VARIATIONAL PRINCIPLES FOR LINEAR ELASTODYNAMICS,

Abstract

Variational principles are established which fully characterize the solution of the mixed problem for a general (inhomogeneous and anisotropic) linear elastic solid. Following certain preliminary definitions and notational agreements, four lemmas are proved that are analogous to the fundamental lemma of the calculus of variations. There are deduced several equivalent formulations of the problem under consideration. Variational principles appropriate to the mixed problem are given. The first of these principles is completely general in the sense that the admissible states are not required to meet any of the field equations, boundary conditions, or initial conditions. In addition there are presented variational theorems based on admissible states that satisfy some of the boundary conditions and field equations. Variational characterizations of the displacements appropriate to the mixed problem are derived and variational principles for the accompanying stresses are presented. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1963
Accession Number
AD0421736

Entities

People

  • M. E. Gurtin

Organizations

  • Brown University

Tags

DTIC Thesaurus Topics

  • Agreements
  • Boundaries
  • Calculus
  • Calculus Of Variations
  • Differential Equations
  • Displacement
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Variational Principles

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Theoretical Analysis.