Collocation Solution for Point-Supported Square Plates

An exact solution for the bending of point-supported orthotropic rectangular thin plates

“…3) under the uniform loading q or central concentrated loading P. The results in nondimensional form ( loDw/qa' for q and lODw/Pa ~ for P) are presented in tables l, 2 and 3. The results in Tables l and 2 show that the central and corner deflection values for the two support cases under the load q and P are very close to the numerical solutions in [3] and [4]. Table 3 shows that as the number of support points is increased, the deflection is observed to tend to that 0fa fully simply supported plate.…”

A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates

“…Nondimensional deflections and bending moments at different locations are tabulated in Table 1 . We first compare the analytic results with those available in the literature 37 , where the collocation method was applied to obtain the deflection distribution along the central line of the plate. Very good agreement is observed.…”

“…Noting that there are only six data available in ref. 37 for the current problem, we perform the refined finite element analysis by the FEM software package ABAQUS 42 to further validate our solutions. The 4-node shell element S4R and 200 × 200 uniform mesh (i.e., with the element size of 1/200 of the plate width) are adopted.…”

“…Several related references are reviewed here, which provide the solutions by numerical results for validation of our approach. Rajaiah & Rao 37 used the collocation method with equidistant points along the plate edge to present a series solution to the problem of laterally loaded square plates simply supported at discrete points around its periphery. Lim et al 29 developed the analytic solutions for bending of a uniformly loaded rectangular thin plate supported only at its four corners, where the symplectic elasticity method was employed and the free boundaries with corner supports were dealt with using the variational principle.…”