Development of an Efficient Zigzag Model with Variable Representation of Displacements across the Thickness

A refined three-dimensional zigzag plate model with hierarchic representation of displacements across the thickness is developed that accurately captures interlaminar stresses directly from constitutive equations with low computational effort. Thanks to the incorporation of high-order terms, the representation can be different from point to point across the thickness; thus, it can be adapted to variations of solutions. However, as in classical models, the functional degrees of freedom are the midplane displacements and the shear rotations because high-order contributions are determined without adding new unknowns. They are computed by enforcing equilibrium conditions at discrete points across the thickness and stress boundary conditions. The model fulfills a priori the interfacial stress continuity conditions at the interfaces thanks to the incorporation of appropriate continuity functions. A new approach is adopted that overcomes the drawbacks of algebraic manipulations because the expressions of high-order terms and continuity functions are derived separately only once in closed form for all conditions with a symbolic calculus tool. As shown by the numerical tests, the model accurately predicts the stress field of thick laminated and sandwich plates with abruptly changing material properties with a lower overall processing time than previously developed models by the authors.