AN ASYMPTOTIC APPROACH FOR THE EVALUATION OF ERRORS RESULTING FROM ESTIMATIONS OF STABILITY LIMITS IN NONLINEAR ELASTICITY

In order to avoid a fully nonlinear analysis to obtain stability limit s on nonlinear load-displacement paths, estimation functions based on linear eigenvalue problems have been presented in the literature. In t his paper, an asymptotic approach is proposed to evaluate the error in duced by different modes of so-called accompanying linear eigenvalue p roblems. Moreover, based on the consistent linearization of the geomet rically nonlinear static stability condition, higher-order estimation functions can be obtained from a scalar postcalculation after the eige nvalue analysis. Finally an ab initio criterion for identification of the type of loss of stability (bifurcation or limit point) is presente d.