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，可以有效地生成具有所需特性的材料几何形状。然而，这些几何形状通常很难制造，或者可能需要额外的后处理，然后才能使用添加制造技术实现。此外，传统的拓扑优化方法不能很好地处理包含不确定性的多物理、多材料问题。该奖项支持开发统一计算框架的基础研究，该框架结合了基于水平集的拓扑优化方法、稳健设计、添加制造和实验表征，以应对这些挑战。该方法将创成式拓扑优化与加法制造无缝结合。由此产生的方法和工具将使下一代多功能材料的创新设计成为可能。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、本科和研究生水平的教育质量和效果，并努力让代表不足的群体参与。在这个项目中，将开发一种新的基于水平集的自动化计算设计方法，以提供拓扑优化、多物理无网格有限元分析、稳健设计和加法制造的无缝集成。这将使系统设计和高效实现高质量和高通量的多功能超材料。本研究的目标将通过：(1)利用无单元Galerkin方法对声子超材料中的声波/弹性波传播进行高保真模拟；(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)开发基于水平集的动态拓扑设计和形状同时稳健优化的新方法；(4)探索利用几何水平集模型中嵌入的信息实现拓扑设计与附加制造的无缝集成的新方法；(5)通过实验测试交叉验证设计方法和模型。数值研究和实验研究的结合将对多功能声子超材料中潜在的多物理机制提供更好的科学理解。将探索精确的多物理建模、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.