Development of an anisotropic, multilayered, shear-deformable rectangular plate element

C0 Layerwise Model with Fixed Degrees of Freedom and Variable In- and Out-of-Plane Kinematics by Strain Energy Updating Technique

“…The zigzag models (iv) inspired by Di Sciuva [29,30] and retaken by many other researchers, e.g., [31][32][33][34][35][36], represent an interesting compromise between accuracy and affordable computational costs since their processing time and memory storage dimension are comparable to those of equivalent single-layer models, but accuracy is much better. In effects, these models are based on equivalent single layer models that are improved through incorporation of zigzag functions that do not introduce new unknown variables and whose expressions are computed once for all, making continuous a priori the out-of-plane stresses through appropriate discontinuous derivatives of displacements.…”

“…(degrees of freedom) that a priori fulfill the stress continuity conditions through incorporation within an overall representation of functions that introduce the appropriate slope discontinuity [29][30][31] through the enforcement of the physical stress continuity constraints at the interfaces.…”

First-Order Displacement-Based Zigzag Theories for Composite Laminates and Sandwich Structures: A Review

“…In the ZZ models (as in ESL models), the number of kinematic unknowns does not depend on the number of layers. The in-plane displacements combine the smooth (generally, polynomial) functions defined across the entire laminate thickness (linear [37,38,39,40,41,52,55,56,57] or higher-order polynomial, [42,43,44,45,46,51,53,58,59] with the piecewise linear (i.e., zigzag) distributions. The zigzag contributions enable a more realistic modeling of the in-plane crosssectional distortion in multilayered composites, giving rise to a computationally efficient theory for the modeling of relatively thick laminated composite and sandwich structures.…”

Hybrid-interface finite element for laminated composite and sandwich beams

“…Toledano and Murakami [33] presented a layer-wise technique based on Reissner's new mixed variational principle by taking transverse stresses to be quadratic function of local thickness. Lu and Liu [34] proposed a layer-wise theory, based on techniques by Di Sciuva [27,28], Hinrichensen and Palazottao [35], Tolendano and Murakmai [33] and Reddy [12], to calculate shear stresses directly from constitutive equations instead of being recovered from equilibrium equation. The hybrid-stress FE method by Mau et al [36] and others satisfies the continuity condition explicitly.…”

“…According to historical review of ZZTs presented by Carrera [23]: (i) Lekhnitskii [24] was the first to propose a ZZT for multilayered plate using elasticity relations; (ii) Ambartsumyan [25] proposed a ZZT by extending the well-known Reissner-Mindlin theory to layered, anisotropic plates; and (iii) Reissner [26], proposed a ZZT using variational theorem that permits both displacement and transverse stress assumptions. Di Sciuva [27,28] also presented first order zig-zag theory (FZZT), wherein in-plane displacements were assumed to be piece-wise linear for each lamina and continuous through-thethickness. FZZT proved to be a numerically efficient method as total number of degrees of freedom (DOF) were independent of the number of layers.…”