Optimization of Systems in Bending - Conjectures, Bounds and Estimates Relating to Moment Volume and Shape

One of the achievements of optimization theory for plate systems in bending has been the exact solution of a broad range of problems of technical interest. Some of these exact solutions are remarkably simple and could be regarded as moderately practical to actually achieve as built components. But many are complicated, and it is likely that at present unsolved problems will prove to be even more complicated.In the present study, the moment volume (V₀) is the primary quantity of interest. For some shapes of plates in bending V₀ is easily calculated; for others the task is much more difficult. For many problems which have been essentially solved, no V₀ values have been calculated, presumably because of the difficulties involved.Certain conjectures which have been made previously are here applied to obtain V₀ estimates, and also to study the role of plate shape as affecting moment volume. Some observations are made about the practicality of some basic solutions, since, it is argued, practicality must be taken into consideration if the potentials of optimization are to be more widely appreciated.