Accession Number:

AD0283010

Title:

ON THE SOLUTION OF A NON-LINEAR PARABOLIC EQUATION WITH A FLOATING BOUNDARY ARISING IN A PROBLEM OF PLASTIC IMPACT OF A BEAM

Descriptive Note:

Corporate Author:

BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s):

Report Date:

1962-05-01

Pagination or Media Count:

1.0

Abstract:

The deformation of a cantilever beam with strain rate sensitivity subjected to impact loading at its base is studied by an approxi a method in whic the inertia forces in the plastic region are neglected. If these forces are taken into account, the equation of motion in the plastic region is a fourt order non-linear parabolic differential equation with a floating boundary, i.e. one whose position varies with time and must be found as part of the solutio . A numerical solution of this equation is prese ted. The result show that the bending moment in the plastic region varies nearly linearly. T HIS RESULT IMPLIES THAT THE SHEAR FORCE IS NEARLY CONSTANT IN THE PLA TIC REGION, AND HENCE AT TH INER I FORCE IN T E PLASTIC REGION ARE SMALL IN COMPARISON WITH THE SHEAR FORCE IN THE SAME REGION. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE