Assessment of plate theories for free-edge effects

This paper deals with a comparative study of several laminated plate theories with respect to their capability to capture the steep transverse stress gradients occurring in vicinity of free edges. The considered laminated plate theories pertain to the family of Equivalent Single Layer (ESL) as well as Layer-Wise (LW) descriptions. Reference is made to the classical displacement-based approach as well as to a partially mixed variational formulation, which allows to introduce independent assumptions for the transverse stresses and the displacements. Finite element solutions are obtained for free-edge effects that arise in several representative laminates subjected to uniaxial tension. An equivalent stress measure is proposed for assessing the three-dimensional (3D) stress fields predicted by the various theories. It is shown that refined LW models can provide quasi-3D results that compare well with full 3D FEM computations, whereas ESL models fail to capture the free-edge effects. Present results indicate that free-edge effects induced by a ±45° interface are most critical for the accuracy of laminated plate models.