Abstract
In this paper, an analytical method is presented in order to determine the static bending response of an axisymmetric thin circular/annular plate with different boundary conditions resting on a spatially inhomogeneous Winkler foundation. To this end, infinite power series expansion of the deflection function is exploited to transform the governing differential equation into a new solvable system of recurrence relations. Singular points of the governing equation are effectively treated by applying the Frobenius theorem in the solution, which in turn permits the use of more-general analytical functions to describe the variation of the foundation modulus along the radius of the plate. Moreover, no special limitation is imposed on the transverse loading function as applied to the system. On employing the proposed method, the deflection response is obtained through an illustrative example for various boundary conditions along the plate edges, considering free, clamped, hinged, and elastically restrained boundaries. In addition, analytical results are validated and compared with those obtained using a finite element analysis, where an excellent agreement is found. Finally, the extension of the method to solve the more-general case of a variable two-parameter (Pasternak) foundation is indicated.
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