A hybrid-stress formulation of isoparametric elements for the analysis of thin multilayer laminated composite plates is presented, and is applied to edge contact analyses. . The element displacement behavior is characterized by laminate reference surface inplane and transverse displacements and laminate non-normal cross-section rotations;​ as a result, the number of degrees of freedom is independent of the number of layers. All components of stress are included and are related to a set of laminate stress parameters, the number of which is independent of the number of layers. Attention is restricted here to thin laminates:​ for thin laminates it is shown that the contributions of transverse shear stress and transverse normal stress to the internal complementary strain energy can be neglected. As a result, a modified stiffness-formation-algorithm can be used which provides a significant improvement in computation efficiency. The formulation is used to develop an 8-node isoparametric thin multilayer plate element. The resulting element is naturally invariant, of correct rank, and non-locking in the thin plate limit. Element performance is documented here for several illustrative examples.

The newly developed element is applied to the analysis of laminate edge contact. A hybrid-stress formulation for the incremental/iterative analysis of contact problems as well as the procedure to locate the surface of contact is presented. The assumed contact surface is divided into contact elements having unknown nodal contact tractions. The fi­nite element equations are solved for the element nodal degrees of freedom as well as unknown nodal contact tractions. The assumed contact surface is checked to determine if it satisfies the contact conditions. If not a new contact surface is assumed and the (iterative) process is repeated. Attention is restricted here to symmetric laminates subject to contact in directions normal to the laminate edge, so that only inplane displacment occurs. Several examples involving elastic, non-frictional contacting bodies are presented to verify the formulation/algorithm. An example involving a laminated plate is also presented.