Eigenfunctions at a Singular Point in Transversely Isotropic Materials under Axisymmetric Deformations,
ILLINOIS UNIV AT CHICAGO CIRCLE DEPT OF CIVIL ENGINEERING MECHANICS AND METALLURGY
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When a two-dimensional elastic body which contains a notch or a crack is under a plane stress or plane strain deformation, the asymptotic solution of the stress near the apex of the notch or crack is simply a series of eigenfunctions of the form rho delta fpsi, delta in which rho, psi is the polar coordinate with origin at the apex and delta is the eigenvalue. If the body is a three-dimensional elastic solid which contains axisymmetric notches or cracks and subjects to an axisymmetric deformation, the eigenfunction associated with an eigenvalue contains not only the rho delta term, but also the rho delta 1, rho delta 2 terms. Therefore, the second and higher order terms of the asymptotic solution are not simply the second and subsequent eigenfunctions. The authors present the eigenfunctions for transversely isotropic materials under an axisymmetric deformation. The degenerate case in which the eigenvalues p sub 1 and p sub 2 of the elasticity constants are identical is also considered. The latter includes the isotropic materials under axisymmetric deformations.