Abstract
A numerical procedure is proposed for the solution of the biharmonic equation for deflections of uniformly loaded plates with all edges clamped. It is shown that the quantity ∇2w at the plate boundary can be determined numerically by noting a linear relationship between ∇2w and w in finite-difference form at the boundary. According to the classical methods of solution, the quantity ∇2w at the clamped edge cannot be determined in advance. The new approach is based on the boundary vorticity method for the vorticity transport equation governing a steady two-dimensional incompressible fluid flow. By using the new procedure, it is now possible to replace the biharmonic equation for clamped plates by two second-order partial differential equations of elliptic type similar to those for simply supported plates with straight edges. The possibility of extending the procedure to various problems in plates and shells is pointed out. The study also serves to illustrate a close relationship between a class of fluid mechanics problems and a class of plate and shell problems.
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