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Matched Asymptotic Expansions of Unbalanced Adhesive Joints

Kember, G. / Shahin, K.

Abstract

A matched asymptotic expansion analysis is used to determine the dependence of shear stress boundary layer thickness on adhesive properties in unbalanced single-lap joints. A uniformly accurate expansion of shear stress, in a small and positive dimensionless parameter $ε$ , is shown to contain a pair of adhesive edge boundary layers and an outer zone where the stress is slowly varying between the two layers. An overlap constraint is also found, and if it can be satisfied for $ε ≪ 1$ , then there is sufficient overlap and a single boundary layer of width the order of $ε^{1 / 2}$ at either adhesive end. The analytic results are presented in a generic format allowing their application and/or extension to similar problems. All results are numerically verified using a finite difference approximation.

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Matched Asymptotic Expansions of Unbalanced Adhesive Joints

Kember, G. / Shahin, K.

Abstract

A matched asymptotic expansion analysis is used to determine the dependence of shear stress boundary layer thickness on adhesive properties in unbalanced single-lap joints. A uniformly accurate expansion of shear stress, in a small and positive dimensionless parameter $ε$ , is shown to contain a pair of adhesive edge boundary layers and an outer zone where the stress is slowly varying between the two layers. An overlap constraint is also found, and if it can be satisfied for $ε ≪ 1$ , then there is sufficient overlap and a single boundary layer of width the order of $ε^{1 / 2}$ at either adhesive end. The analytic results are presented in a generic format allowing their application and/or extension to similar problems. All results are numerically verified using a finite difference approximation.

Matched Asymptotic Expansions of Unbalanced Adhesive Joints

Kember, G. / Shahin, K.

Abstract

A matched asymptotic expansion analysis is used to determine the dependence of shear stress boundary layer thickness on adhesive properties in unbalanced single-lap joints. A uniformly accurate expansion of shear stress, in a small and positive dimensionless parameter $ε$ , is shown to contain a pair of adhesive edge boundary layers and an outer zone where the stress is slowly varying between the two layers. An overlap constraint is also found, and if it can be satisfied for $ε ≪ 1$ , then there is sufficient overlap and a single boundary layer of width the order of $ε^{1 / 2}$ at either adhesive end. The analytic results are presented in a generic format allowing their application and/or extension to similar problems. All results are numerically verified using a finite difference approximation.

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Title:

Matched Asymptotic Expansions of Unbalanced Adhesive Joints

Contributors:

Kember, G. (author) / Shahin, K. (author)

Published in:

Journal of Engineering Mechanics ; 139 ; 1387-1394

Publication date:

2012-11-22

Size:

82013-01-01 pages

ISSN:

0733-9399 , 1943-7889

DOI:

https://doi.org/10.1061/(ASCE)EM.1943-7889.0000574

Type of media:

Article (Journal)

Type of material:

Electronic Resource

Language:

English

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