Analysis of In-Plane Problems with Singular Disturbances for an Isotropic Elastic Medium with Two Circular Holes or Rigid Inclusions

Abstract

In the present paper, we derive a solution for two circular holes or rigid inclusions that are perfectly bonded to an elastic medium (matrix) of infinite extent under in-plane deformation. These two holes or rigid inclusions have different radii and different central points. The matrix is subjected to arbitrary loading, for example, by uniform stresses, as well as a concentrated force at an arbitrary point. The solution is obtained through iterations of the Möbius transformation as a series with an explicit general term involving the complex potential of the corresponding homogeneous problem. This procedure is referred to as heterogenization. Using these solutions, several numerical examples are presented graphically.

Analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loading

“…In a multi-void problem, Honein (1992) and Hirashima (1994) found a general solution that a matrix with two circular inclusions is loaded under the anti-plane problem. We then expand to multi-inclusions for quasi-three-dimensional problems (Miyagawa ,1998(Miyagawa , ,2011(Miyagawa , ,2012(Miyagawa , ,2013a(Miyagawa , ,2013b. However, those problems are only multi-circular inclusions.…”

Stresses in a Spherical Shell Loaded Through Rigid Inclusions

“…It is established that the stresses in the shell increase substantially with decrease in the inclusion radius and the distance between the two inclusions Keywords: shallow isotropic spherical shell, stress state, circular rigid inclusion, bridge between inclusions Introduction. The analysis of the stress state of shells and plates with various stress concentrators such as holes and inclusions [2][3][4][5][6][7][8][9][10][11][12], concentrated [1] and local [3] loads is still of theoretic and practical interest.Analytic and numerical solutions for a spherical shell loaded by a force or a moment through a rigid ring were obtained in [3] for a shell with one perfectly rigid inclusion. However, studies of shells and plates with two circular holes or rigid inclusions showed that the stress concentration can be very high if the stress concentrators are close to each other [2,[4][5][6][7][8][9][10][11][12].…”

“…The analysis of the stress state of shells and plates with various stress concentrators such as holes and inclusions [2][3][4][5][6][7][8][9][10][11][12], concentrated [1] and local [3] loads is still of theoretic and practical interest.…”

“…It is established that the stresses in the shell increase substantially with decrease in the inclusion radius and the distance between the two inclusions Keywords: shallow isotropic spherical shell, stress state, circular rigid inclusion, bridge between inclusions Introduction. The analysis of the stress state of shells and plates with various stress concentrators such as holes and inclusions [2][3][4][5][6][7][8][9][10][11][12], concentrated [1] and local [3] loads is still of theoretic and practical interest.…”

“…However, studies of shells and plates with two circular holes or rigid inclusions showed that the stress concentration can be very high if the stress concentrators are close to each other [2,[4][5][6][7][8][9][10][11][12]. In view of this, we will consider a spherical shell with two circular perfectly rigid inclusions loaded by a force or a moment and will analyze in detail the stress state of a shell with two unequal rigid rings, including the case where they are very close to each other.…”