Journal ArticleDOI
On the stress singularities in the plane elasticity of the composite wedge
John P. Dempsey,G. B. Sinclair +1 more
TLDR
In this paper, a composite, two-dimensional, linear elastic wedge for singular stresses at its vertex is examined and a full range of wedge boundary and matching conditions is considered, using separation of variables on the Airy stress function.Abstract:
This paper examines the composite, two-dimensional, linear elastic wedge for singular stresses at its vertex. A full range of wedge boundary and matching conditions is considered. Using separation of variables on the Airy stress function, the usual determinant conditions for singularities of the formO(r
-λ) asr → 0 are established and further conditions are derived for singularities of the formO(r
-λ lnr) asr → 0. The order of the determinant involved in these conditions depends upon the number of materials comprising the wedge. Two systematic methods of expanding the determinant for theN-material wedge are presented.read more
Citations
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Journal ArticleDOI
The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)
Journal ArticleDOI
Explicit solution and invariance of the singularities at an interface crack in anisotropic composites
TL;DR: In this paper, it was shown that δ is invariant with respect to the orientation of the plane boundary (in the case of half-plane problems), the semi-infinite crack and the crack and interface relative to the materials.
Journal ArticleDOI
On the singular behavior at the vertex of a bi-material wedge
John P. Dempsey,G. B. Sinclair +1 more
TL;DR: In this paper, the singular behavior at the vertex of a bi-material wedge is studied and a summary of the necessary conditions, which depend heavily on the associated eigenvalue equation, for stress singularities of O(ρ-λ 1n r) as r→0 or O(r-λ) asr→0 is stated.
Journal ArticleDOI
Stress singularities in classical elasticity–I: Removal, interpretation, and analysis
TL;DR: In this article, the authors consider the singularities that occur in linear elastostatics and present several interpretations of these singularities, such as the singularity coefficient or stress intensity factor.
Journal ArticleDOI
Free-Edge Effects in Composite Laminates
TL;DR: A survey on relevant literature from more than three decades of scientific research on free-edge effects is given, which deals with approximate closed-form analyses, as well as numerical investigations by the finite element method, the finite difference method, and several other numerical techniques.
References
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Book
The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Journal ArticleDOI
The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)
Journal ArticleDOI
Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension
TL;DR: In this paper, the authors investigated three boundary conditions on the radial edges: free-free, clamped-clamped, and clamped free, and showed that the free free extensional plate behaves locally at the origin exactly the same as a clampedclamped plate in bending, independent of Poisson's ratio.
Journal ArticleDOI
The stresses around a fault or crack in dissimilar media
TL;DR: In this article, the authors investigated the modulus of the singular behavior of the stress remains proportional to the inverse square root of the distance from the point of the crack, but the stresses possess a sharp oscillatory character of the type r^(-1/2) sin (b log r), which seems to be confined quite close to the point, as well as a shear stress along the material joint line.