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
Personal Author(s) : Jin,Yijian ; Ting,T C
PDF Url : ADA183614
Report Date : Jan 1987
Pagination or Media Count : 77
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.
Descriptors : *STRESS ANALYSIS, *FIBERS, AXISYMMETRIC, COORDINATES, DEFORMATION, EIGENVALUES, EIGENVECTORS, NUMBERS, POWER SERIES, SERIES(MATHEMATICS), SOLUTIONS(GENERAL), STRESS ANALYSIS, STRESSES, FRACTURE(MECHANICS), COMPOSITE MATERIALS
Subject Categories : Textiles
Distribution Statement : APPROVED FOR PUBLIC RELEASE