Technical Briefs

On the Stress Singularities at Clamped Butt Joints

[+] Author and Article Information
G. B. Sinclair

e-mail: sinclair@me.lsu.edu

Ajay A. Kardak

Department of Mechanical Engineering,
Louisiana State University,
Baton Rouge, LA, 70803

Other approaches are available for this asymptotic analysis: the Mellin transform as in Ref. [2], and Kolossoff-Muskhelishvili complex potentials. For a given asymptotic problem, all three approaches lead to effectively the same eigenvalue equation when correctly executed.

The value of E2 used in this example is for Locktite HYSOL 9430, an epoxy with a low Young’s modulus.

1Corresponding author.

Manuscript received July 22, 2011; final manuscript received May 2, 2012; accepted manuscript posted May 11, 2012; published online October 29, 2012. Assoc. Editor: Nick Aravas.

J. Appl. Mech 80(1), 014501 (Oct 29, 2012) (5 pages) Paper No: JAM-11-1248; doi: 10.1115/1.4006815 History: Received July 22, 2011; Revised May 02, 2012; Accepted May 11, 2012

This note considers two elastic quarter-planes perfectly bonded together on their common boundary and clamped on their other boundaries. Asymptotic analysis of the stresses in the corners of the quarter-planes identifies the power singularities present for a full range of elastic moduli. Configurations with nonsingular stresses at this juncture are also identified. These last results offer some means for removing stress singularities from clamped butt joints by perturbing elastic moduli.

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Aksentian, O. K., 1967, “Singularities of the Stress-Strain State of a Plate in the Neighborhood of an Edge,” J. Appl. Math. Mech., 31, pp. 193–202. [CrossRef]
Bogy, D. B., 1970, “On the Problem of Edge-Bonded Quarter-Planes Loaded at the Boundary,” Int. J. Solids Struct., 6, pp. 1287–1313. [CrossRef]
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Williams, M. L., 1952, “Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension,” ASME J. Appl. Mech., 19, pp. 526–528.
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Grahic Jump Location
Fig. 1

Example of a clamped butt joint: bimetallic strip under transverse load

Grahic Jump Location
Fig. 2

Local clamped butt joint configuration and coordinates

Grahic Jump Location
Fig. 3

Singularity exponents for varying ratios of shear moduli: (a) κ1=1.0, (b) κ1=1.5, (c) κ1=2.0, and (d) κ1=2.5

Grahic Jump Location
Fig. 4

Nonsingular clamped butt joints: (a) pure shear, (b) matched lateral strains



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