Multi-Fidelity Analysis and Optimization of Lightweight Structures Subject to Significant Fluid-Structure Interaction Effects

Abstract

The motion and deformation of structures such as aircraft, turbomachinery, offshore marine systems, and next-generation prosthetic devices are inherently coupled with the surrounding fluid flow. These interactions, commonly referred to as fluid-structure interaction (FSI), require the simultaneous consideration of the fluid and the structural sub-problems while capturing the effects of coupling at their interface. Motivated by this, the first part of this thesis focuses on developing a coupled simulation framework for modeling the dynamic behavior of lightweight, compliant containment structures subjected to internal detonation-driven fluid loading. These one-time use structures incorporate sacrificial components that undergo large, permanent deformations, while the internal fluid flow exhibits complex shock waves, reflections, and interactions. A three-stage solution strategy is proposed to capture the distinct physics and time scales of explosive burning, shock propagation, and the structural response to the FSI loading. The resulting framework couples compressible computational fluid dynamics (CFD) with nonlinear computational structural dynamics (CSD), and is used to analyze a model problem involving a thin monolithic steel container. The case study shows that accounting for the FSI effects in the analysis of such lightweight containers is essential, as traditional surface pressure approximation methods underpredict the structural deformations, while decoupled simulations overpredict them. Motivated by the excellent energy absorption capacity and low density of cellular materials, the second part of the thesis investigates their application to explosion containment structures to enhance their blast survivability while reducing their structural weight. Specifically, this thesis focuses on metallic foams, which feature an extended plastic plateau during which their cellular structure collapses due to wall buckling or yielding, followed by a nonlinear densification stage where the material rapidly gains strength. To capture this complex behavior, a custom constitutive model is implemented using an extended von Mises yield criterion combined with a nonlinear hardening law. This model is integrated within the CSD solver and used to analyze a model sandwich composite containment vessel featuring foam cores enclosed between thin steel facesheets. Comparative analyses show that the sandwich composite container performs 9 times more plastic work and dissipates 8 times more energy from the applied blast load compared to an equal-weight monolithic steel container. These findings demonstrate the potential of metallic foams to improve blast mitigation performance and highlight the need for an optimization framework capable of systematically exploring the structural design variations while accommodating the coupled FSI effects. The optimization of structures in the presence of FSI effects introduces several challenges. The optimization variables, objective functions, and constraints are often relevant to the structure, while the computational cost is dominated by repeated high-fidelity CFD analyses. Moreover, gradient-based optimization is difficult to apply due to the challenges of differentiating through coupled CFD-CSD solvers. These challenges are addressed in this dissertation by first leveraging gradient-free methods, such as genetic algorithms, to avoid complex gradient evaluations. Specifically, the dissertation introduces the SOFICS (Structural Optimization through Fluid-structure Coupled Simulations) framework, which is a modular optimization workflow that integrates our open-source CFD and CSD solvers with Sandia National Lab's optimization toolkit DAKOTA for its implementation of gradient-free optimization methods. The framework supports parallel batch evaluations on large high-performance computing (HPC) machines through DAKOTA's tiling approach and SOFICS's careful load balancing and resource assignments, thereby speeding up the optimization process. The final part of this dissertation presents a novel adaptive multi-fidelity optimization framework that exploits the imbalance in optimization relevance and computational costs in FSI-based optimization studies. The proposed method combines high-fidelity fluid-structure coupled simulations with a lightweight, on-the-fly surrogate model for fluid-induced loads. To maintain optimization relevance, the approach retains the full CSD model throughout the optimization. As the optimization progresses, the CFD data from the early iterations is used to incrementally build and refine the non-intrusive surrogate model based on a nearest-neighbor search and local interpolation technique. A Gaussian-process decision model is also refined progressively to estimate the surrogate error and automatically determine when a coupled simulation is required. It is expected that, as design evaluations cluster near the optimal solution, the accuracy of the surrogate model will naturally improve, leading to fewer CFD evaluations. The effectiveness of this framework is demonstrated through a numerical example involving the shape optimization of a cantilever panel subjected to shock loading, showing substantial reductions in computational cost while maintaining accuracy comparable to optimizations performed entirely with high-fidelity FSI simulations.