On the general framework of high order shear deformation theories for laminated composite plate structures: A novel unified approach

This paper brings to the readers a unified framework on higher order shear deformation theories (HSDTs), modelling and analysis of laminated composite plates. The major objective of this work is to (1) unify all higher order shear deformation theories in a unique formulation by a polynomial form; (2) propose the new higher shear deformation models systematically based on a unified formulation. In addition, the effect of thickness stretching is taken into account by considering a quasi-3D theory. The principle of virtual displacements is exploited to derive a weak form based on the generalized displacement fields of the higher order shear deformation theories. Numerical results are computed by using isogeometric analysis and verified to show the accuracy and reliability of the present approach. It is found that the unique formulation of a polynomial form can theoretically cover all existing HSDTs models and is thus sufficient to describe the nonlinear and parabolic variation of transverse shear stress. Moreover, the proposed higher order shear deformation theories predict the proper responses for laminated composite plates in comparison with the available ones in the literature.