A simple finite element approach to problems of dynamic structural instability under step loading is discussed. The method proposed is believed to yield important information about the structural behaviour in the non‐linear range. Incorporation of the method into existing finite element codes is straightforward.

Numerical analysis of dynamic quasi-bifurcation

Dynamic buckling of an inelastic column

Elastic-plastic buckling of buried pipelines by seismic excitation

We develop procedures for solving the problems of dynamic nanostructure deformation and buckling numerically. The procedures are based on discretization with respect to time of the nonlinear equations of molecular mechanics whose matrices and vectors are determined using the Morse potential for the central forces of interaction between atoms and fictitious truss elements accounting for the variations of the angle between atomic bonds. To determine the critical values of deformation parameters and the shapes of buckling nanostructures we use a stability loss criterion for solutions to nonlinear ordinary differential equations on a finite time interval. We implemented our procedures in the PIONER code, using which we solve the problem of a twisted nanotube buckling in the conditions of a quasistatic deformation. To determine the postcritical equilibrium modes we solve the same problem in a dynamic formulation. We show that the modes of equilibrium configurations of the nanotube in the initial postcritical deformation correspond to a buckling mode obtained both at the bifurcation point of quasistatic solutions and at the quasibifurcation point of dynamic solutions.

Computer simulation of a twisted nanotube buckling

Coupling Phenomena in Thermoplasticity

In this paper, a dynamic stability concept and a quasi-bifurcation criterion introduced in a recent paper [1] are clarified. A simple dynamic system of four degrees of freedom is employed to illustrate the concept and the significance of the criterion.

On dynamic stability and quasi-bifurcation

An extension of Prager-Ziegler's work-hardening rule for infinitesimal elastic-plastic deformation to a work-hardening rule for finite elastic-plastic deformation of polycrystalline metals at elevated temperatures is developed. Attention is given to the development to satisfy certain invariant, continuity and thermodynamic requirements.

L.H.N. Lee

Papers

On dynamic stability and quasi-bifurcation

A work-hardening rule for finite elastic-plastic deformation of metals at elevated temperatures