A variational asymptotic theory of composite laminated plates: Hybrid transformation to Reissner-Mindlin model

In previous work, a 2D plate model for composite laminates without invoking ad hoc kinematic assumptions is constructed by modifying the asymptotically correct energy functional up to the desired order. However, it is not possible in general to construct an asymptotically correct Reissner-Mindlin model for practical use. To obtain the energy functional that is of practical use, a different manner from the previous works is introduced in this paper. By performing a hybrid transformation procedure composed of modified equilibrium and compatibility equations, all partial derivative terms on the energy functional are systematically eliminated to obtain the 2D generalized and transverse stiffness matrices for the Reissner-Mindlin model. Unlike the previous works, these is no need to relax the established warping constraints and perform the optimization procedure as an unnecessary approximation. Several numerical examples are presented to compare with the classical laminated theory as well as 3D exact solutions, demonstrating the capability and accuracy of this new method.