
Accession Number : AD0283010
Title : ON THE SOLUTION OF A NONLINEAR 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 nonlinear 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