Damped Vibration and Optimization of the Geometrical Parameters of FG Stiffened Cylindrical Shells Resting on Elastic Foundation Using GA

Abstract

Functionally graded materials with their structural characteristics, such as the type of distribution, the size of phases, gradually change from one surface to another and provide a wide range of applications. In this research, the optimization of geometric parameters of FG structure rested on the elastic foundation, including damping effects is of interest. The cylindrical shell’s material properties are assumed to vary smoothly and continuously across the thickness according to the power law distribution of the volume fraction of constituents. The governing equations of stiffened functionally graded cylindrical shell resting on an elastic foundation are obtained using Hamilton’s principle, the first-order shear deformation theory and finite element method. The numerical results are obtained for studying the effect of various factors, such as distribution of volume fraction, length and thickness, different boundary conditions, stiffness and damping coefficients, and also the natural frequency of the dynamic responses of the cylindrical shell. The damping effects are considered which were not presented in previous studies. The frequency responses of the cylindrical FGM shell resting on elastic foundation were obtained by adding the damping term into the governing equations. Besides, analytical formulation results were considered as an objective function (input) for optimization in Genetic Algorithms. Finally, the compatibility of the analytical modeling results with the commercial finite element software was checked which showed good agreement.