Curvilinear finite difference energy method for plate bending analysis

The curvilinear finite difference is applied to the stress analysis of a thin plate subject to lateral load via energy approach. The partial derivatives of the stress and strain expressions are first transformed into the local alpha and beta coordinates before being replaced by curvilinear finite differences in terms of nodal deflections. The total potential energy is computed as the sum of the potential energies summed over the set of non overlapping subdomains associated with each node. A nine node curvilinear mesh is adequate to perform the transformation of partial derivatives except near a corner where an eight node curvilinear mesh is preferred. The curvilinear mesh is in general irregular. The algorithm is readily programmable and a curved boundary requires no special computational treatment. The accuracy and versatility of the procedure are illustrated through numerical solutions to examples. It is concluded that the present method achieves a considerable improvement in computational efficiency (a).