Discussion: “Isotropic Clamped-Free Thin Annular Circular Plate Subjected to a Concentrated Load” (Adewale, A. O., 2006, ASME J. Appl. Mech., 73, pp. 658–663)

Abstract

In this interesting paper (1), a concentrated load was applied to the clamped-free annular plate. The problem domain was divided into two parts by the cylindrical section where a concentrated load was applied. The author used the Trefftz method (2) to construct the homogeneous solutionDisplay Formulau=∑m=0∞Rm(r)cosmθ (1) in each part. By substituting Eq. 1 into the governing equation, the author could determine Rm(r). Mathematically speaking, the series in Eq. 1 can be seen as the summation of Trefftz bases. To simulate the concentrated force, a circularly distributed force using the Fourier series is used. Then, the author utilized two boundary conditions (BCs) in each part, two continuity, and two equilibrium conditions on the interface to determine the eight unknown coefficients. Variation of deflection coefficients, radial moment coefficients, and shear coefficients along radial positions and angles was presented. However, some results are misleading. To investigate these inconsistencies, both null-field integral formulation and finite element method (FEM) using the ABAQUS are adopted to revisit this problem. In addition, two unclear issues in Ref. 1 are discussed. One is the simulation of concentrated load and the other is the operator of shear force.