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WELL-POSEDNESS OF THE FUNDAMENTAL BOUNDARY VALUE PROBLEMS FOR
 

Summary: WELL-POSEDNESS OF THE FUNDAMENTAL
BOUNDARY VALUE PROBLEMS FOR
CONSTRAINED ANISOTROPIC ELASTIC MATERIALS
DOUGLAS N. ARNOLD RICHARD S. FALK
Dedicated to Professor JOACHIM NITSCHE on the occasion of his sixtieth birthday.
Abstract
We consider the equations of linear homogeneous anisotropic elasticity admitting the pos-
sibility that the material is internally constrained, and formulate a simple necessary and
sufficient condition for the fundamental boundary value problems to be well-posed. For
materials fulfilling the condition, we establish continuous dependence of the displacement
and stress on the elastic moduli and ellipticity of the elasticity system. As an application
we determine the orthotropic materials for which the fundamental problems are well-posed
in terms of their Young's moduli, shear moduli, and Poisson ratios. Finally, we derive a
reformulation of the elasticity system that is valid for both constrained and unconstrained
materials and involves only one scalar unknown in addition to the displacements. For
a two-dimensional constrained material a further reduction to a single scalar equation is
outlined.
March 1986
1. Introduction
The equations of anisotropic elasticity are

  

Source: Arnold, Douglas N. - School of Mathematics, University of Minnesota
Falk, Richard S.- Department of Mathematics, Rutgers University

 

Collections: Mathematics