Axisymmetric Problems Of Functionally Graded Circular And Annular Plates With Transverse Isotropy

As a special kind of inhomogeneous materials, functionally graded materials (FGMs), which successfully unify the micro-structures and functions, are superior to the traditional laminated composite materials, and have become a promising field of material science in the present century. Material science has stridden further when the concept of FGM is introduced into Piezoelectricity and Magneto-electro-elasticity.While changing completely the idea of material/structural design, FGMs also result in great opportunities as well as critical challenges for scientific research. In the three-dimensional (3D) analyses available in literature, the following two FGM models have been frequently employed for describing the inhomogeneity of FGM: (1) all material constants vary in the same particular form; or (2) it is approximated by a laminate composed of many thin layers. The first fails due to the diversity of FGMs, and the second is always approximate and may become less efficient for certain problems.In this work, 3D static analyses of axisymmetric problems of FGM circular/annular plates with transverse isotropy are systematically conducted. The stress functions or displacements are expressed in terms of power series with respect to the radial variable, with the coefficients being functions of the axial variable. The analytical solutions, obtained through a step-by-step integration scheme, satisfy exactly the basic equations and boundary conditions on the upper and lower surfaces, but approximately the cylindrical boundary conditions in the Saint Venant's sense. The contributions of the work include(1) 3D analytical solutions of an FGM elastic circular plate subject to a uniformly distributed load or bending moment at its edge;(2) 3D piezoelastic solutions of a functionally graded piezoelectric circular plate subjected to mechanical or electric load;(3) 3D solutions of a uniformly loaded functionally graded magneto-electro-elastic circular plate;(4) The generalization of the method to functionally graded piezoelectric/magneto-electro-elastic annular plate subject to a uniform mechanical load.All analytical solutions can account for the arbitrary variations of the material parameters along the thickness direction of the plate, with all expressions for the elastic/ electric/magnetic field quantities obtained explicitly. The work shall be a breakthrough in the mechanics of inhomogeneous materials since the limits of the available 3D analyses are avoided, and the explicit expressions will facilitate greatly the optimization design of structures based on the concept of FGM.