Modifying the refined zigzag theory to incorporate functional gradation into the bending analysis of laminated beams

Resumo

Extensive research has been conducted in the field of composite materials, particularly in laminated composites. However, laminated composites often face challenges such as stress concentration at interfaces due to the sharp differences in properties between layers. This study proposes an approach to mitigate stress concentrations in laminated composites using functionally graded materials (FGM). FGM is achieved by gradually varying properties across the thickness of each beam layer, employing the power law in conjunction with the rule of mixtures. The modeling is based on the refined zigzag theory (RZT), with an additional introduction of the sublayers to capture the functional gradient. The analysis involves deriving the zigzag function for FGM, which is referred to as modified RZT. Subsequently, the kinematic model is applied based on the principle of minimum total energy to derive the Euler equation and its associated boundary conditions. For analytical resolution, the Navier procedure is employed. The results obtained for displacement and tension fields are compared with other formulations from the literature, demonstrating alignment and validation of the proposed method.