Postbuckling analysis of columns resting on an elastic foundation

The postbuckling response of perfect and geometrically imperfect elastic columns resting on an elastic Winkler type foundation is thoroughly discussed. This is established by employing an approximate analytic technique leading to very reliable results in the vicinity of the critical state. It was found that the critical state of perfect columns is a stable symmetric bifurcation point and consequently there is no sensitivity to initial geometrical imperfections. Moreover, a simple but readily analyzed mechanical model is proposed to simulate the salient features of buckling mechanism of the column on elastic foundation with those of the model. The simplicity, reliability and efficiency of the proposed analysis as well as the successful modeling of the buckling mechanism of the column by that of a single mode mechanical model are illustrated with the aid of numerical examples.     

Gas chromatographic separation of PF3 substituted group 6 metal carbonyl complexes using serially-coupled capillary columns

The retention of group 6 metal trifluorophosphine carbonyl compounds in serially-coupled gas capillary columns has been studied as a function of different column configurations. For the trifluorophosphine-substituted Mo, W, and Cr carbonyls, as well as the analogous Fe compounds, it was observed that the maximum resolution achievable by the coupled column technique was dependent on the order in which the nonpolar (DB-1) and moderately polar (DB-1701) columns were connected. The optimum configuration was different, however, for each series M(PF₃)_x(CO)_6?x(M = Cr, Mo, or W) or Fe(PF₃)_x(CO)_5?x. It was also observed that the use of coupled columns of dissimilar polarity can, in some cases, actually decrease resolution relative to that obtained by coupled identical columns (i. e. DB-1 + DB-1, or DB-1701 + DB-1701).     

Partial pivoting strategies for symmetric gaussian elimination

In an earlier paper [6] it is shown how the use of symmetric additions of rows and columns enables a stableLDL ^T factorization of symmetric indefinite matrices. In this paper we describe partial pivoting strategies. These strategies are faster than the complete pivoting strategies that were introduced in the first paper. Numerical experiments are included. The results show that some of the new strategies share the stable behaviour of complete pivoting while running almost as fast as the well-known Cholesky decomposition.