Moving least square Ritz method for vibration analysis of plates

Abstract

This paper presents a novel numerical method, the moving least square Ritz method (MLS-Ritz), for free vibration analysis of classical thin plates. The proposed method utilizes the strength of the moving least square approach to define the Ritz trial function for the transverse displacement of the plates. A set of points is pre-selected on the calculation domain of a plate that forms the basis for the MLS-Ritz trial function. The edge support conditions of the plate are satisfied by forcing the boundary points to meet the geometric boundary conditions of the plate via a point substitution technique. Virtual points (points outside the plate domain) are introduced for clamped edges to improve the convergence and accuracy of the calculations. Square and right-angled isosceles triangular plates of various combinations of edge support conditions are selected to examine the validity and accuracy of the MLS-Ritz method. Extensive convergence studies are carried out to investigate the influence of the MLS mesh size, the MLS support radius, the number of Gaussian integration points and the shape of the MLS weight function on the proposed method. Comparing with the existing Ritz methods, the MLS-Ritz method is highly stable and accurate and is extremely flexible for dealing with plates of arbitrary shapes and boundary conditions.