The Refined Zigzag Theory (RZT) for homogeneous, laminated composite and sandwich plates is developed from a multi-scale formalism starting with the in-plane displacement field expressed as a superposition of coarse and fine contributions. The coarse displacement field is that of first-order shear-deformation theory, whereas the fine displacement field has a piecewise-linear zigzag distribution through the thickness. The resulting kinematic field provides a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories. The condition of limiting the homogeneity of transverse-shear properties gives rise to a set of robust zigzag functions. Unlike previously used methods, which often result in anomalous conditions and nonphysical solutions, the present theory does not rely on transverse-shear-stress equilibrium constraints. For all material systems, there are no requirements for the use of transverse-shear correction factors to yield accurate results. To model homogeneous plates with the full power of zigzag kinematics, infinitesimally small perturbations of the transverse shear properties are used, thus enabling highly accurate predictions of homogeneous-plate behavior without the use of shear correction factors. The RZT predictive capabilities to model highly heterogeneous sandwich plates have been critically assessed, demonstrating its superior efficiency, accuracy, and a wide range of applicability. The present theory, which is derived from the virtual work principle, is well-suited for developing computationally efficient, C0-continuous finite elements, and is thus appropriate for the analysis and design of high-performance load-bearing aerospace structures.


Related  Refereed Articles/Conference Proceedings published by our research group:

  1. Dorduncu M., 2020, “Stress analysis of sandwich plates with functionally graded cores using peridynamic differential operator and refined zigzag theory”, Thin-walled Structures (Q1), Vol. 146, 106468.
  2. Dorduncu M., 2020, “Peridynamic modeling of adhesively bonded beams with modulus graded adhesives using refined zigzag theory”, International Journal of Mechanical Sciences (Q1), Vol.185, 105866.
  3. Dorduncu M., Apalak M.K., 2020, “Elastic flexural analysis of adhesively bonded similar and dissimilar beams using refined zigzag theory and peridynamic differential operator”, International Journal of Adhesion and Adhesives (Q1), Vol. 101, 102631.
  4. Dorduncu M., 2019, “Stress analysis of laminated composite beams using refined zigzag theory and peridynamic differential operator”, Composite Structures (Q1), Vol.218, pp. 193-203.
  5. Dorduncu, M., Ergin OF, 2019, “Peridynamics for bending analysis of laminated composite plates based on refined zigzag theory”, 29th International Workshop on Computational Mechanics of Materials (IWCMM29), Dubrovnik, Croatia.
  6. Dorduncu, M., Madenci E., 2019, “Peridynamics and refined zigzag theory for progressive failure analysis of viscoelastic composites”, 19th International Conference on New Trends in Fatigue and Fracture, Tucson, AZ.
  7. Dorduncu, M., Ergin OF., 2019, “Bending behavior of laminated composite plates with embedded cracks by using refined zigzag theory”, 1st International Workshop on Plasticity, Damage and Fracture of Engineering Materials, Ankara, Turkey.
  8. Madenci, E., Dorduncu, M., Barut A. Phan N., 2019, “Progressive failure analysis of composites based on peridynamics and refined zigzag theory”, 60th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, San Diego, CA.
  9. Dorduncu M., Tessler A., Madenci E., 2017, “A three-node flat shell element based on Refined Zigzag Theory”, 3rd International Conference on Mechanics of Composites, Bologna, Italy.
  10. Dorduncu, M., Barut, A., Madenci, E. and Tessler, A., 2015, “A refined zigzag element for modeling sandwich construction with embedded stiffeners,” 56th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Kissimmee, Florida.
  11. Dorduncu, M., Atila Barut, A. and Madenci, E., 2013, “Failure prediction in sandwich panels under blast loading using a refined zigzag element,” 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Boston, Massachusetts.

Refined Zigzag Theory