Linear Transformation Relationships Of The Static And Dynamic Responses Between Functionally Graded And Houmogenous Plates

Functionally Graded Materials (FGM) as a new type of inhomogeneous material, because of its innovative design ability and the excellent performance that the traditional composite materials can never match; it has become a kind of selected material to be used in new structures. So, more attentions have been paid on the research of mechanical behaviors of FGM structures. In this paper, we are giving the material properties of FGM plates changing continuously along the thickness direction, the relationships of the static and dynamic responses between FGM plates and those of uniform plates were investigated, based on the classical plate theory (CPT) and the first-order shear deformation theory (FSDT) respectively. Therefore, some innovative numerical results which can be used in engineering conveniently were obtained. The main research including the following three parts:1. Under the assumption of axisymmetric deformation, the interrelations of bending, buckling and free vibration between FGM circular plates and those of homogenous circular plates were studied based on the CPT. a similarity of the displacement-type governing equation of FGM plates with that of homogenous plates was found by theoretical derivation. Therefore, Analogous transform relations between solutions of two different circular plates were derived in analytical forms. As a result, the solution of FGM circular plates can be transformed to the calculation of the same homogenous circular plate, and to compute the non-homogenous transition parameter under the same size, loadings and boundary conditions.2. On the bases of above works, transformation relationships of bending solutions between FGM and homogenous circular plates were further studied based on the FSDT. First, by delimiting the in-plane and transversal displacements, the governing equations for the rotational angles of FGM circular plates were obtained. And according to the similarity theory of differential equations, linearly dependant relationship of rotational angles that exists between FGM circular plate and homogenous one was found. Then through analyzing the equilibrium equations in the transverse direction and the analogous transformation relation of the deflections based on the CPT, a linear relationship between the deflections of FGM circular plate based on FSDT and that of homogenous one based on the CPT were finally derived. As a result, solutions for static bending based on the FSDT of a non-homogenous circular plate can be reduced to that based on the CPT of a homogenous one and the calculation of the transformation factors. The result also shows that there are't exist a strict transformation relationship of the deflections between FGM circular plate based on FSDT and that of homogenous one.3. Based on the CPT, the relations of static and dynamic responses between FGM plates and homogenous circular plates were further studied in the rectangular coordinate system. Firstly, governing equations for bending, buckling and free vibration of FGM plates were established. To eliminate the coupling term of in-plane displacement by introducing in-plane displacement potential function, so the displacement-type governing equations of FGM plate were derived. At last, Analogous transform relations of bending deflection, critical load and natural frequency between FGM circular plates and those of uniform circular plates were obtained, through analyzing the similarity between the governing equations of FGM plate and those of the homogenous plate.