H.A. Mang:

"On the Monotony of the Eigenvalue Function from Complete Accompanying Linear FE Stability Analysis of Thin, Linear-Elastic Shells";

in: "Proceedings of the International Conference on Numerical Methods in Engineering - Theory and Applications", Elsevier Science, London, 1990, 291 - 299.

It is proved that the function of eigenvalues of smallest absolute value (eigenvalue function), obtained from so-called complete accompanying linear finite element (FE) stability analysis of geometrically nonlinear prebuckling analysis of thin, linear-elastic shells, representing a special form of accompanying linear FE stability analysis, is a monotonically increasing function. Consequently, the eigenvalues from this mode of accompanying linear FE stability analysis are lower bounds of \lamba = \lamba_s > 0, where \lamba_s represents the value of the load parameter \lamba at the stability limit, assuming proportional loading. In particular, the eigenvalue of smallest absolute value from complete linear initial FE stability analysis, which is the first step of complete accompanying linear FE stability analysis, must be a lower bound of \lamba_s > 0. This property is important from the viewpoint of engineering practice, where linear initial FE stability analyses are carried out frequently beyond their limitations instead of nonlinear stability analyses.

Created from the Publication Database of the Vienna University of Technology.