# Accession Number:

## AD0269328

# Title:

## ASYMPTOTIC PHENOMENON IN LARGE ROTATION

# Descriptive Note:

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1961-11-01

# Pagination or Media Count:

## 1.0

# Abstract:

IN CYLINDERS SUBJECTED TO LARGE TORSION, IT IS FOUND THAT FOR LARGE VALUES OF THE TWIST THE SOLUTION OF THE NON-LINEAR DIFFERENTIAL EQUATION GIVING THE RADIAL DISPLACEMENT, APPROACHES AN ASYMPTOTIC VALUE, WHICH SUGGESTS THE SETTING IN OF THE PLASTIC STATE ON THE OUTER BOUNDARY OF THE CYLINDER. The case of rapidly rotating cylinders is treated. The stress-strain relation changes on the axis of the cylinder where the transition from the elastic to a plastic state takes place. The radial displacement again satisfies a non-linear differential equation. Its asymptotic solution occurs at a definite value of the angular velocity and shows that the rate of change of the ordinary strains at the center is finite and not zero as in the elastic or classical plastic case. This angular velocity corresponds to what we obtain by using the yield condition, but, its value is somewhat greater than that given by the classical plastic theory. The plastic state first sets in on the axis of the cylinder, and hence, as indicated by the asymptotic solution, it is expected that the ordinary strains will decrease from the axis towards its outer surface at a definite rate. Author