Large Deflection of Elastic Plates under Patch Loading

Two methods based on: (1) the direct finite difference approach; and (2) the dynamic relaxation method are presented for the treatment of the elastic large deflection behavior of plates under transverse loading. The merits of the methods in respect of formulation, accuracy, storage and computing time requirements are pointed out together with the main aspects of the finite element method for the analysis of the same problem. The large deflection behavior of square plates under a central patch loading (a concentrated load distributed over a finite area) is investigated. Numerical solutions are offered in a general and condensed form for plates with simply supported and clamped boundary conditions, and for a range of patch sizes. The solutions are shown to be of particular value in the assessment of stresses under a patch loading in practical plate problems. The solutions can serve as a useful guide line for the advanced design of the plate components of plated structures.