Eigenfunctions at a Singular Point for Transversely Isotropic Composites with Applications to Stress Analysis of a Broken Fiber.

Abstract

When a transversely isotropic elastic body that contains a notch or a crack is under an axisymmetric deformation, it is shown that the eigenfunction solution near the singular point is in the form of a power series, rho delta f psi, >,rho delta + 1)f, psi, delta, rho f2 psi, delta...in which rho, psi is the polar coordinate with origin at the singular point and delta is the eigenvalue, or the order of singularity. A difficulty arises when delta as well as delta +k where k is a positive integer is also an eigenvalue. In this case the higher order terms of the series solution may not exist. A modified solution is required and presented here. As an application, we consider the stresses near a broken fiber in a composite which is under an axisymmetric deformation. The interface between the broken fiber and the matrix also suffers a delamination. This creates stress singularities at several points some of which require the modified eigenfunctions presented here.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1987
Accession Number
ADA183614

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  • T. C. Ting
  • Yijian Jin

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  • University of Illinois at Chicago

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