A statically compatible layerwise stress model for the analysis of multilayered plates

Abstract

This paper proposes a new layerwise model for multilayered plates. The model, called SCLS1 for Statically Compatible Layerwise Stresses with first-order membrane stress approximations per layer in thickness direction, complies exactly with the 3D equilibrium equations and with the free-edge boundary conditions. As in the LS1 model initially proposed by Naciri et al. (1998), 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. Also, a refined version of the new model is obtained by introducing several mathematical layers per physical layer. Contrary to the LS1 model which is derived by means of the Hellinger–Reissner principle, the new model is derived by means of the minimum of the complementary energy principle. This ensures the convergence of the refined SCLS1 solution to the exact 3D solution as the number of mathematical layers per physical layer increases. The new model has been implemented in a new version of the in-house finite element code MPFEAP . Several comparisons are made between LS1, SCLS1 and full 3D FE models in order to assess the performances of the new model which shows itself very effective.