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

Corporate Author : BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s) : TING,THOMAS C.T.

Report Date : MAY 1962

Pagination or Media Count : 1

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)

Descriptors :   *BEAMS (ELECTROMAGNETIC), *BEAMS (STRUCTURAL), *CANTILEVER BEAMS, *DIFFERENCE EQUATIONS, *IMPACT SHOCK, *LOADING, *STRESSES, ELASTIC PROPERTIES, NONLINEAR DIFFERENTIAL EQUATIONS, PLASTIC PROPERTIES

Distribution Statement : APPROVED FOR PUBLIC RELEASE