The basic building blocks of nano-structured hierarchical cellular materials are nano-sized wires or plates. Due to the effects of surface elasticity and the initial stress/strain, their bending, torsion, stretching and transverse shear rigidities are not only size-dependent, but also tunable and controllable over a large range. Based on the closed form results of the bending, torsion, stretchi...

Metallic sandwich panels with periodic, open-cell cores are important new structures, enabled by novel fabrication and topology design tools. Fabrication protocols based on the sheet forming of trusses and shell elements (egg-boxes) as well as textile assembly have allowed the manufacture of robust structures by inexpensive routes. Topology optimization enables control of failure mechanisms at ...

Negative stiffness honeycomb materials are comprised of unit cells that exhibit negative stiffness or snap-through-like behavior. Under an external load of small magnitude, a negative stiffness honeycomb exhibits large effective elastic modulus, equivalent to those of other standard honeycomb topologies. When the external load reaches a predetermined threshold, the negative stiffness cells begi...

Honeycombs with thermal expansion coefficients equal to zero are described analytically. The two dimensional lattice microstructure designs described are made of positive expansion materials. This work builds upon previous results, and provides further analysis into creating an optimal rib cross section. The design of ribs with Tee shaped and I shaped cross sections is developed. The behavior o...

A convex triangular grid is a planar digraph G embedded in the plane so that each bounded face is an equilateral triangle with three edges and their union R forms a convex polygon. A function h : E(G) → R is called a concave cocirculation if h(e) = g(v) − g(u) for each edge e = (u, v), where g is a concave function on R which is affinely linear within each bounded face of G. Knutson and Tao obt...

References 2.full.html#ref-list-1 http://rspa.royalsocietypublishing.org/content/469/2156/2013002 This article cites 34 articles, 8 of which can be accessed free Subject collections (164 articles) mechanical engineering • Articles on similar topics can be found in the following collections Email alerting service here the box at the top right-hand corner of the article or click Receive free ema...

Stainless steel square-honeycombs have been manufactured by slotting together steel sheets and then brazing the assembly. Their out-of-plane compressive response has been measured as a function of the relative density, the ratio of specimen height to cell size, and the degree of constraint associated with bonding of the honeycomb to face-sheets. It has been found that, for the practical range o...

We define the hive ring, which has a basis indexed by dominant weights for GLn(C), and structure constants given by counting hives [KT1] (or equivalently honeycombs, or Berenstein-Zelevinsky patterns [BZ1]). We use the octahedron rule from [RR, FZ, P, S] to prove bijectively that this “ring” is indeed associative. This, and the Pieri rule, give a self-contained proof that the hive ring is isomo...