A statically compatible layerwise stress approach for multilayered materials

This paper presents a new layerwise model for multilayered plates, named SCLS1, as an abbreviation of Statically Compatible Layerwise Stresses with first-order membrane stress approximations per layer in thickness direction. The new model is derived by means of the minimum of complementary energy principle and is designed to exactly comply with free-edge boundary conditions. As in the LS1 model proposed in [1], the laminated plate is considered as a superposition of Reissner plates coupled by interfacial stresses which are considered as generalized stresses. However, the divergences of the interlaminar transverse shears are introduced as additional generalized stresses in the SCLS1 model. In order to get enhanced LS1 and SCLS1 models, a refinement strategy through the thickness is applied by considering several mathematical layers per physical layer. The refined SCLS1 model increases the accuracy of the non refined model near singularities. A new version of an in-house finite element program called MPFEAP, based on SCLS1 model, is developed using an 8-node with 6n-1 d.o.f. per node (n: total number of layers). The new model shows itself very effective as shown by several comparisons between the predictions of LS1, SCLS1, their refined versions and Abaqus full 3D FE for straight free edge plate under uniaxial tension.