Method of matched sections as a beam-like approach for plate analysis

Abstract

A new numerical method in application to the plate problem is suggested. It starts from consideration of the rectangular elements, each operating by 6 beam-like parameters: four bending parameters (displacement, angle of rotation, bending moment, transverse force) and two rotation parameters (angle of rotation and twisting moment). So, contrary to the classical FEM approach, the conjugation between the adjacent elements occurs between the adjacent sections rather than in polygon vertexes (nodes), and this gives the name to the method – method of matched sections, MMS. Technically, 6 left-side and 6 lower-side parameters are 12 inlet parameters, while 6 upper-side and right-side parameters are 12 outlet parameters; each element is defined by 24 parameters. Outlet parameters are related to inlet ones by 12 matrix relations, which are derived from the approximate solution of each differential equation (equilibrium, physical, and geometrical equations) of the plate theory. The matrix relation between inlet and outlet parameters is written in a form suitable for applying the transfer matrix method. The numerical examples for the thin and Mindlin plates show the high efficiency and accuracy of the method. In particular, the results for the Mindlin plate for minimal thickness give the same results as the thin plate (no shear locking); the method is insensitive to cases when, for adjacent elements, the ratio of dimensions or ratio of rigidities (elastic constants) differ by several orders of magnitude. The application of the method for the thermal as well as for the vibration problem is considered. The possible extension of the method to any curved geometry is discussed, too.