimizers employing a quasi-Newton approximation scheme. Superiority and scalability are demonstrated based on linear compliance and natural frequency problems. For the second part, an integrated computational framework is under development that aims to be capable of performing topology optimization considering both geometric and material nonlinearity, and performing numerical experiments on a very large scale by utilizing both intra-node threaded parallelism on accelerators (GPUs) and node-level parallelism via message passing.
- Prof. Graeme J. Kennedy – School of Aerospace Engineering (advisor)
- Prof. Brian J. German – School of Aerospace Engineering
- Prof. Claudio V. Di Leo – School of Aerospace Engineering
- Prof. Kai A. James – School of Aerospace Engineering