SECOND GRADIENT OF STRAIN IN LINEAR ELASTICITY AND ITS APPLICATIONS.

Abstract

This study is an attempt to apply the Mindlin theory of elasticity, where the energy density is a function of strain and its first and second gradients, to several mathematically tractable problems and to examine and compare the results obtained with the discrete particle theory and with experiment. A simple physically understandable discrete particle theory is developed for a two-dimensional lattice using differences and difference equations in place of derivatives and differential equations. This gives further insight into the Mindlin theory. In the Mindlin theory, some problems associated with cylindrical and spherical surfaces are solved. The Mindlin theory and the discrete particle theory are compared with experiments such as low energy electron diffraction and neutron diffraction studies. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1967
Accession Number
AD0654774

Entities

People

  • Seiichi Iwata

Organizations

  • Columbia University

Tags

DTIC Thesaurus Topics

  • Difference Equations
  • Differential Equations
  • Diffraction
  • Elastic Properties
  • Electron Diffraction
  • Electrons
  • Equations
  • Mathematics
  • Neutron Diffraction
  • Particles
  • Two Dimensional
  • Wave Phenomena

Readers

  • Calculus or Mathematical Analysis
  • Game Theory.
  • Mechanical Engineering/Mechanics of Materials.

Technology Areas

  • Microelectronics