Homogenized and classical expressions for bending solutions offunctionally graded levinson circular plates

Based on Levinson's third-order shear deformation plate theory, axisymmetrical bending of functionally graded material (FGM) circular plates with arbitrary material property variation through the thickness was investigated. First, differential equations were formulated in terms of the displacements governing the axisymmetric bending of the FGM plate under Levinson plate theory. The effects of tension-bending coupling and third-order shear deformation were included in these equations. Then, by using load equivalence relations and the governing differential equation of a homogenous classical plate, the analytical transitional relationship between solutions of FGM circular plates based on the Levinson plate theory and those of the corresponding homogenous ones based on classical plate theory were derived. The analytical formulations of the transition coefficients were given in the expressions. As a result, solutions to static bending of FGM Levinson circular plates can be transformed into those of the corresponding homogenous plates based on classical plate theory and the calculation of the transformation coefficients. ©, 2015, Tsinghua University. All right reserved.