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

Abstract

Fibre-reinforced plates and shells are find- ing 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 el- ements 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 First- order Shear Deformation Theory (i.e. assuming that par- ticles of the plate originally lying along a straight line which is normal to the undeformed middle surface re- main aligned along a straight lineduring the deformation process)and assumingperfect bondingbetween laminae. Thein-planecomponentsofthe(infinitesimal)strain ten- sor are interpolated and by making use of the constitu- tive law, the correspondingin-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 continuityrequire- ments. Out-of-planeshear strains are finally obtained via the inverse constitutivelaw. The resulting global strain field depends on a fixed num- ber of parameters, regardless of the total number of lay- ers; 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 de- scription of inter-laminar stresses. Results are compared with both analytical and other finite element solutions.