A New Numerical Method for Axisymmetrical Bending of Circular Plates with Large Deflection

Abstract

A simple and efficient spline integral equation method is presented in this paper for the axisymmetrical bending of circular plates with large deflection. Based on two second-order differential equations in terms of the slope of the deflection surface and the radial displacement of the circular plate, two integral equations are derived. The circular plate is then equidistantly divided into a circular plate element and a series of annular plate elements along its radial direction and the slope of the deflection surface and the radial displacement are both approximated by cubic spline interpolation. The two integral equations are solved numerically and the displacements and internal forces at any point within the circular plate can be obtained. Finally, some numerical results are presented for illustrating the validity of the proposed method. It can be concluded that the proposed numerical method can be used to analyze circular plates with large deflection with reasonable accuracy.