Optimum design of functionally graded cylindrical shell with piezoelectric layer under moving load

In this paper a method has been developed to obtain an optimum material distribution for a cylindrical shell with Functionally Graded (FG) material and additional piezoelectric outer layer. The objective of the optimization is to satisfy full stress loading criterion. For this purpose; firstly, a solution method has been outlined in which, the governing equations are developrd by combining First order Shear Deformation Theory (FSDT) and Maxwell equations, with the use of Hamilton principle. Dynamic analysis is a major concern in this solution method because of the significant dynamic displacements, strains and stresses due to the effect of moving load. Hence, the time dependent transient responses of the structure and stress distribution have been obtained. At the next stage, a methodology has been introduced to obtain the optimum material distribution. In this method, instead of using pre-assumed material distribution functions which impose limitations to the manufacturing of the shell and also to the optimization solution, control points with Hermite functions are used. The thickness of the shell and volume fraction of the FG material at these points have been regarded as optimization variables. The optimization method is based on the genetic algorithm and to reduce the solution time, calculations are carried out using parallel processing in four cores. The results show that the developed method is capable of analyzing the FG structures and provide optimum solution. The major advantage of this method is its flexibility in providing volume fraction distribution of the material.