Nonlinear dynamic response of symmetric laminated composite beams under combined in-plane and lateral loadings using full layerwise theory

• A full-layerwise theory is developed to analyse the nonlinear dynamic response of composite beams.
• The studied composite beams are subjected to combined in-plane and lateral loadings.
• The proposed method is capable of predicting the inter-laminar stresses.
• The presented method is suitable to apply for thick composite beams.
• The number of DOFs in this model is markedly less than those used in FEM.

The nonlinear dynamic responses of symmetric laminated composite beams subjected to combined in-plane and lateral loadings are studied in this paper. The composite laminates are modelled using the full layerwise theory (FLWT) based on the advanced first order shear deformation theory (AFSDT). The nonlinear governing differential equations of the laminated composite beams are derived using Hamilton's principle. The partial discretization based on Galerkin method is used to obtain the nonlinear ordinary differential equations (ODEs); in addition, the obtained nonlinear ODEs are solved numerically using step-by-step Newmark-Beta algorithm. In this study, the effects of two different cross-ply lay-up sequences and in-plane loading on the dynamic responses of composite beams are investigated. Moreover, the normal and interlaminar shear stress distributions are obtained. The results of present study are compared with the results of Partial Layerwise theory (PLWT) and validated with the exist results in this field of subject. Furthermore, the obtained results are compared with those obtained from finite element method (FEM) of analysis, which are in good agreement. Beside these, the number of used degrees of freedom in the present method is remarkably less than the FEM, leading to a significant computational cost reduction. Moreover, because of using FLWT, the present method is capable of predicting through the thickness normal stress and strain distributions.