The Plane Solution for Anisotropic Elastic Wedges Under Normal and Shear Loading

1972 ◽  
Vol 39 (4) ◽  
pp. 1103-1109 ◽  
Author(s):  
D. B. Bogy
Keyword(s):  
Half Plane ◽  
Complex Function ◽  
Stress Singularity ◽  
Shear Loading ◽  
Elementary Functions ◽  
Linear Elastostatics ◽  
Full Plane ◽  
Plane Solution ◽  
Logarithmic Singularities ◽  
Anisotropic Elastic

The plane traction problem for an anisotropic wedge is solved within the theory of linear elastostatics. The technique employs the complex function representation of the plane solution in conjunction with the Mellin transform. Special attention is given to the orthotropic wedge; the uniform load solution is given in terms of elementary functions for wedge angles less than π, the logarithmic singularities in the stress field resulting from discontinuous loads on the half plane are studied, and the stress singularity at the apex is investigated for the reentrant wedges. Simplified results for the anisotropic half plane and cracked full plane are also presented.

Plane Solutions for the Displacement and Traction-Displacement Problems for Anisotropic Elastic Wedges

1974 ◽  
Vol 41 (1) ◽  
pp. 197-202 ◽  
Author(s):  
M. C. Kuo ◽  
D. B. Bogy
Keyword(s):  
Mellin Transform ◽  
Symmetry Axis ◽  
Wedge Angle ◽  
Complex Function ◽  
Material Symmetry ◽  
Stress Singularities ◽  
Material Parameters ◽  
Plane Solution ◽  
Anisotropic Elastic ◽  
Plane Displacement

The plane displacement and traction-displacement problems for anisotropic elastic wedges are solved by use of the complex function representation of the plane solution in conjunction with the Mellin transform. The special forms of the solutions pertinent to orthotropic wedges with a material symmetry axis along the wedge bisector is also presented and the dependence of the order of the stress singularities at the apex on the wedge angle and material parameters is shown graphically for this case.

The Plane Solution for the Elastic Contact Problem of a Semi-Infinite Strip and Half Plane

1976 ◽  
Vol 43 (4) ◽  
pp. 603-607 ◽  
Author(s):  
G. G. Adams ◽  
D. B. Bogy
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Numerical Solutions ◽  
Stress Singularity ◽  
Singular Integral Equations ◽  
Infinite Strip ◽  
Elastic Contact ◽  
Shearing Stress ◽  
Elastic Materials ◽  
Plane Solution

The solution is obtained for both smooth and bonded contact between the strip and half plane of different elastic materials. First, the problems are reduced to singular integral equations of the second kind. Then the order of the stress singularity at the corners is extracted from the integral equations and numerical solutions are obtained. Interface normal and shearing stress are exhibited graphically for several material combinations.

Mixed Mode Stress Singularities in Anisotropic Composites

1999 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Stress Intensity ◽  
Asymptotic Solution ◽  
Stress Intensity Factors ◽  
Stress Singularity ◽  
Free Edge ◽  
Complex Conjugate ◽  
Circular Path ◽  
Intensity Factors ◽  
Element Analysis ◽  
Anisotropic Elastic

Abstract Multi-material wedges composed of fully anisotropic elastic sectors generally show intrinsic coupling of the anti-plane and in-plane modes of deformation. Each anisotropic sector has three complex conjugate pairs of material eigensolutions whose form of expression depends on five distinct types of anisotropic materials. Continuity of the displacements and the tractions across the sector interfaces and the traction-free conditions on two exterior boundary edges determine an infinite sequence of eigenvalues and eigensolutions of the multi-material wedge. These eigensolutions are linearly combined to match the traction-boundary data (generated by global finite element analysis of the structure) on a circular path encircling the singularity. The analysis method is applied to a bimaterial wedge near the free edge of a four-layer angle-ply laminate, and to a trimaterial wedge surrounding the tip of an embedded oblique crack in a three-layer composite. Under a uniform temperature load, the elasticity solution based on the eigenseries yields interfacial stresses that are significantly different from the asymptotic solution (given by the first term of the eigenseries), even as the distance from the singularity decreases to subatomic scales. Similar observations have been found previously for isotropic and orthotropic multi-material wedges. This raises serious questions with regard to characterizing the criticality of stress singularity exclusively in terms of the asymptotic solution and the associated stress intensity factors or generalized stress intensity factors.

Thermal Distortion of an Anisotropic Elastic Half-Plane and its Application in Contact Problems Including Frictional Heating

2005 ◽  
Vol 128 (1) ◽  
pp. 32-39 ◽  
Author(s):  
Yuan Lin ◽  
Timothy C. Ovaert
Keyword(s):  
Heat Flux ◽  
Half Plane ◽  
Frictional Heating ◽  
Contact Problems ◽  
Local Heat ◽  
Extended Version ◽  
Parabolic Profile ◽  
Local Heat Flux ◽  
Anisotropic Elastic ◽  
Thermoelastic Contact Problem

The thermal surface distortion of an anisotropic elastic half-plane is studied using the extended version of Stroh’s formalism. In general, the curvature of the surface depends both on the local heat flux into the half-plane and the local temperature variation along the surface. However, if the material is orthotropic, the curvature of the surface depends only on the local heat flux into the half-plane. As a direct application, the two-dimensional thermoelastic contact problem of an indenter sliding against an orthotropic half-plane is considered. Two cases, where the indenter has either a flat or a parabolic profile, are studied in detail. Comparisons with other available results in the literature show that the present method is correct and accurate.

Fracture Analysis near Interface Crack Tip for Mode I of Orthotropic Bi-Materials

2012 ◽  
Vol 490-495 ◽  
pp. 3242-3252
Author(s):  
An Qiang Dong ◽  
Wei Yang Yang ◽  
Jun Lin Li
Keyword(s):  
Interface Crack ◽  
Linear Equations ◽  
Complex Function ◽  
Stress Singularity ◽  
Crack Tip ◽  
Analytic Solutions ◽  
Mode I ◽  
Biharmonic Equations ◽  
Singularity Exponents ◽  
Orthotropic Composites

The mechanical behaviors near interface crack tip for mode I of double dissimilar orthotropic composites are studied. By translating governing equations into generalized biharmonic equations, the stress functions containing two stress singularity exponents are found with the help of a complex function method. Based on the boundary conditions, two systems of non-homogeneous linear equations are obtained. Through solving these systems two real stress singularity exponents are determined under appropriate condition of bimaterial engineering parameters. By the uniqueness theorem of limit,both the theoretical formulae of stress intensity factors and analytic solutions of stress field and displacement field near interface crack tip are deduced.

Stress Singularity at the Tip of a Rigid Line Inhomogeneity Under Antiplane Shear Loading

1986 ◽  
Vol 53 (2) ◽  
pp. 459-461 ◽  
Author(s):  
Z. Y. Wang ◽  
H. T. Zhang ◽  
Y. T. Chou
Keyword(s):  
Stress Singularity ◽  
Shear Loading ◽  
Antiplane Shear ◽  
Rigid Line

Analysis of Stress Singularity Induced in Viscoelastic Thin Layer Subjected to Shear Loading

2003 ◽  
Vol 17 (08n09) ◽  
pp. 1248-1253
Author(s):  
Myung Kyu Park ◽  
Sang Soon Lee ◽  
Chang Min Suh
Keyword(s):  
Thin Layer ◽  
Edge Crack ◽  
Viscoelastic Model ◽  
Stress Singularity ◽  
Adhesive Layer ◽  
Rigid Bodies ◽  
Shear Loading ◽  
Linear Viscoelastic ◽  
Viscoelastic Theory ◽  
Linear Viscoelastic Theory

This paper deals with the stress singularity developed in a viscoelastic thin layer bonded between two rigid bodies and subjected to a shear loading. A boundary element method is employed to investigate the behavior of interface stresses. Within the context of a linear viscoelastic theory, a stress singularity exists at the point where the interface between one of the rigid adherends and the adhesive layer intersects the free surface. Numerical results are presented for a given viscoelastic model, indicating that such stress singularity might lead to edge crack or delamination.

Thermal Distortion of an Anisotropic Elastic Half-Plane and Its Application in Contact Problems Including Frictional Heating

2004 ◽  
Author(s):  
Yuan Lin ◽  
Timothy C. Ovaert
Keyword(s):  
Heat Flux ◽  
Half Plane ◽  
Frictional Heating ◽  
Contact Problems ◽  
Local Heat ◽  
Extended Version ◽  
Parabolic Profile ◽  
Local Heat Flux ◽  
Anisotropic Elastic ◽  
Thermoelastic Contact Problem

The thermal surface distortion of an anisotropic elastic half-plane is studied using the extended version of Stroh’s formalism. In general, the curvature of the surface depends both on the local heat flux into the half-plane and the local temperature variation along the surface. However, if the material is orthotropic, the curvature of the surface depends only on the local heat flux into the half-plane. As a direct application, the two-dimensional thermoelastic contact problem of an indenter sliding against an orthotropic half-plane is considered. Two cases, where the indenter has either a flat or a parabolic profile, are studied in detail. Comparisons with other available results in the literature show that the present method is correct and accurate.

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