Equivalent Single Layer, Zig-Zag, and Layer Wise theories for variable angle tow composites based on the Generalized Unified Formulation Articles uri icon



publication date

  • October 2017

start page

  • 54

end page

  • 79


  • 177

International Standard Serial Number (ISSN)

  • 0263-8223

Electronic International Standard Serial Number (EISSN)

  • 1879-1085


  • Variable Angle Tow (VAT) composites remove the constraint of having straight fibers, typical of traditional composite structures. This dramatically increases the design space and allows a more effective tailoring of the material properties to minimize the weight and increase structural performance. To provide an accurate prediction of the displacement and stress fields in an efficient computational framework, a multi-theory architecture based on the Generalized Unified Formulation (GUF) is proposed. In particular, Equivalent Single Layer, Zig-Zag, and Layer Wise theories with different orders of expansions for the different variables are generated with a theory-invariant mathematical model. This feature allows the user to tailor the computational accuracy and cost to the needs of the case under investigation and is inherently well suited for optimization and reliability problems. For the in-plane discretization, a fourth-order triangular shell element presenting 15 nodes is adopted. The interlaminar displacement continuity is imposed in the finite element assembling in the thickness direction of the layer stiffness matrices, whereas the inter-element displacement compatibility is enforced with the penalty method. This approach allows one to use independent GUF discretization for any desired direction within each element, providing significant versatility (accuracy vs computational time) in the structural modeling. A transverse stress recovery procedure taking into account the variability of the structural properties due to the fibers' curvilinear paths is also presented. Results are compared with the literature and a commercial software (NX NASTRAN) featuring 3D finite elements. (C) 2017 Elsevier Ltd. All rights reserved.


  • generalized unified formulation; variable angle tows; tailorable directional accuracy; multi-theory framework; zig-zag theories