Use of the 3D Equilibrium Equations in the Free‑Edge Analyses for Laminated Structures with the Variable Kinematics Approach

This paper compares out-of-plane stresses evaluated with Hooke’s Law and the stress recovery technique, focusing on the free edges of composite plates and shells. The Carrera Unified Formulation and the finite element method are adopted to derive the governing equations. Lagrange polynomials are implemented in the equivalent single-layer, layer-wise, and variable kinematics approaches. The latter is used to refine structural models locally and reduce computational overheads. Laminated plates and shells subjected to uniaxial tension are considered. The out-of-plane stresses are compared with references from the existing literature for most cases. The results demonstrate that the stress recovery technique effectively calculates stresses and improves the accuracy of equivalent single-layer models. Furthermore, layer-wise models are needed for accurate results near the free-edge zone. Finally, variable kinematics theories are helpful in accurately detecting local phenomena along the structure’s thickness.