Buckling analysis of FRP pultruded frames using locking-free finite elements

A finite element formulation for the buckling analysis of orthotropic fiber-reinforced polymers (FRP) thin-walled beams with open section is presented. A second-order approximation of the displacement field is adopted, accounting for the shear strain effects on both non-uniform torsion and bending. The proposed model holds for composite beams with any given cross-section subjected to concentrated or distributed surface loads. Cubic and quadratic polynomials of the Hermitian family are used. Such shape functions contain parameters that explicitly indicate the influence of shear deformations, resulting in a locking-free finite element. Numerical analysis of beams subjected to compressive or lateral forces illustrates accuracy and convergence properties of the proposed formulation. Finally, the beam element is adopted for the buckling analysis of pultruded thin-walled frames subjected to in-plane and lateral loads. Particular attention was paid to the influence of out-of-plane constraint conditions, warping restraints and shear deformations.