Hybrid-Trefftz finite element model for antisymmetric laminated composite plates using a high order shear deformation theory

A novel hybrid-Trefftz finite element (HTFE) has been developed for the static analysis of thick and thin antisymmetric cross-ply and angle-ply laminated composite plates. For the first time a high order shear deformation theory is used for both the internal and auxiliary displacement fields for constructing the Trefftz functions. The usual tedious approach of converting the system of governing partial differential equations into a single governing equation has been avoided in the present development. The Trefftz functions have been derived from the exact solutions of the homogeneous governing equations of equlibrium. The current HTFE formulation does not need to find the particular solutions of the system of governing partial differential equations. Comparison with exact and analytical solutions reveals that the HTFE developed here is excellently capable of predicting the responses of the antisymmetric laminated composite plates. The Trefftz functions developed here can be used for deriving the polygonal HTFE with any number of sides.