Mechanical Systems

The second class of problems to be addressed was in the field of mechanical systems. Hollow cylindrical shells are able to carry an axial load (acting along the long axis of the shell) far in excess of the weight of the shell. However, even tiny geometrical imperfections in the shape of the shell can vastly reduce the load-bearing capability of the shell. Geometrical imperfections can arise in manufacture or during use, and their shape, depth, and location on the shell are unknown. The designer must be able to evaluate the reduced strength of the shell resulting from uncertain geometrical imperfections. Many probabilistic tools have been developed to deal with this problem. However, verifying a probability model for the spatial uncertainty of the imperfection requires considerable effort. This was an eminently suitable problem for study with the conceptual tools developed for studying unknown spatial distributions of analyte. Indeed, these investigations led to applications in many other areas of mechanics, including vehicle dynamics, pulse buckling, crack growth, and more (Ben-Haim and Elishakoff, 1990).
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