Certain behaviors of some material are characterized by the periodic bar and joint elements. We present a kinematic, geometric and graph theoretic connected model that describes the stability, rigidity property of these rhombic tiling materials in two dimensions. Cables, struts or rods are placed as bracing elements between opposite pairs of diagonal joints, to prevent the rhombic tiling from the rotation of the bars around their common joint. We characterize the rigidity of the finite parts of the rhombic bracing structure in the plane. The results of this paper are based on the theorem of the rigidity of one-dimensional tensegrity framework from Recski and Shai. We have applied our results to describe some auxetic type structures that were mentioned earlier in the scientific literature. We also introduce the model as a possible candidate for the mechanical information processing system in a repetitive bar and joint structure.

Bracing rhombic structure by one-dimensional tensegrities

Repetitive skeletal structures controlled with bracing elements

In this paper we deal with edge-to-edge, irreducible decompositions of a centrally symmetric convex $(2k)$-gon into centrally symmetric convex pieces. We prove an upper bound on the number of these decompositions for any value of $k$, and characterize them for octagons.

Decompositions of a polygon into centrally symmetric pieces

In this paper we deal with edge-to-edge, irreducible decompositions of a centrally symmetric convex (2k)-gon into centrally symmetric convex pieces. We prove an upper bound on the number of these decompositions for any value of k, and characterize them for octagons.

Júlia Frittmann

Papers

Decompositions of a polygon into centrally symmetric pieces

Decompositions of a Polygon into Centrally Symmetric Pieces