A serendipity plate element free of modeling deficiencies for the analysis of laminated composites

An eight-node serendipity element free of shear locking and spurious zero-energy modes is formulated to model laminated composite plate problems. The element is based on a first-order shear deformation theory and on the equivalent lamina assumption. Stresses are calculated through the thickness of the plate. As the model is only capable of representing transverse shear strains and stresses as constants, while their actual variations are parabolic, a shear correction factor is used. The element is formulated using strain gradient notation, which is a physically interpretable notation that allows for a detailed a-priori analysis of the finite element model. The element’s shear strain polynomials are inspected, and the spurious terms which are responsible for shear locking are identified. The element is corrected by simply removing such spurious terms from those shear strain expansions. Further, the compatibility modes are also clearly identified and maintained in the shear strain expansions in order to prevent the introduction of spurious zero-energy modes. Numerical results show the shear locking effects caused by the spurious terms on displacement and transverse stress solutions. They also show that properly refined meshes composed of corrected elements provide solutions which converge rather well for moderately thick to thin plates.