Symmetry perspectives on some auxetic body-bar frameworks

Scalar mobility counting rules and their symmetry extensions are reviewed for finite frameworks and also for infinite periodic frameworks of the bar-and-joint, body-joint and body-bar types. A recently published symmetry criterion for the existence of equiauxetic character of an infinite framework is applied to two long known but apparently little studied hinged-hexagon frameworks, and is shown to detect auxetic behaviour in both. In contrast, for double-link frameworks based on triangular and square tessellations, other affine deformations can mix with the isotropic expansion mode.P.W. Fowler acknowledges support from the Royal Society/Leverhulme Trust in the form of a Senior Research Fellowship for 2013. T. Tarnai is grateful for financial support under OKTA grant K81146.This is the final published version distributed under a Creative Commons Attribution License, which can also be found on the publisher's website at: http://www.mdpi.com/2073-8994/6/2/36

Equiauxetic Hinged Archimedean Tilings

There is increasing interest in two-dimensional and quasi-two-dimensional materials and metamaterials for applications in chemistry, physics and engineering. Some of these applications are driven by the possible auxetic properties of such materials. Auxetic frameworks expand along one direction when subjected to a perpendicular stretching force. An equiauxetic framework has a unique mechanism of expansion (an equiauxetic mode) where the symmetry forces a Poisson’s ratio of −1. Hinged tilings offer opportunities for the design of auxetic and equiauxetic frameworks in 2D, and generic auxetic behaviour can often be detected using a symmetry extension of the scalar counting rule for mobility of periodic body-bar systems. Hinged frameworks based on Archimedean tilings of the plane are considered here. It is known that the regular hexagonal tiling, {63}, leads to an equiauxetic framework for both single-link and double-link connections between the tiles. For single-link connections, three Archimedean tilings considered as hinged body-bar frameworks are found here to be equiauxetic: these are {3.122}, {4.6.12}, and {4.82}. For double-link connections, three Archimedean tilings considered as hinged body-bar frameworks are found to be equiauxetic: these are {34.6}, {32.4.3.4}, and {3.6.3.6}.NKFI

Reduced order models for 3D parametric lattice structures: computation and post-processing in portable devices

The Proper General ized Decomposition (PGD) provides explicit parametric solutions of parametric PD Es. Here, the same ideas are used to obtain parametric solutions of the algebraic equations arising from lattice structural models. Once the explicit parametric solution is available, the optimal design problem is a simple post-process. The same strategy is applied in the numerical illustrations, first to a unit-cell (and then homogenized with periodicity conditions), and in a second phase to the complete structure of a lattice material specimen

Light-Weight Structural Optimization Through Biomimicry, Machine Learning, and Inverse Design

In load-bearing lightweight architectures, cellular materials were frequently utilized. While octahedron, tetrahedron, and octet truss lattice truss were built for lightweight architectures with stretching and flexural dominance, it can be believed that new cells could easily be designed that might perform much better than the present ones in terms of mechanical and architectural characteristics. Machine learning-based structure scouting and design improvisation for better mechanical performance is a growing field of study. Additionally, biomimicry—the science of imitating nature’s elements—offers people a wealth of resources from which to draw motivation as they work to create a better quality of life. Here, utilizing machine learning approaches, novel lattice truss unit cellular architectures with enhanced architectural characteristics were designed. An inverse design methodology employing generative adversarial networks is suggested to investigate and improvise the lightweight lattice truss unit cellular architectures. The proposed framework was utilized to identify various lattice truss unit cellular architectures with load carrying capacities 40–120% greater than those of octet unit cells. A further 130–160% raise in buckling load bearing capacity was made possible by substituting porous biomimicry columns for the solid trusses in the light-weight lattice truss unit cellular architectures. This dissertation\u27s main goal is to investigate various improvisation strategies for creating lightweight architectures, particularly when using data analysis and machine learning methods. Lightweight cellular architectures with thin-walls and lattice truss unit cellular architectures with improved shape memory capabilities were created using the knowledge gleaned from numerous of the research projects mentioned in the preceding paragraphs load-bearing architectures and devices, lightweight architecture with shape memory and with better strength, better stretchability, and better elastic stress recovery are widely desired. As compared to the bulk shape memory polymeric cylinders, the cellular architectures with thin walls show 200% betterer elastic stress recovery that is normalized with respect to base designs. The architectural improvisation of many other additional designs and practical implementation can be accomplished using the inverse design framework