A positional Unconstrained Vector Layerwise (UVLWT) FEM formulation for laminated frame element modeling

Abstract The analysis of laminated structures presents three major challenges that will be handled in this study: (i) Accurate determination of transverse stresses. (ii) Nonlinear geometric behavior of structural elements which are usually slender and present large displacements and rotations. (iii) Conditioning improvement of stiffness matrix that, in general, is weakened when using very thin elements. In this study, a geometrically exact nonlinear formulation based on positions is proposed to model straight and curved laminated frame elements. This formulation has similarity with the well known Layerwise Theory (LWT), however it uses positions and generalized vectors as nodal parameters instead of displacement degrees of freedom for different nodes and laminas. The proposed formulation is called Unconstrained Vector/Layerwise Theory (UVLWT). The proposed kinematics eliminates the ill conditioning of stiffness matrix for thin elements, as the positions of any point of the continuum are tied to nodal positions. The Saint–Venant–Kirchhoff constitutive law is adopted to describe geometrical nonlinearity. The developed formulation is total Lagrangian and the considered degrees of freedom are positions and laminated cross sections generalized vectors. Results for various straight and curved elements with different height/length ratios are used to demonstrate the capabilities of the proposed formulation.