HAM-Based Prediction of Circular Thin Plate Deflection Under Four Boundary Conditions

Abstract This study presents an analytical investigation of the non-linear deformation behavior of circular thin plates subjected to concentrated loads under four different boundary conditions: fixed-clamped, movable-clamped, simple-supported, and simple-hinged supports. Firstly, the Homotopy Analysis Method (HAM) is employed to derive a series of convergent solutions for each case, providing insights into the relationship between the applied load and the resulting central deflection. Secondly, the deformation patterns are analyzed and compared with numerical results to validate the accuracy of HAM. The findings demonstrate that HAM effectively captures the influence of edge constraints on deformation behavior, with the highest stiffness observed in the fixed-clamped condition. Finally, this research offers valuable references for structural engineers, particularly in applications where rapid evaluation of load-deflection characteristics is essential. The study contributes to advancing analytical techniques for structural analysis and provides a robust framework for addressing complex boundary conditions in thin plate theory.