The Stability and Post-Buckling State of a Rectangular Disk Under Unidirectional Bending and Simultaneous Shear

The problem stated in the title concerns an isotropic, rectangular disk, simply supported along its edges. In order to obtain an approximate solution of the problem, the deflection function w(x,y) describing the middle surface of the disk after stability loss is assumed in the form of the series which satisfy the boundary conditions of the problem. The Airy's stress function D (x,y) was also introduced.
To determine these functions, the Kármán differential equations of the nonlinear theory of plates were used. The parameters in the deflection function w (x,y) were determined by means of the Bubnov-Galerkin method.
As a result of this, equations from which the stress and strain components could be determined by dimensionless coefficients were obtained. These equations were then used for detailed computations of the disk for which the ratio of the edge lengths =a/b=0.9. The results of computations were presented in the form of graphs prepared in a form useful for practical calculations.