A general assessment of a new inverse trigonometric shear deformation theory for laminated composite and sandwich plates using finite element method

Abstract

In this study, a general assessment of inverse trigonometric shear deformation theory, recently developed by the authors, is performed and the structural responses (static, buckling, and free vibration) of laminated-composite and sandwich plates are investigated. The in-plane displacement components are expressed in terms of an inverse cotangent function, which yields the nonlinear shear deformation while the constant transverse displacement is assumed over the thickness of the plate. A computationally efficient finite element model for the implementation of above-mentioned theory is proposed. The continuity requirement of the finite element model is maintained as C0 by a suitable choice of nodal field variables. Numerous analysis problems are selected to study the effects of various parameters such as span-to-thickness ratio, lamination sequence, loading conditions, boundary conditions, etc. on the response characteristics of plates. Higher modes are also obtained for the buckling and vibration problems and the ability to investigate higher modes is ensured. The comparison of the present results with the established results in literature indicates the efficiency and range of applicability of the present formulation. Moreover, the formulation is presented in a generalized approach which enables the implementation of all existing seven degree-of-freedom theories in a single computer algorithm thereby making it practically more significant.