# Accession Number:

## AD0271471

# Title:

## PLANE-STRAIN AND GENERALIZED PLANE-STRESS ANALYSIS OF A ROTATING VISCOELASTIC CYLINDER

# Descriptive Note:

# Corporate Author:

## BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

# Personal Author(s):

# Report Date:

## 1962-02-01

# Pagination or Media Count:

## 1.0

# Abstract:

The departure of the plane-strain from the generalized plane-stress solution is explored quantitatively in connection with a particular boundary-value problem in the special case of isothermal viscoelastic theory. The problem is that of a viscoelastic circular cylinder which rotates about its geometric axis. The corresponding angular velocity is assumed to be switched on instantaneously at some initial instant and is supposed to be constant thereafter. The solutions obtained are particularize to each other in the initial elastic state, diverge monotonically as time progresses. It is also found that the generalized plane-stress value of the radial displacement at the periphery of the cylinder tends to infinity with time, while the corresponding displacement in the plane-strain so to, and discussed numerically for, the Maxwell solid. It is found that the plane-strain and the generalized plane-stress values of the hoop stress at the periphery of the cylinder, which are relatively close to each other in the initial elastic state, diverge monotonically as time progresses. It is also found that the generalized plane-stress value of the radial displacement at the periphery of the cylinder tends to infinity with time, while the corresponding displacement in the plane-strain solution approaches a finite value in this limit. Author