Bridging Locally Stress‐Constrained Topology Optimization and Additive Manufacturing

力学在各种尺度的工程结构优化中起着基础性的作用。从世纪后期开始，结构优化领域从对载荷路径的临界性及其对空间变形的影响的关键观察中发展起来。然而，随着该领域在追求复杂的工程挑战方面的发展，其重点已经转向易于处理的优化语句的配方，而不是指导结构优化的力学。该奖项将支持基于局部应力约束的通用拓扑优化框架的开发，该框架将力学的基本原理置于结构优化的中心。理论和计算框架将与先进的增材制造技术相结合，以实现趋同的结果。这项工作将使下一代工程师能够解决涉及大量局部约束的具有挑战性的结构优化问题，并以一种廉价且易于使用的方式将拓扑优化和增材制造联系起来，用于各级教育。在理论，计算，实验和制造挑战的指导下，该奖项将通过大学课程和研究与研究生课程的整合为K-12学生提供教育机会，并通过计算机代码，外联会议，和研讨会。这项研究推进了有效耦合力学和高度约束问题的优化所需的理论，解决这些问题所需的计算框架，以及制造所得到的空间变化的多网格部件的制造方法。从数学的角度来看，将采用定制的增广拉格朗日方法来解决应力约束的质量最小化问题，通过纳入局部应力。具体贡献将包括：（i）统一应力约束拓扑优化问题的局部公式，以处理具有单一强度函数的各种失效准则，并从可用于定义应力约束的无限荷载情况中解析推导最坏情况应力状态;（ii）重新表达应力约束问题以处理任意数量的线性，非线性，和/或微结构材料，并导出可用于在材料界面处加强应力约束的界面行为;以及（iii）使用新的制造技术设计和实验验证功能梯度、单格和多格优化部件，例如灰度数字光处理（g-DLP），无需昂贵的立体光刻（STL）文件。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Mechanics plays a fundamental role in the optimality of engineering structures at various scales. Starting in the late nineteenth century, the field of structural optimization grew out of key observations on the criticality of load path and its implication on spatial deformation. Yet, as the field has evolved in pursuit of complex engineering challenges, its focus has shifted towards formulations of tractable optimization statements more than on mechanics guiding structural optimization. This award will support the development of a general topology optimization framework based on local stress constraints that will bring the fundamental principles of mechanics at the center of structural optimality. The theoretical and computational framework will be bridged with advanced additive manufacturing techniques for convergent outcomes. The work will empower the next generation of engineers to solve challenging structural optimization problems involving a large number of local constraints, and to connect topology optimization and additive manufacturing in an inexpensive and easy‐to‐use way for education at all levels. Guided by theoretical, computational, experimental, and manufacturing challenges, the award will provide educational opportunities to K‐12 students through university programs and integration of research with the graduate curriculum, and support dissemination of the findings to the industry and the broader community through computer codes, outreach meetings, and workshops.This research advances the theory needed to effectively couple mechanics and optimization of highly constrained problems, the computational framework needed to solve such problems, and the manufacturing approach to fabricate the resultant spatially varying multi‐lattice parts. From a mathematical perspective, a tailored augmented Lagrangian approach will be employed to solve the stress‐constrained mass minimization problem by incorporating local stresses. Specific contributions will include: (i) unifying local formulations of the stress‐constrained topology optimization problems to handle a wide range of failure criteria with a single strength function and analytically deriving worst‐case stress states from infinite load cases that can be used to define the stress constraints; (ii) reformulating the stress constrained problem to handle an arbitrary number of linear, nonlinear, and/or microstructural materials and deriving interfacial behavior that can be used to enforce stress constraints at material interfaces; and (iii) engineering and experimentally validating functionally‐graded, single‐ and multi‐lattice optimized parts using novel manufacturing techniques, such as gray‐scale digital light processing (g-DLP) without expensive stereolithography (STL) files. The research will explore a multi‐phase design space with on demand structural fidelity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.