Robust pareto multiobjective optimum design of FG-Beam under moving mass

The optimal selection of Functionally Graded Material (FGM) materials profiles, with regard to cost functions such as weight and stress, is an important issue in the optimization field. In this study, the optimal multiobjective design of FG-beam, subjected to dynamic load as moving mass, has been investigated. Because of the importance of shear stress in FGMs, Timoshenko beam theory has been used in dynamic Analysis. By substituting terms of energy into the Lagrange equation, differential equations of motion are obtained. Displacement fields as a function of time and x-coordinate are calculated by means of the numerical solution of the above-mentioned equations. The mass and velocity of the moving object and the beam’s width were considered certain parameters. Weight and maximum deflection were assumed as cost functions in multiobjective optimization. In addition to the means, the variance of the mentioned cost functions was considered to obtain robust behaviour in an uncertain space of parameters. By using a genetic algorithm, a fraction of constituents and an index of volume fraction (design variables) were selected so that objective functions were optimized. Pareto fronts’ optimum points are presented, and trade-off points are proposed. Cumulative Distribution Function (CDF) curves demonstrated robust behaviour of the expressed design points.