Sharif Digital Repository

A Semi-Separated Pair Decomposition (SSPD), with parameter s>1, of a set SâŠ"Rd is a set {(Ai,Bi)} of pairs of subsets of S such that for each i, there are balls DAi and DBi containing Ai and Bi respectively such that d(DAi,DBi)≥s×min(radius(DAi), radius(DBi)), and for any two points p,qâ̂̂S there is a unique index i such that pâ̂̂Ai and qâ̂̂Bi or vice versa. In this paper, we use the SSPD to obtain the following results: First, we consider the construction of geometric t-spanners in the context of imprecise points and we prove that any set SâŠ"Rd of n imprecise points, modeled as pairwise disjoint balls, admits a t-spanner with O(nlogn/(t-1)d) edges that can be computed in O(nlogn/(t-1)d)... 

Two-dimensional elastic contact problem of an asymmetrical rounded apex wedge with a half plane is considered and an analytical solution is presented for vertical and horizontal external loading in the presence of coulomb friction. The pressure and shear distribution functions are found in closed form under partial slip condition. Further by utilizing a new relation Muskhelishvili's potential function is obtained and results are analyzed. Designing better cutting tools, selecting fretting fatigue test pads and deeper lap joint analyzing are several practical applications of the outcomes  

In this article, the sliding frictional contact problem for a half-plane which is graded in two dimensions is studied. The effect of medium properties gradient and coefficient of friction in contact mechanics of two dimensional (2D) graded materials which is loaded by a flat stamp have been investigated by developing two Finite Element (FE) models, in macro and micro scales. Discretizing the graded half-plane by quadrants for whose material properties are specified at the centroids by Mori-Tanaka method in both directions has been used to model the 2D FGM in macro scale. In micro scale, the ideal solid quadrant particles which are spatially distributed in a homogeneous matrix used to model... 

The growth of slant cracks by fretting fatigue of a half plane in contact with a flat rounded pad was studied. The mode I and mode II stress intensity factors for cracks of various lengths and directions were calculated using the semi-analytical method of the distribution of dislocations, and their cumulative effect on the crack growth was investigated using the strain energy density criterion. The results showed dominance of mode I fracture on crack growth, and based on the observation of strain energy density factor versus crack orientation, the results also suggest that depending on the crack length, the most critical orientations of cracks are at 0° to 20° outward the contact zone. Good... 

The effect of the interface stresses is studied upon the size-dependent elastic deformation of an elastic half-plane having a cylindrical inclusion with distinct elastic properties. The elastic half-plane is subjected to either a uniaxial loading at infinity or a uniform non-shear eigenstrain in the inclusion. The straight edge of the half-plane is either traction-free, or rigid-slip, or motionless, which represents three practical situations of mechanical structures. Using two-dimensional Papkovich-Neuber potentials and the theory of surface/interface elasticity, the elastic field in the elastic half-plane is obtained. Comparable with classical result, the new formulation renders the... 

An internal crack located within a functionally graded material (FGM) strip bonded with two dissimilar half-planes and under an anti-plane load is considered. The crack is oriented in an arbitrary direction. The material properties of strip are assumed to vary exponentially in the thickness direction and two half-planes are assumed to be isotropic. Governing differential equations are derived and to reduce the difficulty of the problem dealing with solution of a system of singular integral equations Fourier integral transform is employed. Semi closed form solution for the stress distribution in the medium is obtained and mode III stress intensity factor (SIF), at the crack tip is calculated...