Optimal Plastic Design with Imprecise Data

Abstract

The well‐known formulation of the optimal design of plastic frames presupposes that all the relevant data are known deterministically. It is realistic to recognize that more usually this information is known only imprecisely. In the paper it is shown how imprecision regarding the stipulations may be encoded in a fuzzy programming format and how this class of problems can be transformed to a standard linear programming form. Two methods are outlined. In the first the objectives are restated as fuzzy goals and incorporated in the constraint set. The optimal solution is that solution which maximizes the grade of membership within the constraints. This maximal grade of membership can be considered to be a measure of the degree of acceptability of the design in the face of the imprecision of the data. The second method retains the original objective function and adds an additional constraint which sets a lower limit on the degree of acceptability. Both methods involve only a slight increase in computational effort when compared with the corresponding deterministic formulation. Some numerical illustrations are presented.