Bending behaviour of new sandwich structures for future constructions based on the equivalent single-layer trigonometric shear deformation theory

A novel single-layer trigonometric shear deformation theory (TSDT) is proposed for the static bending analysis of sandwich plates and cross-ply laminated composite plates. This theory incorporates the effects of transverse shear deformation and transverse normal strain, which are often neglected in classical plate theories. The TSDT employs a sinusoidal function for the in-plane displacement field and a cosine function for the transverse displacement field through the thickness of the plate. This kinematic assumption provides a more accurate representation of the deformation behavior compared to conventional higher-order shear deformation theories (HSDTs), while maintaining computational efficiency. The governing equations and associated boundary conditions are derived using the principle of virtual work. To validate the accuracy and efficiency of the proposed TSDT, numerical results are obtained for various benchmark problems and compared with those obtained from Reddy's higher-order shear deformation theory, classical plate theory, first-order shear deformation theory, and three-dimensional elasticity theory. The results demonstrate that the TSDT offers accurate predictions of deflections and stresses, particularly in the regions near the edges and interfaces of the layers.