IJPAM: Volume 43, No. 1 (2008)

A COMPUTATIONAL STUDY ON THE NONLINEAR
HARDENING CURVED BEAM PROBLEM

Ahmet N. Eraslan$^1$, Eray Arslan$^2$
$^{1,2}$Department of Engineering Sciences
Middle East Technical University
Ankara, 06531, TURKEY
$^1$e-mail: aeraslan@metu.edu.tr
$^2$e-mail: erarslan@metu.edu.tr


Abstract.A computational model is developed to estimate the partially plastic stress state in a slender curved beam subjected to couples at its end sections. The model proposed is based on the von Mises' yield criterion, the total deformation theory, and nonlinear strain hardening material behavior. A state of plane stress and infinitesimal deformations are presumed. Using formal nondimensional variables and an appropriate stress function, a single second order nonlinear differential equation describing the deformation behavior of the curved beam is obtained. A shooting technique using Newton iterations with numerically approximated tangents is used for the numerical integration of the governing equation. The stress responses of the beam are computed in purely elastic and partially plastic stress states and the results are presented in graphical forms.

Received: January 8, 2008

AMS Subject Classification: 26A33

Key Words and Phrases: curved beam, stress analysis, elastoplasticitiy, von Mises' criterion, nonlinear hardening

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 43
Issue: 1