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

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)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1962
Accession Number
AD0283010

Entities

People

  • Thomas C.t. Ting

Organizations

  • Brown University

Tags

DTIC Thesaurus Topics

  • Bending Moments
  • Boundaries
  • Cantilever Beams
  • Differential Equations
  • Equations
  • Lepidoptera
  • Mathematics
  • Sensitivity
  • Strain Rate

Readers

  • Control Systems Engineering.
  • Mechanical Engineering/Mechanics of Materials.
  • Snow Cover Descriptors for Reptiles and Their Illustrations.