Dual maps have been introduced as a generalization to higher dimensions of word substitutions and free group morphisms. In this paper, we study the action of these dual maps on particular discrete planes and surfaces – namely stepped planes and stepped surfaces. We show that dual maps can be seen as discretizations of toral automorphisms. We then provide a connection between stepped planes and ...

in this paper, in order to analyze the transverse vibration of a uniform bernoulli-euler beam containing one single edge crack, a new continuous model is proposed for the cracked section. to this end, by using the fracture mechanics, the crack is modeled as a continuous disturbance in the stress and strain fields. by applying the hamilton’s principle, the equation of motion and the correspondin...

We find bounds on the effective elastic moduli of cracked materials in terms of the effective conductivity of such media. These represent the first non-trivial bounds on the effective properties of cracked media which are independent of the shapes and spatial distribution of the cracks. Different approximations for the elastic moduli of cracked media are tested against our bounds. The microgeom...

CONVENTIONAL SURFACE INSPECTION We have developed a new apparatus to cope W I T H LASER BEAM. with the surface inspection of products having even undulating or stepped surfaces. To realize such surface inspection, we combined the three dimensi~nal shape measurement through laser beam scanning and the flaw and defwct identification t h m u g h diffraction light pattern analysis. This combination...

Considering the influence of visible load-induced transverse cracks on chloride ion diffusion in cracked concrete in-service reinforced (RC) elements under marine environment, a typical volume with one crack was taken to establish governing equation. Assuming widths at outer lateral and bottom surfaces were equal, model predict equivalent coefficient put forward consider average width, spacing ...

The Existence of crack in a structure leads to local flexibility and changes  the stiffness and dynamic behavior of the structure. The dynamic behavior of the cracked structure depends on the depth and the location of the crack. Hence, the changes in the dynamic behavior in the structure due to the crack can be used for identifying the location and depth of the crack. In this study the first th...

This article reviews the diagnosis and treatment of cracked teeth, and explores common clinical examples of cracked teeth, such as cusp fractures, fractures into tooth furcations, and root fractures. This article provides alternative definitions of terms such as cracked teeth, complete and incomplete fractures and crack lines, and explores the scientific rationale for dental terminology commonl...