Strength analysis of an elastic plane containing a square lattice of circular holes under mechanical loading

The strength characteristics of an elastic plane weakened by a square lattice of circular holes are considered. The stress concentrations in three distinct lattices under the conditions of uniaxial tension/compression in various directions are studied. The minimum and maximum values of the stress concentrations are calculated, and the stress fields in various lattices are considered. We show that under the compression conditions fracture can occur inside the material rather than on the hole boundaries. It is demonstrated that in dense lattices the stress concentrations exhibit power-law dependence on the structure parameter equal to the ratio of the length of the interval between the holes to the hole radius.     

Stress concentration localization in doubly periodic square systems of circular holes in uniaxial compression

We consider the stress concentration points in infinite elastic doubly periodic perforated plates (lattices) under the conditions of external uniaxial compression. Special attention is paid to the internal localization of stress concentrations (i.e., to the case of stress concentration origination inside the material rather than on the boundaries of the holes). We consider a parametric domain (depending on the angle of application of the external load and the structure parameter of the lattice) and calculate the domain dimensions (the extreme values of the parameters). We discover a point in the parametric domain at which the following three cases of fracture initiation are possible: two cases on the hole contour and one case inside the material.     

Stresses in Pochhammer–Chree Axisymmetric Waves in the Medium-Wavelength Range

Acoustical Physics - Pochhammer–Chree axisymmetric waves propagating along an elastic rod with a circular cross section are analytically investigated. The stress-strained state of the rod is...     

Stresses of a Symmetric Lamb Wave in the Middle-Wavelength Range: Study of an Internal Wave

Acoustical Physics - The paper considers the stress-strain state of an elastic unbounded plate during propagation of the fundamental mode of a symmetric Lamb wave. Particular attention is paid to...     

Application of the multipole method to the problem on two close holes

We consider the plane elasticity problem on the interaction of two close identical holes under biaxial loading conditions at infinity. We study the stress state in the region of mutual interaction of the holes and near their contours. We propose a method for solving this problem on the basis of the representation of the jump displacement function as a sum of multipoles. Special attention is paid to the dependence of stress concentration on the parameters of the system of holes and its orientation with respect to the applied load. The stress fields are obtained for various locations of the holes. We also present the dependences of the maximum stress attained on the contour and the point of maximum stress concentration on the orientation of the pair of holes with respect to the external load.