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REVIEW ARTICLES

Stress singularities in classical elasticity—II: Asymptotic identification

[+] Author and Article Information
GB Sinclair

Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803-6413; sinclair@me.lsu.edu

Appl. Mech. Rev 57(5), 385-439 (Dec 21, 2004) (55 pages) doi:10.1115/1.1767846 History: Online December 21, 2004
Copyright © 2004 by ASME
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References

Figures

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Geometry and coordinates for the angular elastic plate
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Singularity exponents for varying vertex angles: a) free-free and clamped-clamped (from (2.9), (2.13) and (2.10), (2.14), respectively), b) frictionless contact-frictionless contact (from (2.11), (2.15)), c) contact with friction-contact with friction (from (2.12), (2.16)), d) clamped-free (from (2.17)), e) contact-free (from (2.18)), f) contact-clamped (from (2.19))
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Examples of configurations with logarithmic stress singularities: a) Levy’s problem for a reentrant corner (ϕ=ϕ*),b) pressure on a clamped acute corner (κ=2),c) symmetric indentation by a frictionless rigid sharp plate, d) displacement shape functions as boundary conditions for a submodel in FEA
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Geometry and coordinates for the composite angular elastic plate
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Sketches of interfaces; a) separating locking surfaces (Conditions C), b) adhesive law action (Conditions E)
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Bimaterial “crack” geometries analyzed for stress singularities: a) interface crack, a) interface crack ending at a kink on the interface, b) crack ending orthogonal to an interface, b) crack ending obliquely to an interface
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Open bimaterial plate geometries analyzed for stress singularities: a) butt joint, a) oblique butt joint, b) two plates of equal vertex angles, c) angular plate on a half-plane
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Butt joint subjected to uniform tractions
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Geometry and coordinates for the elastic wedge
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Singularity exponents in out-of-plane shear for varying wedge angles
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Examples of wedges with logarithmic stress singularities: a) half-space with discontinuous shear traction, b) bimaterial wedge with continuous shear traction
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Geometry and coordinates for the angular elastic plate in bending
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Stress resultants on plate elements: a) positive moment resultants (element viewed from z=h face), b) positive shear resultants
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Examples of configurations with logarithmic stress singularities: a), a′ ) plates with applied moments and log singularities in σrθ, and τ;b), b) plates with applied shears and log singularities in τrz and τθz.
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Singular axisymmetric configurations
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Spherical polar coordinates for a cone vertex
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Cylindrical polar coordinates for a cylindrical boundary
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Section through the cylinder and the half-space with local coordinates at the reentrant corner
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Bimaterial elastic wedge with vertex locus a smooth curve
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Constant pressure on a surface sector of an elastic half-space
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Elastic half-space with a crack terminating at its surface
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a) Rigid punch with a wedge-shaped flat base pressed into an elastic half-space, b) dual crack problem
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Singularity exponents for varying wedge angles
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Three-dimensional reentrant corner
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Singularity exponents for varying Poisson’s ratios for a quarter-plane crack in an elastic half-space
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Singularity exponents for varying angles of intersection for a symmetrically-loaded crack in an elastic half-space
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Classes of configurations that are effectively equivalent with respect to singularity identification: a) configurations equivalent to plates in extension, b) configurations equivalent to wedges in antiplane shear

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