A four-node hybrid assumed-strain finite element for laminated composite plates

Fibre-reinforced plates and shells are finding an increasing interest in engineering applications. Consequently, efficient and robust computational tools are required for the analysis of such structural models. As a matter of fact, a large amount of laminate finite elements have been developed and incorporated in most commercial codes for structural analysis. In this paper a new laminate hybrid assumed-strain plate element is derived within the framework of the Firstorder Shear Deformation Theory (i.e. assuming that particles of the plate originally lying along a straight line which is normal to the undeformed middle surface remain aligned along a straight line during the deformation process) and assuming perfect bonding between laminae. The in-plane components of the (infinitesimal) strain tensor are interpolated and by making use of the constitutive law, the corresponding in-plane stress distribution is deduced for each layer. Out-of-plane shear stresses are then computed by integrating the equilibrium equations in each lamina, account taken of their continuity requirements. Out-of-plane shear strains are finally obtained via the inverse constitutive law. The resulting global strain field depends on a fixed number of parameters, regardless of the total number of layers; 12 degrees of freedom are for instance assumed for the developed rectangular element. The proposed model does not suffer locking phenomena even in the thin plate limit and provides an accurate description of inter-laminar stresses. Results are compared with both analytical and other finite element solutions. keyword: Laminated composite plates, hybrid finite elements, assumed strain methods, shear-locking. 1 DIMS, University of Trento, Trento, ITALY; corresponding author. 2 Italferr, Milano, ITALY. 3 DI, University of Ferrara, Ferrara, ITALY. 4 UCI, Irvine, CA, USA.