H.A. Mang, P. Helnwein:

"A Priori Estimates of Stability Limits on Nonlinear Load-Displacement Paths";

in: "Proceedings of the International Conference on Lightweight Structures in Civil Engineering", J.B. Obreski (ed.); Magat, Warschau, Poland, 1995, Vol. II, 811 - 821.

An a priori estimate of a stability limit is an estimate of the location of a bifurcation point or a snap-through point on a load-displacement path at the beginning of tracing nonlinear load-displacement paths of an elastic structure. Hence, such an estimate only requires such information about the structural behavior, which can be obtained at lambda = 0, where lambda is a dimensionless parameter by which the static, conservative reference load is multiplied. The vehicle for determination of a priori estimates of stability limits is a special accompanying liear eigenproblem within the framework of the finite element method (FEM). Essential features of the solution of this eigenproblem will be discussed in the paper. Determination of a priori estimates of stability limits on nonlinear prebuckling paths will be explained. The theoretical findings will be verified numerically. It will be shown that even for strongly nonlinear prebuckling paths the quality of these estimates is good.

Keywords: estimates, stability limits, nonlinearity

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