Nonlinear geometric analysis of orthotropic laminated plates and shells with zig-zag effect

Resumo

In this study, a positional Finite Element Method (FEM) formulation is applied to simulate orthotropic
symmetric laminated plates and shells. Alternatively to the traditional FEM, the positional formulation uses a total
Lagrangian description based on generalized vectors and nodal positions, providing an inherently nonlinear
geometric formulation. However, basic kinematics are not able to satisfy a continuous stress distribution along the
laminate thickness. The stress discontinuity is related to the emergence of a zig-zag displacement profile in the
transverse direction caused by mechanical properties changing between adjacent laminas. Therefore, the proposed
formulation introduces new degrees of freedom to regularize the classical Reissner-Mindlin kinematics and

reproduce the zig-zag effect. In addition, the mechanical model uses Green-Lagrange strain and the Saint Venant-
Kirchhoff constitutive law, which allows moderate strain. A numerical example is employed to validate the

proposed formulation and demonstrate its quality when compared with literature results.