Numerous research publications purport to give in-plane buckling loads for unsymmetrically laminated composite plates. In many of these cases, bifurcation buckling is impossible; that is, transverse deflection is initiated, regardless of the magnitude of the loading. In the present work, finite element studies are made of four types of unsymmetrical laminates, including antisymmetrical ones. Twelve sets of edge constraints are considered. Maximum values of transverse deflection are determined for uniform and linearly varying in-plane boundary forces, including uniaxial, biaxial, and shear. Cases where the plate remains flat are thereby also identified. Results confirm a theoretical analysis previously made. Cases for which improper buckling results are often reported in the published literature are identified.

Buckling or transverse deflections of unsymmetrically laminated plates subjected to in-plane loads

Nondestructive experimental methods to calculate the buckling load of imperfection sensitive thin-walled structures are one of the most important techniques for the validation of new structures and numerical models of large scale aerospace structures. Vibration correlation technique (VCT) allows determining equivalent boundary conditions and buckling load for several types of structures without reaching the instability point. VCT is already widely used for beam structures, but the technique is still under development for thin-walled plates and shells. This paper intends to explain the capabilities and current limitations of this technique applied to two types of structures under buckling conditions: flat plates and cylindrical shells prone to buckling. Experimental results for a flat plate and a cylindrical shell are presented together with reliable finite element models for both cases. Preliminary results showed that the VCT can be used to determine the realistic boundary conditions of a given test setup, providing valuable data for the estimation of the buckling load by finite element models. Also numerical results herein presented show that VCT can be used as a nondestructive tool to estimate the buckling load of unstiffened cylindrical shells. Experimental tests are currently under development to further validate the approach proposed herein.

Vibration Correlation Technique for the Estimation of Real Boundary Conditions and Buckling Load of Unstiffened Plates and Cylindrical Shells

Buckling load prediction of grid-stiffened composite cylindrical shells using the vibration correlation technique

Advances in the understanding of vibration and buckling behavior of laminated plates made of filamentary composite material are summarized in this survey paper. Depending upon the number of laminae and their orientation, vibration and buckling analyses of composite plates may be treated with: (7) orthotropic theory, (2) anisotropic theory, or (3) more complicated, general theory involving coupling between bending and stretching of the plate. The emphasis of the present overview is upon the last. Special consideration is given to the complicating effects of: inplane initial stresses, large amplitude (nonlinear) transverse displacements, shear deformation, rotary inertia, effects of surrounding media, inplane nonhomogeneity and variable thickness. Nonclassical buckling considerations such as initial imperfections are included, as well as postbuckling behavior.

Advances in Vibration, Buckling and Postbuckling Studies on Composite Plates

Buckling loads and modes of flat composite laminates were measured and compared with theory. Laminates were subjected to simply supported boundary conditions and biaxial loading. Displacements were measured both mechanically using dial gages and optically using shadow moire. Predictions were obtained numerically using the Galerkin method. Buckling loads were measured during 49 tests. Overall, measurements confirmed expected trends. Buckling loads increased with an increase in transverse tensile loading as predicted. Measured buckling modes were also well predicted, including an observed increase in mode number with an increase in transverse tensile loading. Measured buckling loads were not as well predicted, and substantial error was encountered during individual tests. Discrepancies between measurement and prediction are reported in terms of the percentage error in prediction. The average and standard deviation in percentage error for 49 measurements was 1.6 percent ±15.4 percent. These discrepancies are thought to be due to specimen imperfections, difficulties in simulating truly “simply supported” boundary conditions and/or nonuniform loading of the composite panels.

Y. Hans

Papers

Experimental study of the buckling of laminated composite columns and plates