A generalized energy approach to the optimum design of plates and skeletal structures

Abstract

The problem of the optimum design of discretized elastic systems is formulated as an energy extremization problem. Unlike conventional optimality criteria methods in which only the optimality condition itself is derived directly from an energy extremization process, the approach proposed here derives all the pertinent equations of the problem, viz. (1) the governing equations of equilibrium; (2) the optimality criteria; and (3) the constraint equations; from the stationary conditions of a single functional. To accomplish this, the constraints on stresses, deflections, fundamental frequencies and critical buckling loads are posed in the form of equivalent potentials. It is shown that the construction of a functional with the required stationary properties necessitates the invocation of the adjoint system. The main advantage of this formulation is that all categories of excitation, constraint conditions and structural types can be put into a unifying framework of energy extremization and the redesign procedure is a simple scaling process. A further advantage is that the design of non-conservative systems, hitherto formulated as a separate class, belongs naturally to this unifying framework.