A Finite Element Investigation on the Effect of Cross-sectional Warping on Flexural Response of Laminated Composites and Sandwiches using Higher-order Shear Deformation Theory

Abstract

An investigation on the effect of cross-sectional warping on the flexural response of laminates and sandwiches has been presented in this work. A simple C0finite element formulation of a higher-order shear deformation theory for thick and thin laminated composite and sandwich plates have been put forward. The assumed displacement model accounts for nonlinear variation of in-plane displacements and constant transverse displacement through the plate thickness. Moreover, this theory does not require any fictitious shear correction factors generally associated with the first-order shear deformation theory. For thick laminated plates, the bending response is highly affected by the cross-sectional warping. The so-called Mindlin's theory cannot capture this warping phenomenon due to linear variation of in-plane displacements. Only higherorder theories with higher-order terms in the in-plane displacement expression are required to compute displacements and stresses in the correct way. It has been shown that the free shear condition at the top and bottom bounding planes can be imposed in a simple way. The accuracy and validity of the present approach has been established through the numerical evaluation of deformation and stresses and their comparison with the available analytical/3D elasticity solutions and other published finite element results. The results from the present investigation compare fairly well with that of the other methods and finally some important conclusions have been made regarding the basic assumptions of CLT and Mindlin-type theories. It has been established that higher-order shear deformation theories and the modeling of cross-sectional warping are necessary for analyzing thick layered plates, specially soft-core sandwich plates.