The solution of Navier equations of classical elasticity using Lie symmetry groups


Ozer T.

MECHANICS RESEARCH COMMUNICATIONS, vol.30, no.2, pp.193-201, 2003 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 2
  • Publication Date: 2003
  • Doi Number: 10.1016/s0093-6413(02)00365-8
  • Title of Journal : MECHANICS RESEARCH COMMUNICATIONS
  • Page Numbers: pp.193-201

Abstract

The analytical solutions of axially-symmetric Navier equations in classical elasticity are found by applying Lie group theory. We investigate two different systems of partial differential equations corresponding elastostatics and elastodynamics problems, and find similarity solutions of both cases by solving the reduced system of ordinary differential equations which have fewer independent variables. As an example of the elastostatics case, the displacements and stress components are obtained for porous, polymeric foam material by using similarity solutions. (C) 2002 Elsevier Science Ltd. All rights reserved.