Discrete Ritz method for buckling analysis of arbitrarily shaped plates with arbitrary cutouts

• Published in: Thin-walled structures 2023-12, Vol.193, p.111294, Article 111294
• Main Authors: Jing, Zhao, Duan, Lei
• Format: Article
• Language: English
• Subjects: Arbitrarily shaped plates; Buckling; Cutouts; Discrete Ritz method (DRM); Gauss quadrature
• ISSN: 0263-8231; 1879-3223
• DOI: 10.1016/j.tws.2023.111294

•A novel general numerical method, discrete Ritz method (DRM), is proposed for buckling analysis of arbitrarily shaped plates with arbitrary cutouts.•DRM combines the extended interval integral, Gauss quadrature, and variable stiffness, and builds a discrete energy system over a standard rectangular domain.•Cutouts with zero stiffness are used to simulate the shape of plates as well as inner cutouts.•Using variable stiffness and Gauss integration points in combination, DRM discretizes energy and uses cutouts to control the geometric boundary of the plate.•Standard energy functionals are established within a rectangular domain in terms of cutouts for arbitrarily shaped perforated plates, making the computation procedure standard. To overcome the difficulties of the Ritz method when dealing with complex geometric domain problem, a novel general numerical approach, discrete Ritz method (DRM), is proposed for buckling analysis of arbitrarily shaped plates with arbitrary cutouts. Accounting for a variety of boundary conditions, Legendre polynomials are adopted to construct the admissible function. By using the global trial function with variable stiffness properties within a virtual rectangular design domain, the deformation of arbitrarily shaped plates can be captured with the help of numerical integration using Gauss quadrature. The shapes and cutouts of plates are both numerically simulated by using cutouts, where the stiffness is assigned zero within the cutouts in the virtual rectangular domain. Moreover, boundary conditions and load potential can be applied to any contour of the plate. Based on the above formulation, standard energy functionals and computation procedures are established to extract the buckling eigenvalues and mode shapes. Variously shaped plates with arbitrarily shaped cutouts are investigated. Under several boundary conditions, multiple inplane loads are applied, and the results are compared with those obtained by other numerical and analytical methods in the literature. Demonstrating the stability and accuracy of the DRM.