A deformation-based unified theory for composite plates

Abstract

A deformation-based unified theory (DUT) for composite plates is established. The new theory contains four unknown displacement components that are explicit and can be interpreted with physical reasoning. Apart from the three common displacement components for a point on the reference plane, the remaining higher-order displacement component is exclusively attributed to the transverse bending and shear deformations. The elucidation of the thickness locking mechanism (TLM) relies on the innovative displacement component introduced in this study, which improves the kinematic assumptions inherent in conventional plate theories. The transverse shear deformation of the function distribution for composite plates can be described by a general thickness function, thus enabling DUT to be degenerated into any existing shear deformation plate theory. Further, the present plate theory explains the physical terms associated with transverse normal stress and strain. The present unified theoretical framework, along with the corresponding assumptions, can induce further simplification and transition to existing plate theories, namely, classical plate theory (CPT), first-order shear deformation theory (FSDT), and third-order shear deformation theory (TSDT). Exact analytical solutions of laminated composite plates are obtained. Comprehensive numerical results are presented for various plate theories and different plate structures. The clarity and unity in the physical interpretation of the present theory can be elaborated by integrating the conventional theories under certain assumptions. In addition, the extensive applicability of the theoretical framework of DUT enables the customization of the kinematic modeling of various composite plate structures.