Partial discretization solution for flexure of a circular plate

This paper presents an analytical solution for the axisymmetric flexure problem of a rotationally symmetric circular plate using the method of partial discretization of differential equations. The plate is considered under transverse loading and radial boundary action, which lead to a fourth-order differential equation describing the deflection of the plate. Since direct analytical integration of the governing equation may be difficult for non-uniform loading and boundary conditions, the partial discretization approach is applied to transform the original problem into a more convenient analytical-discrete form. Explicit expressions are obtained for the plate deflection, rotation angle, bending moments, and transverse shear force. The derived solution makes it possible to evaluate the influence of radial boundary load on the deformation behavior of the circular plate. Numerical examples and graphical results demonstrate that increasing the radial load leads to a systematic increase in deflection and internal force factors. The obtained results confirm the effectiveness of the proposed method and show its applicability for engineering analysis of circular plates and thin-walled structural elements subjected to axisymmetric loading.