Análise mecânica de vigas compósitas laminadas quase-3D de alta ordem com funções zig-zag

Abstract

The extensive use of laminated composite materials in various engineering applications has been driven by their high stiffness-to-weight ratio, combined with ease of fabrication. The complexity of analyzing laminated composite beams, especially the zig-zag phenomenon of the beam’s longitudinal displacement, motivates the need for more advanced approaches. Thus, to better describe the mechanical behavior of laminated composite beams, this work proposes three models aimed at overcoming the limitations of classical beam theories. The first model uses zig-zag functions, which incorporate the effect generated by the difference in stiffness between layers, combined with high-order shear deformation theories, incorporating the quasi3D effect to account for three-dimensional characteristics in a simplified analysis. This approach aims to avoid the use of shear correction factors and address the discontinuity problem of the shear stress distribution in the cross-section by using equilibrium equations. The second model adds a continuity approach for shear stress, obtained directly from the constitutive relation. The third model, in turn, uses a refined higher-order zig-zag theory, imposing continuity of stresses at the layer interfaces. For all models, domain differential equations and variationally consistent boundary conditions are obtained by imposing the nullity of the first variation of the total energy functional. The solutions for the strong formulations were constructed using the Navier method, and additionally, for the first and third models, using the Ritz-Lobatto method, with the goal of analyzing the mechanical behavior of laminated beams under different boundary conditions. Finally, the results of displacement, normal, and shear stress fields obtained by the three models are compared with analytical results from elasticity theory. The results showed that the first model, when using the hyperbolic-exponential zig-zag function, provides accurate results for all response fields when transverse normal and shear stresses are calculated by the equilibrium equation. The second model presents shear stress continuity when calculated by the constitutive relation; however, it exhibits a behavior that diverges from the reference. The third model offers an accurate description of displacements and stresses calculated through constitutive relations, showing agreement with data available in the literature.