The nonlinear response of unsymmetric multilayered plates using smeared laminate and layerwise models

Abstract A continually growing interest in the response of unsymmetric multilayered plates is apparent. Analyses were recently completed addressing the load-deflection behaviour of these plate geometries. The characteristic feature of the analyses is the use of nonlinear strain-displacement relations, even at low loading levels, in reaction to the large-deflection effect enhanced by the bending-extension and twisting-shearing coupling. Approaches where use is made of Higher Order Shear Deformation Theories (HSDT) for predicting global quantities, such as deflections and critical loads, are not found in the open literature. Such modelling approaches, in particular those of the layerwise type, are reserved to predict distributions across the thickness. Thus, a further assessment of the influence of the transverse shear effect on global quantities should be required. To give some preliminary contributions on this subject, the load-deflection behaviour of a [90 4 /0 4 ] cross-ply plate with pinned edges, subjected to cylindrical bending under uniform transverse pressure, is investigated. Use is made of the Layerwise Higher Order Shear Deformation Layerwise Theory (RHSD) to serve this purpose. From the numerical results presented, the influence of modelling is enhanced or reduced, depending on the sign of loading. It is concluded that, depending on the loading, boundary conditions and lay-up, higher-order approaches can be used for predicting global quantities in unsymmetric multilayered plates. In order to investigate stability, nonlinear equations are developed where critical points are located under boundary and combined loading conditions which vary during perturbation.

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