To main content

SYMMETRY-RELATIONS FOR ELASTICALLY DEFORMED PERIODIC ROD-STRUCTURES

Abstract

In this paper we study periodic elastic rod-structures which are locally anisotropic and symmetric with respect to some plane. In order to find the effective behavior and approximate local behavior (so-called corrector-results) of such structures, one has to solve a finite number of boundary-value problems on one period of the rod-structure, the cell problem. For the solution of the cell-problem, it is shown that the components of the displacement satisfy either Neumann or Dirichlet conditions on the sides of the cell of periodicity parallel with the symmetry-plane. This is very useful from a computational point of view since the derived boundary conditions can easily be incorporated into standard numerical schemes. We also study resultant forces and moments and their variations along the rod-structure in several types of cases, even when no symmetry is required.

Category

Academic article

Language

English

Author(s)

  • Dag Lukkassen
  • Annette Meidell
  • Andrey Piatnitski
  • Alexey Shamaev

Affiliation

  • SINTEF Narvik
  • Russian Academy of Sciences
  • UiT The Arctic University of Norway

Year

2009

Published in

Mathematical Models and Methods in Applied Sciences

ISSN

0218-2025

Volume

19

Issue

4

Page(s)

501 - 525

View this publication at Norwegian Research Information Repository