Buckling analysis of shear deformable plates using the quadrature element method

Abstract

a b s t r a c tThe recently proposed weak form quadrature element method (QEM) is applied to buckling analysis of shear deformable plates. Integrals involved in the variational description a plate are evaluated first by an efficient numerical integration scheme wherein the partial derivatives at the integration points are approximated using differential quadrature analogs. In a quadrature element, neither the node pattern nor the number of nodes is fixed, being adjustable according to convergence need. Three examples are presented and comparison with finite element results is made to demonstrate the effectiveness and computational efficiency of the QEM for buckling analysis of shear deformable plates.

A weighted extended B-spline solver for bending and buckling of stiffened plates

“…The pre-buckling stress field has been computed by means of the method in section 3.2. This stress field is then used to solve the buckling problem (10) by the present method with splines of degree p The results by Zhong et al were digitized from figure 13 in [14]. The present results lie neatly on top of the graph by the data obtained by [14].…”

“…This case has been solved in several works, for example [47,14,16]. A square plate with a free hole in its center is uniformly loaded in-plane at its left and right boundary, cf.…”

“…This stress field is then used to solve the buckling problem (10) by the present method with splines of degree p The results by Zhong et al were digitized from figure 13 in [14]. The present results lie neatly on top of the graph by the data obtained by [14]. In addition, we checked that, apart from the smallest hole for h = 0.1, the present results are indistinguishable on a plotting scale for h = 0.025, 0.05, 0.1.…”

“…The physics and methods for plate bending and buckling problems with stiffener arrangements are treated and reviewed in [2,3,4,5]. There is a relatively long history on the numerical treatment of the plate bending and buckling equations, for which the finite element method [6,7,8,9], the boundary element method [10,11,12], the finite strip method [13] and the quadrature element method [14] probably account for the most widespread methods. Another class of methods are the sometimes called semi-analytic methods based on Navier's sine solution.…”

Geometrically nonlinear transient analysis of thick deep composite curved beams with generalized differential quadrature method

“…The general form combines the advantages of both GDQ method and FEM is often referred to as generalized differential quadrature element method (GDQE) [32]. Recently GDQ method was also included in the weak form solution of differential equations in which derivatives of field variables are calculated with GDQ method [33][34][35][36]. This method is called as weak form quadrature element method [35].…”