Journal Article10.1016/S0022-5096(02)00107-2
On the determinacy of repetitive structures
TL;DR: In this paper, it was shown that repetitive, infinite structures cannot be simultaneously statically and kinematically determinate, and that infinite structures can not be statically determinate with respect to each other.
read more
Abstract: This paper shows that repetitive, infinite structures cannot be simultaneously statically, and kinematically, determinate.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Robustness of stress focusing in soft lattices under topology-switching deformation
Caleb Widstrand,Xiaoming Mao,Stefano Gonella +2 more
TL;DR: This study investigates the robustness of stress focusing in soft lattices under nonlinear finite deformation, demonstrating its persistence despite topology-switching deformation, and proposes a geometric indicator for the transition, leveraging silicone hyperelastic prototypes.
Topological boundary modes in jammed matter
TL;DR: In this paper, the authors study two model systems for jammed matter, and find states that exhibit distinct mechanical topological classes, protected surface modes, and ubiquitous Weyl points, and show that parts of this argument are invalid.
The in-plane, elastic-plastic response of a filled hexagonal honeycomb at finite strain
TL;DR: In this article , the authors derived finite strain numerical solutions for the in-plane, elastic-plastic response of a filled hexagonal honeycomb in uniaxial compression and in uníaxial tension, where the cell walls and core are treated as elastic von Mises solids.
Excess floppy modes and multibranched mechanisms in metamaterials with symmetries.
Luuk A. Lubbers,Martin van Hecke +1 more
TL;DR: In this paper, the authors study the number of excess floppy modes in symmetric geometries with identical topologies and show that the number is extensive, peaks at intermediate connection densities, and exhibits mean field scaling.
Supersymmetry protected topological phases of isostatic lattices and kagome antiferromagnets
TL;DR: In this paper, the theory of phonon topological band structures of isostatic lattices was generalized to frustrated antiferromagnets and a many-body supersymmetry (SUSY) model was proposed.
References
Foam topology bending versus stretching dominated architectures
TL;DR: In this paper, the authors investigated the topological criteria that dictate the deformation mechanism of a cellular solid by analysing the rigidity (or otherwise) of pin-jointed frameworks comprising inextensional struts.
1.4K
On graphs and rigidity of plane skeletal structures
TL;DR: In this paper, the combinatorial properties of rigid plane skeletal structures are investigated, and the properties are found to be adequately described by a class of graph-structured graphs.
1.2K
Matrix analysis of statically and kinematically indeterminate frameworks
TL;DR: In this paper, the structural mechanics of assemblies of bars and pinjoints, particularly where they are simultaneously statically and kinematically indeterminate, are investigated, and an algorithm is set up which determines the rank of the matrix and the bases for the four subspaces.
772
Buckminster Fuller's “Tensegrity” structures and Clerk Maxwell's rules for the construction of stiff frames
TL;DR: In this article, it was shown that a single state of self-stress in the frame has the effect of imparting first-order stiffness to the frame, and it seems from experiments that such states can stiffen a large number of modes.
681