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Frames are important structures found in many transportation applications such as automotive bodies and train cars. They are also widely employed in buildings, bridges, and other load bearing designs. When a frame is carrying multiple loads, it can potentially risk a catastrophic buckling failure. The loads on the frame may be non-proportional in that one force stays constant while the other is increased until buckling occurs. In this study the buckling problem is formulated as a constrained eigenvalue problem (CEVP). As opposed to other CEVP in which the eigenvectors are forced to comply with a number of the constraints, the eigenvalues in the current CEVP are subject to some equality constraints. A numerical algorithm for solving the constrained eigenvalue problem is presented. The algorithm is a simple trapping scheme in which the computation starts with an initial guess and a window containing the potential target for the eigenvalue is identified.

Countless articles and publications3,4,5 have documented and proven the efficacy, benefits and value of operating within a lean system. Furthermore, there exists common agreement amongst leading organizations successfully implementing a lean system that in order to do so it must take into consideration the entire enterprise, that is, from supplier to customer and everything in between6. One of the core issues this paper addresses is when the optimal time is to train and educate the people who currently have, or will have, influence over the ‘enterprise’.