A C0 continuous mixed FE formulation for bending of laminated composite plates based on unified HSDT

Abstract

This study proposes a unified C0 continuous mixed finite element (MFE) formulation for the accurate and efficient prediction of stress components in laminated composite plates relying on Higher Order Shear Deformation Theory (HSDT). This unified form of the MFE accepts any convenient function for the representation of transverse shear deformation. The Hellinger–Reissner variational principle is employed for the derivation of MFE equations within a two-field formulation involving stress resultants along with kinematical variables. Thus, the displacement and stress resultant fields are obtained directly from the global solution of the system of equations. In this manner, the in-plane stress components are calculated over constitutive relations at the nodes without any need for error-prone spatial derivatives. Furthermore, the independent interpolation of kinematic and stress resultant type variables allows the numerical solution to overcome the shear-locking problem and ensure C0 continuity requirement. Numerical examples include convergence and comparison tests of predicted displacements and stress components under various boundary conditions and material configurations. Various test cases are considered for both the thin and thick plates subjected to sinusoidal and uniformly distributed loads. It is demonstrated that the proposed MFE formulation can capture stress components with high accuracy while being computationally efficient.