Analysis of general quadrilateral orthotropic thick plates with arbitrary boundary conditions by the Rayleigh–Ritz method

Abstract

SUMMARYA numerical method is developed for the analysis of general quadrilateral, moderately thick orthotropic plates having arbitrary boundary conditions. The procedure is based on the application of the RayleighRitz method in conjunction with the Reissner-Mindlin thick plate theory. A set of complete polynomials in terms of natural co-ordinates comprising of boundary and domain terms, which satisfy the boundary conditions, is deployed as the basic functions to approximate the real displacement ÿeld. The generalized displacements and the eigenvalues are determined by imposing the principle of stationary potential energy. Although the procedure has the ability to solve problems involving thick quadrilateral plates, the numerical examples presented are mostly for skew plates. The results herein are compared with their counterparts determined by other investigators.

On the application of the Ritz method to free vibration and buckling analysis of highly anisotropic plates

“…Examples can be found in Refs. [11][12][13], where different boundary conditions can be handled by proper modification of the trial functions. While different kinds of polynomial expansions were found to have similar convergence properties, they are generally characterized by dissimilar stability properties [14].…”

Local buckling of FRP thin-walled plates, shells and hollow sections with curved edges and arbitrary lamination

“…Application of the Rayleigh Ritz energy method for calculating the local buckling capacity of composite laminated rectangular plates has been extensively studied by multiple authors [27,28]. In this section, a methodology to extend the existing work to non-rectangular plates is presented.…”

Post-buckling analysis of cracked multilayered composite plates by pb-2 Rayleigh–Ritz method

“…(17) where the trial functions wðn; gÞ have to be appropriately selected. In the present paper the chosen approximation is based on the so-called pb-2 interpolation scheme [14,43,44] in which the interpolation of the generic unknown displacement function f, with f 2 fu; v; w; # x ; # y g, is assumed as where the exponents c i can take the values 0 and 1 according to the condition of constrained or unknown value of f along the side described by the power base corresponding to the considered exponent (see Table 1 …”

“…Focusing on FSDT modeling solved by the Rayleigh-Ritz method, which is the subject of the present paper, different kind of trial functions have been proposed, proving the suitability and effectiveness of such an approach for static, free vibrations, buckling and postbuckling analysis of composite laminates. Liew [10] proposed the use of the p-Ritz method with a set of self-generating orthogonal polynomials; Wang [11], Cheung and Zhou [12]and Zhou [13] employed Timoshenko beam B-spline and functions, respectively; Saadatpour et al [14] used a set of complete polynomials in terms of natural co-ordinates comprising of boundary and domain terms, which satisfy the boundary conditions; Tamijani and Kapania [15] investigated the approximation by Chebyshev polynomials; Rango et al [16] used beam orthogonal polynomials as coordinate functions whereas Eftekhari and Jafari [17,18] formulated a Ritz procedure in which natural boundary conditions are implemented in an averaging manner; Liew and co-workers [19,20] proposed the mesh-free kp-Ritz method which is based on the kernel particle approximation for the field variables and more recently they introduced the solution by the improved moving least square approximation of the displacements (e.g. Ref.…”