Elastic Buckling of Rectangular Plates with Curved Internal Supports

This paper considers the elastic buckling of rectangular plates with curved internal supports. In contrast to commonly used discretization methods, the buckling analysis is performed on a continuum plate domain, including its supporting edges. This is made possible by using the Rayleigh‐Ritz method, which employs the newly proposed pb‐2 Ritz functions. The pb‐2 Ritz functions consist of the product of a two‐dimensional polynomial function (p‐2) and a basic function (b). The basic function is defined by the product of equations specifying the location of the internal supports and equations of the prescribed continuous piecewise boundary shape; in which each of the latter is raised to the power of either 0, 1, or 2, corresponding to free, simply supported, or clamped edge, respectively. Such combination of functions ensures the satisfaction of all kinematic boundary conditions at the outset. The pb‐2 Rayleigh‐Ritz method offers simplicity and easy automation so that very complicated plate shapes and curved internal supports may be solved efficiently and with high accuracy. To illustrate the method, the buckling loads for rectangular plates with straight lines, circular, and cubic curved internal supports are determined.