A semi-analytical solution on static analysis of circular plate exposed to non-uniform axisymmetric transverse loading resting on Winkler elastic foundation

This paper is concerned with static analysis of functionally graded (FG) circular plates resting on Winkler elastic foundation. The material properties vary across the thickness direction so the power-law distribution is used to describe the constituent components. The differential transforms method (DTM) is utilized to solve the governing differential equations of bending of the thin circular plate under various boundary conditions. By employing this solution method, governing differential equations are transformed into recurrence relations and boundary/regularity conditions are changed into algebraic equations. In this study, the plate is subjected to uniform/non-uniform transverse load in two cases of boundary conditions (clamped and simply-supported). Some numerical examples are presented to show the influence of functionally graded variation, different elastic foundation modulus, and variation of the symmetrical transverse loads on the stress and displacement fields. Based on the results, the obtained out-plane displacement coincide with the available solution for a homogenous circular plate. It can be concluded that the applied method provides accurate results and it is easily used for static analysis of circular plates on an elastic foundation.