# Computational algorithm for geometrically nonlinear analysis of laminated composite frames with zig-zag enhancement of the transverse strain field

## Palavras-chave:

Zig-zag enhancement, Geometrically nonlinear analysis, Positional FEM, Laminated composites## Resumo

Laminated composite materials are widely used in engineering applications due to the high control

and flexibility over the design of its mechanical properties. It is known, however, that when subjected to loads,

structural elements made of laminated composites display a zig-zag pattern on their strain field in the transverse

direction, behaving differently from the usual assumption that considers transverse sections as planes after the

load application for calculation purposes. Therefore, this work proposes the implementation of a finite element

method computational algorithm, based on positions, that numerically solves laminated composite frames by

enhancing the strain field in the transverse direction. The first order shear deformation theory (FSDT) adapted

for generalized vectors is used as the basic kinematic assumption, and then enhanced by a normalized zig-zag-

shaped function multiplied by an amplitude factor, which is a new nodal degree of freedom. In addition, the

cross section direction and height variation are represented by generalized vectors, which are also nodal degrees

of freedom. The developed formulation is total Lagrangian, comprising large displacements and rotations, and

uses the Saint-Venant-Kirchhoff constitutive law, which allows moderate strains.