Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system

Abstract

A complete and consistent 3-D set of field equationshas been developed by tensor analysis to characterizethe behavior of FGM thick shells of revolution with arbitrarycurvature and variable thickness along the meridionaldirection. A sixth order set of differential equations of motionin terms of displacement components were also developedfor functionally graded materials. Developed withrespect to the curvilinear coordinate system are a set ofpartial differential equations for the three displacementcomponents. The equations derived could be used to determinestresses and/or to analyze the vibrations in thickshells of revolution.Assuming that material properties vary nonlinearlyin the radial direction, and the Poisson’s ratio is constant,exact solutions for stresses and displacement in afunctionally graded (FGM) pressurized thick-walled hollowcircular cylinder are obtained under generalized planestrain and plane stress assumptions, respectively. Displacement and stress distributions dependingon an inhomogeneity constant are compared with the solutionsof the finite element method and are presented in theform of graphs. The exact solutions and the solutions carriedout through the finite element method show goodagreement.