## Introduction

## Concentrated Load

## Definition of Shear Force

## Alternative Derivation of the Analytical Solution Using the Null-Field Integral Formulation

## Results and Discussions

In order to verify the accuracy of Adewale’s results, two alternatives, null-field approach and FEM using ABAQUS, are employed to revisit the annular problem. A concentrated load was applied at the radial center of the annular plate, as shown in Fig. 2. For the clamped-free boundary condition, Figs.3a,3b show the displacement contours for the Green’s function by using FEM (ABAQUS) and the present method, respectively. Good agreement is obtained between our analytical solution and FEM result although Adewale (1) did not provide the displacement contour of his analytical solution. For comparison with the available results in Ref. 1, Fig.4 shows the variation of deflection coefficients, moment coefficients, and shear force coefficients along radial positions or angles for different inner radii. It is also found that FEM results match well with our solution but deviates from Adewale’s outcome (1).

## Concluding Remarks

To verify the accuracy of Adewale’s results and to examine the response of the clamped-free annular plate subjected to a concentrated load, the null-field integral formulation was employed in solving this problem. The transverse displacement, moment, and shear force along the radial positions and angles for different inner radii were determined by using the present method in comparison with the ABAQUS data. Good agreements between our analytical results and those of ABAQUS were made but deviated from Adewale’s data. The outcome of Adewale’s results may not be correct.