Automorphism groups of some variants of lattices

In this paper we consider variants of the power set and the lattice of subspaces and study automorphism groups of these variants. We obtain irreducible generating sets for variants of subsets of a finite set lattice and subspaces of a finite vector space lattice. We prove that automorphism group of the variant of subsets of a finite set lattice is a wreath product of two symmetric permutation groups such as first of this groups acts on subsets. The automorphism group of the variant of the subspace of a finite vector space lattice is a natural generalization of the wreath product. The first multiplier of this generalized wreath product is the automorphism group of subspaces lattice and the second is defined by the certain set of symmetric groups.

Converting three-space matrices to equivalent six-space matrices for Delone scalars in S6

The transformations from the primitive cells of the centered Bravais lattices to the corresponding centered cells have conventionally been listed as three-by-three matrices that transform three-space lattice vectors. Using those three-by-three matrices when working in the six-dimensional space of lattices represented as Selling scalars as used in Delone (Delaunay) reduction, one could transform to the three-space representation, apply the three-by-three matrices and then back-transform to the six-space representation, but it is much simpler to have the equivalent six-by-six matrices and apply them directly. The general form of the transformation from the three-space matrix to the corresponding matrix operating on Selling scalars (expressed in space S6 ) is derived, and the particular S6 matrices for the centered Delone types are listed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.)

Behavior of eccentrically loaded welded hollow spherical joints after elevated-temperature exposure

Welded hollow spherical joint is an extremely widely used connection pattern in space lattice structures. Understanding the behavior of the welded hollow spherical joint after elevated-temperature exposure is critical for the fire damage assessment of the entire space lattice structures. In this study, both experimental and numerical studies were conducted to reveal the mechanical behavior of eccentrically loaded welded hollow spherical joints subjected to eccentric loads after cooling from three elevated temperatures up to 1000°C, wherein two different methods were considered, namely, air and water cooling. Associate mechanical performance, such as load versus longitudinal displacement and load versus steel tube rotation responses, initial stiffness, load-bearing capacities, and strain development, were obtained and further analyzed. The results showed that the behavior of welded hollow spherical joints began to change when the exposure temperatures exceeded 600°C, with obvious reductions in both stiffness and strength. In addition, the influences of different cooling methods were significant. The joints cooled by water generally presented higher load-bearing capacities than those cooled by air. Furthermore, three-dimensional finite element analysis was conducted via ABAQUS software. After validating the finite element model against experimental results, parametric studies were performed and a practical formula was proposed to calculate the load-bearing capacity of welded hollow spherical joints subjected to eccentric load after elevated-temperature exposure.