Shear flexible element based on coupled displacement field for large deflection analysis of laminated plates

A shear deformable theory accounting for the transverse-shear (in the sense of Reissner–Mindlin’s thick plate theory) and large deflections (in the sense of von Karman theory) is employed in the construction of variational statement. A four-node, lock-free, shear-flexible rectangular plate element based on the coupled displacement field is developed in this paper to carry out the large deflection analysis. The displacement field of the element is derived by making use of the linearized equations of static equilibrium. A bi-cubic polynomial distribution is assumed for the transverse displacement ‘w’. The field distribution for the in-plane displacements (u,v) and plate normal rotations (θx, θy) and twist (θxy) is derived using equilibrium of composite strips parallel to the plate edges. The displacement fields so derived are coupled through material couplings. The transverse shear strain fields of the proposed element do not contain inconsistent terms, so that the element predicts even shear-rigid bending accurately. The element is validated for a series of numerical problems and results for deflections and stresses are presented for rectangular composite plates with various boundary conditions, loading and lay-ups. The influence of the sign of the loading on the deflection of unsymmetrically laminated plates, in the large deflection regime is also investigated.