Bifurcation buckling from a membrane stress state

Abstract

SUMMARY A membrane stress state may be considered as a general stress state in which mechanical constraints have been imposed. Therefore, it would appear that there are mathematical subsidiary conditions for bifurcation buckling from such a stress state. In this work, such conditions are derived in the frame of the Finite Element Method. The basic condition follows from disintegration of the second derivative of the mathematical formulation of the so-called consistently linearized eigenproblem with respect to a dimensionless load parameter. It is used for deriving another condition, characterized by the vanishing of a particular bilinear form. Linear stability analysis and bifurcation buckling from linear prebuckling paths are two special cases for which this condition is satisfied. Sensitivity analysis of bifurcation buckling of a two-hinged arch, subjected to a uniformly distributed static load, by varying the geometric form of its axis serves the purpose of non-trivial verification of the derived condition for the special case of a thrust-line arch. Copyright © 2011 John Wiley & Sons, Ltd.