Elasto-plastic and geometrically nonlinear vibrations of
beams by the p-version finite element method
P. Ribeiro & G.H.M. van der Heijden
A model based on a Timoshenko beam p-version finite element is
developed to analyse oscillations that are, simultaneously, elasto-plastic
and geometrically nonlinear. The geometrical nonlinearity is represented by
Von Kármán type strain-displacement relations and the stress-strain relation
is of the bilinear type, with mixed strain hardening. The equations of motion
are obtained using the principle of the virtual work and are solved in the
time domain by an implicit Newmark method. The Von Mises yield criterion is
employed and the flow theory of plasticity applied; if plastic flow is found
at a point of the domain, the total plastic strain is determined by summation.
Numerical examples are carried out in order to demonstrate that the
p-version element here advocated has a number of advantages and to
show the influence of the plastic and geometrically nonlinear terms on the
oscillations of beams.
keywords: beam, vibrations, geometrically nonlinear, elasto-plastic
Journal of Sound and Vibration 325, 321-337 (2009)