General Theory of Optimal Layouts for Elastic Structures

Abstract

A general theory is presented for optimizing the layout of elastic structures for a prescribed deflection at a given point. This development is an extension of an earlier layout theory which was derived in the context of optimal plastic design and based on optimality criteria. After comparing the ``classical'' layout theory for low-density, grid-like structures with the ``advanced'' layout theory for elastic continua having a high material volume/feasible volume ratio, general optimality criteria are developed for both non-vanishing (optimal) and vanishing potential members of elastic systems having a prescribed deflection. The above theory is then applied to elastic circular grillages (beam-grids or truss-grids) with a given central deflection. It is shown that a grillage or uniform stiffness has almost 41% higher weight than that of the optimal solution. In light of some recent work the above theory is being applied to the optimization of solid plates.