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

板和壳已被用于不同的领域，如民用，机械，航空和海洋工程。这些结构的一个标志性特征是它们能够支撑大负载，尽管它们的结构很薄。一个这样的壳结构，负责保护我们细胞内的基因组，是核被膜（即，核的边界）。这种结构具有独特的几何形状，由两个同心的中空球壳在数千个具有环形孔的位置处融合而成，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，本研究探讨了一类新的最佳仿生壳结构，称为torenes，包括同心壳层与圆环形孔融合。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时实现高弹性。这些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载荷的保护装备。研究结果将通过实践教学演示、科学卡通（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进行传播。在推进建筑板和壳领域的同时，该研究将吸引和培养一批多样化的学生，包括来自代表性不足的群体的学生。 本研究立足于力学、几何和优化的交叉点，研究超高亏格板壳结构的力学性能和破坏机理。该研究将进行有限元分析，以调查在平面内和平面外载荷下的torene结构的力-变形响应和稳定性。这些信息将被用来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，数值优化将被用来确定拓扑结构，最大限度地提高性能的托琳结构在不同的外部负载和功能要求。该研究将应用所发现的几何原理来设计和实验测试来自2D材料的3D torene架构，以实现超弯曲刚度。总体而言，这项工作将解开微分几何和相关的几何参数在调制一类新的拓扑结构的强度和稳定性的作用。这种方法允许在不同的长度尺度下对结构进行调查，从而确定尺度律和尺度不变性。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。

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.