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# Accession Number:

## ADA183614

# Title:

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

# Descriptive Note:

## Final rept. 1 Apr 85-31 Aug 86,

# Corporate Author:

## ILLINOIS UNIV AT CHICAGO CIRCLE DEPT OF CIVIL ENGINEERING MECHANICS AND METALLURGY

# Report Date:

## 1987-01-01

# Pagination or Media Count:

##
77.0

# 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 1f, 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.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#