Vigas sanduíche compósitas funcionalmente graduadas reforçadas com fibras, modeladas via função ziguezague modificada com continuidade da tensão de cisalhamento

Abstract

Composite sandwich beams have been widely employed in different engineering fields due to their advantageous structural properties, such as high mechanical strength, high stiffness-to weight ratio, and good durability, which favor their widespread application in civil, aeronautical, and aerospace engineering. In this context, composite sandwich beams reinforced with continuous fibers stand out for providing structures with high strength and stiffness. However, these laminates are susceptible to delamination due to the heterogeneity of the material properties across the layers. As an alternative, functionally graded materials have attracted considerable attention because they provide a continuous variation of material properties, thereby reducing interfacial discontinuities. Nevertheless, within laminated structures, the accurate prediction of displacement fields and the proper representation of the variation of transverse shear stresses across the layers remain challenging tasks, even for several higher-order beam theories. Accordingly, this work presents a formulation based on refined zigzag theory, in which a modified zigzag function is proposed to naturally capture the continuity of shear stresses. The proposed model was applied to the analysis of different sandwich beam configurations, including fiber-reinforced laminates, cross-ply laminates, homogeneous sandwich beams, and sandwich beams with functionally graded cores. For fiber reinforced sandwich beams, the influence of the slenderness ratio, stacking sequence, and layer thickness ratio was investigated. For sandwich beams with functionally graded cores, only the mid-span vertical displacement under a concentrated load was evaluated due to the lack of additional reference response fields available in the literature. The formulation was developed separately under the assumptions of plane stress and plane strain within the framework of linear elasticity. Furthermore, the governing equations were derived using Lagrange's Principle and solved through the Ritz method. The results showed good agreement with analytical solutions, experimental results, and reference data available in the literature for different sandwich beam configurations, demonstrating the capability of the proposed formulation to accurately predict displacement and stress fields. Finally, the proposed formulation was shown to accurately reproduce the continuity of transverse shear stresses in both fiber-reinforced and functionally graded sandwich beams, thereby contributing to reducing a gap identified in the literature. Despite the advances achieved, there is still a lack of experimental studies allowing for more comprehensive comparisons.