Airy stress function for describing the non-linear effect of simply supported plates with movable edges

The general form of the solution of the Airy function for the stress distributions that describe the non-linear effect developed from the large deflection of simply supported plates with movable edges are found by superposition of the Airy functions, which satisfy the large deflection condition and the boundary conditions of the edges. Each term of the Airy function consists of a particular solution and a homogeneous one. The particular solution satisfying the large deflection condition is classified into six cases, depending on the combinations of the modal numbers of the comparison functions. The corresponding homogeneous solution is found to make each Airy function satisfy the boundary condition by using the Fourier series method. The solution is applied to the non-linear analysis of the deflection of the simply supported plates with movable edges under transverse loading, and is verified by comparison with other investigation.