Collaborative Research: Mechanics of Optimal Biomimetic Torene Plates and Shells with Ultra-high Genus

板壳已广泛应用于土木、机械、航空和海洋工程等领域。这些结构的一个标志性特征是尽管其架构很薄，但它们仍能够支撑大负载。负责保护细胞内基因组的一种这样的壳结构是核膜（即细胞核的边界）。该结构具有独特的几何形状，由两个同心空心球壳组成，在数千个位置融合有圆环形状的孔，并且在弯曲刚度方面表现出一个数量级的放大。受这一发现的启发，本研究研究了一种新型的最佳仿生壳结构，称为 torene，由与环形孔融合的同心壳层组成。 torene 架构可以使飞机、潜艇和火箭的新设计能够在对抗极端自然力方面实现高弹性。所发现的原理可以指导国防人员和运动员的轻型假肢和防护装备的设计，以应对高冲击载荷。研究结果将通过实践教学演示、scientoons（基于科学的卡通）、虚拟力学实验室、期刊出版物和高中生客座讲座来传播。在推进建筑板和壳领域的发展的同时，该研究将吸引和培训不同的学生群体，包括来自代表性不足群体的学生。 该研究立足于力学、几何学和优化的交叉领域，研究超高变形板壳结构的力学性能和失效机制。该研究将进行有限元分析，以研究 torene 结构在面内和面外载荷下的力变形响应和稳定性。该信息将用于构建适当的目标函数和约束，以执行多层板和壳的拓扑优化。特别是，数值优化将用于确定在不同外部负载和功能要求下最大化 torene 结构性能的拓扑。该研究将应用发现的几何原理来设计和实验测试源自 2D 材料的 3D torene 架构，以实现超弯曲刚度。总体而言，这项工作将阐明微分几何和相关几何参数在调节新型拓扑结构的强度和稳定性中的作用。这种方法允许对不同长度尺度的结构进行研究，从而确定标度定律和标度不变性。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Plates and shells have been used in diverse fields such as civil, mechanical, aeronautical, and marine engineering. A hallmark feature of these structures is their ability to support large loads despite their thin architecture. One such shell structure, responsible for guarding the genome inside our cells, is the nuclear envelope (i.e., the boundary of the nucleus). This structure has a unique geometry comprised of two concentric hollow spherical shells fused at thousands of sites with torus-shaped holes, and exhibits one order of magnitude amplification in flexural stiffness. Inspired by this finding, this study investigates a new class of optimal biomimetic shell structures, termed torenes, comprising concentric shell layers fused with torus-shaped holes. The torene architecture could enable new designs in aircrafts, submarines, and rockets to achieve high resilience in countering extreme natural forces. The discovered principles can guide the design of lightweight prosthetics, and protective gear for defense personnel and athletes to counter high impact loads. The research findings will be disseminated by hands-on pedagogical demonstrations, scientoons (science-based cartoons), virtual mechanics labs, journal publications and guest lectures for high school students. While advancing the field of architected plates and shells, the research will engage and train a diverse group of students, including those from underrepresented groups. Poised at the interface of mechanics, geometry, and optimization, the research will investigate the mechanical properties and failure mechanisms of plate and shell structures with ultra-high genus. The study will perform finite element analyses to investigate force-deformation response and stability of torene structures under in-plane and out-of-plane loadings. This information will be used to construct proper objective functions and constraints to perform topology optimization of multilayer plates and shells. In particular, numerical optimization will be used to identify topologies that maximize performance of torene structures under different external loads and functional requirements. The study will apply the discovered geometric principles to design and experimentally test 3D torene architectures derived from 2D materials for achieving ultra-flexural stiffness. Overall, the work will disentangle the roles of differential geometry and associated geometric parameters in modulating the strength and stability of a new class of topological structures. This approach allows an investigation of structures at different length scales leading to the determination of scaling laws and scaling invariance.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.