ON THE UNIQUENESS PROBLEM IN THE SECOND BOUNDARY VALUE PROBLEM IN ELASTICITY

Abstract

Kirchhoff's uniqueness proof shows that, if the shear modulus is different from zero and Poisson's ratio T lies in the interval (-1, 1/2), the second boundary value problem in elasticity (surface tractions prescribed) has a unique solution (up to a rigid body motion). A demonstration is given that for general domains uniqueness holds provided T lies in the interval (-1, 1-K/2(1 + K)), where K is a constant depending on the geometry of the region. If the bounding surface is star shaped, K is equal to zero. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1961
Accession Number
AD0270211

Entities

People

  • J.h. Bramble
  • L.e. Payne

Organizations

  • University of Maryland

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Demonstrations
  • Elastic Properties
  • Geometry
  • Intervals
  • Mathematics
  • Mechanical Properties
  • Modulus Of Elasticity
  • Physical Properties
  • Shear Modulus
  • Traction

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Mechanical Engineering/Mechanics of Materials.