Laminated Composites Modeled by Elements Corrected for Locking A-Priori

Abstract

An eight node serendipity element free of locking and spurious zero energy modes is formulated to model laminated composite plates. A first-order shear deformation theory and equivalent lamina assumption are adopted. The model represents transverse shear strains and stresses as constants while their actual variations are parabolic. Thus, a shear correction factor is used. Strain gradient notation is employed which allows for a detailed a-priori analysis of the finite element model. Its polynomial expansions are inspected and spurious terms which are responsible for shear locking are identified. The element is corrected by simply removing the spurious terms from those expansions. The compatibility modes are also clearly identified and maintained, preventing the introduction of spurious zero energy modes. Numerical results show locking effects caused by the spurious terms on displacement and transverse stresses solutions. They also show that properly refined meshes composed of corrected elements provide solutions which converge rather well to analytical solutions.