Unified Solution Method of Rectangular Plate Elastic Bending

摘要

The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of boundary, such as simply supported edge, clamped edge, free edge, free corner point and pillar support corner point, can be solved under arbitrary loads, such as the loads on plate, the loads in plate edge, the load at free corner point, and when the plate edge and the pillar support corner point have settlement or when the plate edge has rotation. The method can organically unite the Navier solution and the Levy solution and has the advantages of rapid convergence and high precision.