Bending Analysis of Mindlin Plates by Extended Kantorovich Method

Abstract

In this paper, the extended Kantorovich method originally proposed by Kerr is further extended to the bending problem of rectangular Mindlin plates. A substantial extension made in this study, in addition to the employment of the Mindlin theory, is the use of multiterm trial functions. This eventually requires an iterative procedure at each iteration step of which a set of simultaneous ordinary differential equations (ODEs) must be solved. Despite the use of a state-of-the-art general-purpose ODE solver, which is supposed to be able to solve the derived system of ODEs to a user specified set of error tolerances, numerical stability proved to be a prohibitive obstacle if left untreated, especially when more terms are used and for thin plates. To ensure numerical stability and to overcome the “shear locking” difficulty, an orthogonalization technique is proposed that maintains good independence of each term of the trial functions. This enables virtually any number of trial function terms to be accommodated with excellent numerical accuracy and stability. Several typical numerical examples given in the paper consistently show that the proposed method performs excellently even in extreme cases such as extremely thin plates and the steep variation of internal forces near the free edges.