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H.A. Mang, P. Helnwein:
"Second-Order A-Priori Estimates of Bifurcation Points on Geometrically Nonlinear Prebuckling Paths";
in: "Computational Mechanics 95 - Proceedings of the International Conference of Computational Engineering Science", S.N. Atluri, G. Yagawa, T.A. Cruse (Hrg.); Springer, Berlin, 1995, Vol. II, S. 1511 - 1516.

An a-priori estimate of a bifurcation point on a geometrically nonlinear prebuckling path is an estimate of the location of such a point, which is based exclusively on information available at the beginning of tracing the nonlinear load-displacement path of a perfect elastic structure, i.e., at lambda = 0, where lambda is a dimensionless parameter by which the static reference load is multiplied. A second-order a-priori estimate is defined as an estimate requiring knowledge of lambda^*(lambda = 0= equivlambda^*_0 and of dlambda^*/dlambda|_{lambda = 0}, where lambda^*_0 is the eigenvalue of a specific accompanying linear eigenvalue problem at lambda = 0. In the theoretical investigation it will be explained how to obtain the aforementioned estimates. In the numerical study it will be shown that even for a strongly nonlinear prebuckling path the quality of these estimates is good.

Keywords: stability, second-order estimates, bifurcation, nonlinearity