Stress concentration in an anisotropic half-plane with holes and cracks

1998 ◽  
Vol 90 (1) ◽  
pp. 1840-1845
Author(s):  
S. A. Kaloerov ◽  
E. V. Avdyushina
Keyword(s):  
Stress Concentration ◽  
Half Plane

scholarly journals The influence of surface effects in the problem of theory of elasticity for a circular hole in a half-plane

2020 ◽  
pp. 250-259
Author(s):  
D. V Gandilyan
Keyword(s):  
Fourier Series ◽  
Stress Concentration ◽  
Half Plane ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Theory Of Elasticity ◽  
Plane Boundary ◽  
Problem Solution ◽  
Stress Components

Surface effects are important for modeling structures, such as nanofilms, nanoporous materials, and other nanoscale constructions. In the current study, we consider the problem of the theory of elasticity - the problem of a half-plane containing a circular hole, stretched by constant stresses applied at infinity, and take into account surface effects such as surface elasticity and surface stresses. The problem solution has been obtained by expanding the Fourier series with the variables written in the bipolar coordinate system (which simplifies the problem solution because one of the coordinates becomes a constant on the hole contour), where the stress components are expressed through a bi-harmonic stress function. The parametric coefficients involved in the solution, namely in the Fourier series, are determined in order to satisfy the boundary conditions on the hole contour. To solve the problem, in addition to the equations of the theory of elasticity, the equations of surface elasticity were used, in particular, by applying the generalized Young-Laplace’s law and the Shuttleworth’s law; the surface stress on the hole contour has been calculated directly. Using recurrence relations for the stress components at the boundary, stress concentration values have been obtained. The resulting expressions can be considered as a generalized solution of the problem in case of the classical elasticity. The stress concentrations are compared for the cases with and without taking into account surface effects at various points on the hole contour. The contribution caused by the surface effects depending on the relative distance between the hole and the half-plane boundary is studied. It is shown that despite a quite simple geometry, owing to the fairly small distance between the hole and the half-plane boundary, the stress concentration with and without taking into account the surface stress are significantly different from each other, due to the significant contribution of surface effects.

Dynamic Stress Concentration of a Cylindrical Cavity Buried in an Elastic Half-Plane Subjected to a Standing Goodier-Bishop Stress Wave

2002 ◽  
Author(s):  
C. S. Yeh ◽  
T. J. Teng ◽  
W. I. Liao ◽  
W. S. Shyu
Keyword(s):  
Stress Concentration ◽  
Boundary Conditions ◽  
Stress Wave ◽  
Half Plane ◽  
Cylindrical Cavity ◽  
Dynamic Stress ◽  
Scattering Problem ◽  
Ground Surface ◽  
Radiation Condition ◽  
Dynamic Stress Concentration

In this paper, based on a expansion technique proposed by Yeh et al. (1995), the dynamic stress concentration of a cylindrical cavity buried in an elastic half-plane is studied. The cavity and the half-plane are excited by a harmonic standing Goodier-Bishop stress wave which, as a result of taking the normalized frequency tends to zero, is equivalent to a simple uniform static tension parallel to the ground surface. In the formulation, the scattered waves are represented by series expansion and their associated modal fields of the expansion satisfy the boundary conditions on the ground surface as well as the radiation condition at infinity, thus the scattering problem is reduced to the determination of the expansion coefficients by matching the boundary conditions on the cavity. Some numerical results for the dynamic hoop stresses around the wall of the cavity as well as the dynamic stress concentration factors with various buried depth and excitation frequencies are presented.

Dynamic Stress Concentration of a Cylindrical Cavity in Half-Plane Excited by Standing Goodier-Bishop Stress Wave

2012 ◽  
Vol 28 (2) ◽  
pp. 269-277 ◽  
Author(s):  
W.-I Liao ◽  
T.-J. Teng
Keyword(s):  
Stress Concentration ◽  
Boundary Conditions ◽  
Stress Wave ◽  
Half Plane ◽  
Cylindrical Cavity ◽  
Dynamic Stress ◽  
Scattering Problem ◽  
Ground Surface ◽  
Wave Number ◽  
Dynamic Stress Concentration

AbstractBased on expansion technique, the dynamic stress concentration of a cylindrical cavity buried in an elastic half-plane is studied in the paper. The cavity and the half-plane are excited by a harmonic standing Goodier-Bishop stress wave which, as a result of taking the normalized frequency tends to zero, is equivalent to a simple uniform static tension parallel to the ground surface. In the formulation, the scattered waves are represented by a series expansion, and their associated modal fields of the expansion satisfy the boundary conditions on the ground surface as well as the radiation condition at infinity. As a consequence, the scattering problem is reduced to the determination of the expansion coefficients by matching the boundary conditions on the cavity. The numerical technique based on the steepest descent method is used to calculate the integral representation of potential functions in wave-number domain. Numerical results for the dynamic hoop stresses around the wall of the cavity and the dynamic stress concentration factors with various buried depth and excitation frequencies are presented.

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