Multi-objective optimization of a functionally graded sandwich panel under mechanical loading in the presence of stress constraint

Abstract

A method was presented for multi-objective optimization of material distribution of simply supported functionally graded (FG) sandwich panel, and sensitivity analyses of optimal designs were also conducted based on design variables and objective functions. The material composition was assumed to vary only in the thickness direction. Piecewise cubic interpolation of volume fractions was used to calculate volume fractions of constituent material phases at a point; these fractions were defined at a limited number of evenly spaced control points. The effective material properties of the panel were obtained by applying the linear rule of mixtures. The behavior of FG sandwich panel was predicted by Reddy’s assumptions of third-order shear deformation theory. Exact solutions for deflections and stresses of simply supported sandwich panel were presented using the Navier-type solution technique. The volume fractions at control points, material, and thickness of the faces which were selected as decision variables were optimized by a multi-objective evolutionary algorithm known as the fast and elitist multi-objective genetic algorithm (NSGA-II). The mass and deflection of the model were considered the objective functions to be minimized with stress constraints. This model was optimized to verify the capability and efficiency of the proposed model under mechanical loading. The framework proposed for designing FG sandwich panel under pure mechanical conditions was furnished by the results.

Keywords

• functionally graded materials
• genetic algorithm
• mechanical loading
• multi-objective optimization
• sandwich panel