Bridging Locally Stress‐Constrained Topology Optimization and Additive Manufacturing

桥接局部应力——约束拓扑优化和增材制造

• 批准号: 2105811
• 负责人: Glaucio Paulino
• 金额: $ 49.88万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-11-01 至 2024-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2105811&HistoricalAwards=false
• 关键词: Bridging; Locally; Stress; Constrained; Topology; Bridging; Locally; Stress; Constrained; Topology

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.

力学在各种规模的工程结构的最优性中起着基本作用。从十九世纪后期开始，结构优化生长的领域是对负载路径的关键性及其对空间变形的影响的关键观察。然而，随着该领域在追求复杂的工程挑战方面的发展，其重点已转向可拖动优化陈述的公式，而不是指导结构优化的力学。该奖项将基于本地压力限制的一般拓扑优化框架的开发，这将使机械师的基本原理成为结构优化的中心。理论和计算框架将与高级添加剂制造技术桥接，以进行收敛结果。这项工作将使下一代工程师能够解决涉及大量本地限制的结构优化问题，并以廉价且易于使用的各个级别的教育方式连接拓扑优化和成瘾性制造。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，并支持将调查结果传播给行业和更广泛的社区，并通过计算机代码，通过计算机代码，外展览会和研讨会来构建特定的贡献。处理具有单个强度函数的广泛故障标准，并从无限载荷案例中分析得出最坏的应力状态，该案例可用于定义应力限制； （ii）重新解决应力约束问题，以处理任意数量的线性，非线性和/或微观结构材料，并得出可用于在材料界面上实现应力限制的界面行为； （iii）使用新颖的制造技术（例如灰度的数字光处理（G-DLP））的工程和实验验证了功能分级，单位和多晶格优化零件，而无需昂贵的立体光刻（STL）文件。该研究将探索具有按需结构性保真度的多相设计空间。该奖项反映了NSF的法定任务，并通过使用基金会的知识分子优点和更广泛的影响评估标准来评估，被认为是珍贵的支持。