A New Level-Set-Based Robust Topology Optimization Approach with Applications to Design of Phononic Metamaterials

拓扑优化是一种计算设计方法，用于有效地生成具有所需性能的材料几何形状。然而，这些几何形状通常难以制造，或者在使用增材制造技术实现它们之前可能需要额外的后处理。此外，涉及不确定性的多物理场、多材料问题用传统的拓扑优化方法不能很好地解决。该奖项支持基础研究，以开发统一的计算框架，结合基于水平集的拓扑优化方法，稳健设计，增材制造和实验表征，以应对这些挑战。这种方法将生成式拓扑优化与增材制造无缝集成。由此产生的方法和工具将能够创新设计下一代多功能材料。研究结果将向学术界和公众广泛传播。教学和推广活动将提高教师和学生在K-12、本科生和研究生阶段的教育质量和效率，并大力促进代表性不足的群体的参与。在该项目中，将开发一种新颖的基于水平集的自动计算设计方法，以提供拓扑优化、多物理场无网格有限元分析、稳健设计、和增材制造。这将使高质量和高通量的多功能超材料的系统设计和有效实现成为可能。本研究的目标是：（1）采用无网格Galerkin方法对声子超材料中的声波/弹性波传播进行高保真度的模拟;（2）设计新的数值方法来处理具有非凸目标函数和多个非线性约束的大规模拓扑优化问题;（3）发展了基于水平集的动态拓扑设计方法，实现了形状和拓扑的同时鲁棒优化;（4）探索利用几何水平集模型中嵌入的信息的新方法，以实现拓扑设计与增材制造的无缝集成;（5）通过实验检验对设计方法和模型进行交叉验证。数值和实验研究的结合将提供一个更好的多物理机制的多功能声子超材料的科学理解。将探索用于精确的多物理场建模、高效的大规模拓扑优化和不确定性量化以及不确定性传播的新技术。

Topology optimization is a computational design approach for efficiently generating material geometries with desired properties. However, these geometries are often difficult to manufacture or may require additional post-processing before they can be realized using additive manufacturing techniques. In addition, multi-physics, multi-material problems involving uncertainty are not well addressed with conventional topology optimization methods. This award supports fundamental research towards the development of a unified computational framework that combines level-set-based topology optimization methods, robust design, additive manufacturing, and experimental characterization to address these challenges. This approach seamlessly integrates generative topology optimization with additive manufacturing. The resulting methods and tools will enable innovative design of next-generation multifunctional materials. The findings of the research will be broadly disseminated to the academic community and general public. The teaching and outreach activities will improve the quality and effectiveness of education for teachers and students at the K-12, undergraduate and graduate levels, with a significant effort towards involvement of underrepresented groups.In this project, a novel level-set-based automated computational design method will be developed to provide seamless integration of topology optimization, multiphysics mesh-free finite element analysis, robust design, and additive manufacturing. This will enable systematic design and efficient realization of high-quality and high-throughput multifunctional metamaterials. The goal of this research will be accomplished by: (1) conducting high-fidelity simulations on acoustic/elastic wave propagation in phononic metamaterials using an element-free Galerkin method; (2) devising new numerical methods to handle large-scale topology optimization problems with non-convex objective functions and multiple nonlinear constraints; (3) developing new design methods for simultaneous robust shape and topology optimization with level-set-based dynamic topological design; (4) exploring new methods that leverage the information embedded in geometric level-set models to enable seamless integration of topology design with additive manufacturing; (5) cross validating the design methods and models through experimental tests. The combination of numerical and experimental studies will provide a better scientific understanding of the underlying multiphysics mechanisms in multifunctional phononic metamaterials. New techniques for accurate multi-physics modeling, efficient large scale topology optimization and uncertainty quantification, and uncertainty propagation will be explored.