Optimal design of laminated composite plates in a fuzzy environment

Abstract

The present study focuses on a fuzzy optimization approach to the optimal design of simply supported laminated composite plates. The goal is minimum weight design of the composite plates. The design constraints are the magnitude of center displacement and lamina failure criteria. A procedure of two-level optimization in a fuzzy environment is presented and this procedure is applied to the design of laminated composite plates to consider the influences of fiber direction and thickness of each lamina separately. It is shown that the membership function in the case of failure can be deduced from continuum damage mechanics. The membership function for failure criteria is the function of the internal state variable for degree of damage in the continuum damage mechanics. The modified Weibull membership function is chosen to be used as a simple case of damage progression. The finite element method is used to calculate the displacement of the plate and the stresses of each lamina. The fuzzy optimization formulation as a max-min problem is transformed into a classical one. This classical optimization problem is solved using the augmented Lagrange multiplier method with the quasi-Newton method. Two examples are solved to demonstrate the procedure. From the results, it is shown that optimal design of laminated composite plates is more useful in a fuzzy environment and the modified Weibull membership function characterizes the fuzziness of failure. Nomenclature bi = upper limit of the inequality constraint D = fuzzy decision f(X) = objective function f(X) = fuzzy goal