A new algorithm for buckling analyses under non-proportional loading - with application to CERN CMS experiment

Full text: The following items might be of interest when the stability of a structure under interacting load cases with independent load factors is investigated: 1. in the case of an interaction between variable loads, their most unfavorable combination with respect to buckling and the corresponding stability limit might be sought after. 2. if variable loads interact with parameter loads the buckling load factor applies only to the former ones, while the latter ones might vary within predefined limits. In this case the most unfavorable values for the parameter loads might be needed as well. For simple structures under simple load cases (e.g. rectangular plates under combined in-plane compression and bending) the above investigations can be easily performed with the aid of analytically determined interaction diagrams, which represent limit curves dividing the load space (a space spanned by the contributing load cases, in which the coordinates of each point correspond to a set of load factors) into stable and unstable sub-regions. However, conventional treatment of more complex structures and loading conditions requires a series of buckling analyses with discrete ratios between the contributing load cases to provide a sufficient number of discrete stability limit points on the interaction diagrams. Further inconvenience arises when a standard FE-code with an eigenvalue solver capable of treating proportional loading only is utilized, whereby even the combination of one variable load with one constant load requires an iterative solution with a series of buckling analyses. In lower bounds for buckling load factors delivered by initial linear eigenvalue analyses under interacting load cases were obtained, providing a means for iterative determination of the worst direction in the load space and the corresponding stability limit, i.e., for the treatment of the first of the above items. In the present paper the second item is addressed. Based on the same bounding method a novel algorithm is developed to determine the worst values of the parameter loads and the corresponding stability limit using a standard eigenvalue solver in an iteration scheme with fast, monotone convergence. The method was successfully applied to the buckling analyses of a lightweight structure (an assembly of thin aluminum plates and shells supporting a maximum load of about 8 kN) within CMS (a high-performance, general-purpose particle detector to be commissioned in 2005 at CERN). For four different load case combinations, each consisting of one variable load interacting with one parameter load six individual analyses were sufficient to determine the worst load case combination and the corresponding buckling load factor with a sufficiently high accuracy (error band smaller than 8 %), demonstrating the applicability and efficiency of the new algorithm. Refs. 2 (author)