Mass optimization of functionally graded plate for mechanical loading in the presence of deflection and stress constraints

In this work, a method for the single-objective optimization of material distribution of simply supported functionally graded isotropic plates is presented. The material composition is assumed to vary only in the thickness direction. Piecewise cubic interpolation of volume fractions are used to calculate volume fractions of constituent material phases at a point; these fractions are defined at a limited number of evenly spaced control points. The effective material properties of the plate are obtained by applying linear rule of mixtures. Behavior of functionally graded plate is predicted by the assumptions of the third-order shear deformation theory of Reddy. Exact solutions for deflections and stresses of simply supported plates are presented by using Navier type solution technique. Those volume fractions at control points that are selected as decision variables are optimized by two evolutionary algorithms: (1) Real-coded genetic algorithm and (2) particle swarm optimization algorithm. Three models are optimized as primary goal to verify the capability and efficiency of the proposed model with flexibility and stress constraints under various transverse loads. Secondary goal of this article is survey accuracy and convergence of two algorithms aforementioned. The proposed framework for designing functionally graded plates under pure mechanical conditions has been furnished by the founded results.