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P. Helnwein, H.A. Mang:
"An Asymptotic Approach for the Evaluation of Errors Resulting from Estimations of Stability Limits in Nonlinear Elasticity";
Acta Mechanica, 125 (1997), 235 - 254.

In order to avoid a fully nonlinear analysis to obtain stability limits on nonlinear load-displacement paths, estimation functions based on linear eigenvalue problems have been presented in the literature. In this paper, an asymptotic appproach is proposed to evaluate the error induced by different modes of so-called accompanying linear eigenvalue problems. Moreover, based on the consistent linearization of the geometrically nonlinear static stability condition, higher-order estimation functions can be obtained from a scalar postcalculation after the eigenvalue analysis. Finally an ab initio criterion for identification of the type of loss of stability (bifurcation or limit point) is presented.

Keywords: stability, accompanying eigenvalue analysis, error analysis, estimation, nonlinear elasticity