A Novel Exponential Zigzag Function Coupled High-order Beam Theory for Advanced Laminated Composite Analysis

Document Type : Research Paper


Department of Civil Engineering, Laboratory of Building Materials and Structures (LAMCE), Federal University of Sergipe, São Cristovão, Aracaju-SE, 49100-000, Brazil


Various industrial sectors require highly specialized and efficient materials for applications in fields such as the military, aeronautics, aerospace, and mechanical and civil engineering. Composite materials that meet the stringent requirements across these domains have become prominent, often serving as structural components and requiring precise mathematical modeling. Zigzag (ZZ) and Layerwise (LW) theories are commonly used for laminated-beam structural analysis. Although the LW theory provides superior accuracy, it suffers from an increase in unknowns as the number of layers grows. Conversely, the ZZ theory is less computationally intensive and less accurate. This study proposes an exponential high-order zigzag function with a unified kinematic formulation to enhance the accuracy of the ZZ theory. The results were compared with those of existing models and demonstrated excellent agreement with the reference solutions, irrespective of the layer count or slenderness index, making it a more efficient choice for laminated-beam analysis.


Main Subjects

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[1] Sayyad, A.S., Comparison of various refined beam theories for the bending and free vibration analysis of thick beams, Applied and Computational Mechanics, 5, 2011, 217-230.
[2] Timoshenko, S.P., On the correction factor for shear of the differential equation for transverse vibrations of bars of uniform cross-section, The London Edinburgh, Dublin Philosophical Magazine, and Journal of Science Edinburgh, 43, 1921, 125-131.
[3] Kruszewski, E.T., Effect of transverse shear and rotary inertia on the natural frequency of a uniform beam, National Advisory Committee for Aeronautics, 1949.
[4] Reddy, J.N., A general non-linear third order theory of plates with moderate thickness, International Journal of Nonlinear Mechanics, 25, 1990, 677–686.
[5] Touratier, M., An efficient standard plate theory, International Journal of Engineering Science, 1, 1991, 901–916.
[6] Soldatos, K.P., A transverse shear deformation theory for homogeneous monoclinic plates, Acta Mechanica, 94, 1992, 195–220.
[7] Karama, M., Afaq, K.S., Mistou, S., Mechanical behavior of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity, International Journal of Solids and Structures, 40, 2003, 1525–1546.
[8] Akavci, S.S., Buckling and Free Vibration Analysis of Symmetric and Antisymmetric Laminated Composite Plates on an Elastic Foundation, Journal of Reinforced Plastics and Composites 26, 2007, 1907–1919.
[9] Vinson, J.R., Sierakowski, R.L., The Behavior of Structures Composed of Composite Materials, Second Ed. Ontario et al., 2008.
[10] Sayyad, A.S., Ghugal, Y.M., Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature, Composite Structures, 171, 2017, 486–504.
[11] Murakami, H., Maewal, A., Hegemier, G.A., A Mixture Theory with a Director for Linear Elastodynamics of Periodically Laminated Media, International Journal of Solids and Structures, 17, 1981, 155-173.
[12] DI Sciuva, M., A Refined Transverse Shear Deformation Theory for Multilayered Anisotropic Plates, Atti Accademia delle Scienze di Torino, 118, 1984, 279– 295.
[13] DI Sciuva, M., An Improved Shear-Deformation Theory for Moderately Thick Multilayered Anisotropic Shells and Plates, Journal of Applied Mechanics, 54, 1987, 589-596.
[14] Tessler, A., DI Sciuva, M., Gherlone, M., A refined zigzag beam theory for composite and sandwich beams, Journal of Composite Materials, 43, 2009, 1051-1081.
[15] Lularon, L., Gherlone, M., Tessler, A., DI Sciuva, M., Assessment of the Refined Zigzag Theory for bending, vibration, and buckling of sandwich plates: a comparative study of different theories, Composite Structures, 106, 2013, 777-792.
[16] Vidal, P., Polit, O., A sine finite element using a zig-zag function for the analysis of laminated composite beams, Composites Part B: Engineering, 42, 2011, 1671-1682.
[17] Zhen, W., Yang, C., Zhang, H. and Zheng, X., Stability of laminated composite and sandwich beams by a Reddy-type higher-order zig-zag theory, Mechanics of Advanced Materials and Structures, 26(19), 2019, 1622-1635.
[18] Prado Leite, L.F., da Rocha, F.C., A novel Higher-Order Zigzag Function Applied to Refined Unified Beam Theory for the Analysis of Composite Laminated Materials, Periodica Polytechinca Civil Engineering, 67(3), 2023, 867-874.
[19] Pagano, N.J., Exact solution for composite laminates in cylindrical bending, Journal of Composite Materials, 3, 1969, 398–411.
[20] Reddy, J.N., Mechanics of laminated composite plates and shells: Theory and analysis, Second Edition, Boca Raton, CRC Press, 2004.
[21] Liu, D., Lu, X., An Interlaminar shear stress continuity theory for laminated composite analysis, Computers and Structures, 42, 1992, 9-78.