A mechanical model for the buckling of unilaterally constrained rectangular plates

Abstract

A mechanical model is described for the problem of buckling of unilaterally constrained, finite, rectangular plates. Due to the nature of the imposed constraint on the plate's lateral deflection, w, solving for the buckling load required the solution of a nonlinear partial differential equation in w. While the plates were modeled along the lines of classical plate theory, the nonlinearity arose from the fact that the plates were attached to nonlinear elastic foundations exhibiting a deformation sign dependent force-displacement relationship. This feature was introduced to model the unilateral constraint. The influence of different boundary conditions, material orthotropy and transverse load distributions was investigated. For each case, the weak form of the governing differential equation was solved via the Galerkin's method. Investigations of the buckling loads of rectangular plates attached to such foundations and subjected to a uniform inplane stress field showed the validity of this approach for the cases investigated and compared to some previous exact results reported in the literature. NOMENCLATURE generalized displacement (Galerkin's) coefficients (also denoted A) generalized displacement coefficients at I = 0 and Q(x, y) # 0 @ate-bending stiffnesses D,lD, I foundation force pre-buckling inplane loads q(-%9))b4/6,h strain energy density of the elastic foundation plate's dimension in the &direction plate's dimension in the jjdirection displacement function that characterizes the foundation model plate's thickness stiffness parameter transverse load length coordinate E [0, a]

Experimental study and numerical simulation on compressive buckling behavior of thin steel skins in unilateral contact with rigid constraints

“…Seide analyzed a simply supported plate resting on a tensionless rigid foundation [1]. Since then, other studies have prevailed and contributed to the development and understanding of contact buckling including Chai et al [2,3], Shahwan and Waas [4,5], and Ma et al [6][7][8][9][10]. However, most of the above studies only focus on theoretical analysis.…”

Postbuckling analysis of unilaterally constrained laminated thin plates

“…This work was later extended to the case of orthotropic thin plates with simply supported and clamped-free boundary conditions by Shahwan and Waas [2]. The buckling strength of finite size plates with unilateral constraints was studied by Bezine et al [3], Wright [4], Shahwan and Waas [5] and Smith et al [6] using the finite element method (FEM) and Rayleigh-Ritz approaches. All the aforementioned studies were focused on the linear buckling problem, and they all concluded that the unilateral constraints increase the buckling load.…”

Large Deflection Compressional Analysis of Unsymmetric Delaminated Composite Plates with Consideration of Contact Phenomenon

“…They have then used the developed spring simulated model to determine the strain energy release rate of delaminated composite plates [11]. Shahwan et al have used the nonlinear spring distribution between a thin plate which is bonded laterally to a thick plate to analyze the buckling problem [12]. Sleight et al have compared the results for the buckling loads of debonded sandwich panel under compression obtained by using spring distribution between face sheet and core with the corresponding results obtained by utilizing FEM and Rayleigh-Ritz methods separately [13].…”