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

板壳在土木工程、机械、航空和海洋工程等领域有着广泛的应用。这些结构的一个显著特点是，尽管它们的体系结构很薄，但它们仍能够支持大负载。负责保护我们细胞内基因组的一种壳结构是核膜(即核的边界)。这种结构具有独特的几何结构，由两个同心空心球壳组成，在数千个地点熔化成环形孔，并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，这项研究调查了一类新的最佳仿生贝壳结构，称为Torenes，由同心贝壳层与环状孔洞融合而成。Torene架构可以使飞机、潜艇和火箭的新设计在对抗极端自然力量方面实现高弹性。发现的原理可以指导轻型假肢的设计，以及国防人员和运动员对抗高冲击负荷的防护装备的设计。研究成果将通过实践教学演示、科学漫画、虚拟力学实验室、期刊出版物和面向高中生的客座讲座来传播。在推进建筑板壳领域的同时，这项研究将吸引和培训不同的学生群体，包括那些来自代表不足的群体的学生。本研究站在力学、几何和优化的交界处，研究具有超高亏格的板壳结构的力学性能和破坏机理。本研究将进行有限元分析，以研究平面内和平面外荷载作用下环面结构的力-变形响应和稳定性。这些信息将被用来构造适当的目标函数和约束，以执行多层板壳的拓扑优化。特别是，数值优化将被用来确定在不同的外部载荷和功能要求下使环缝结构的性能最大化的拓扑结构。这项研究将应用已发现的几何原理来设计和实验测试由2D材料衍生的3D Torene结构，以实现超弯曲刚度。总而言之，这项工作将解开微分几何和相关几何参数在调节一类新的拓扑结构的强度和稳定性方面的作用。这种方法允许对不同长度尺度的结构进行调查，从而确定比例定律和比例不变性。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.