Linear and non-linear finite element analysis of shearcorrected composites box beams

Abstract

The Updated Lagrangian formulation for non-linear finite element analysis is applied to the problem of thin-walled composites box beams undergoing large displacements. A shear correction factor for thinclosed rectangular sections is introduced into some terms of the variational formulation and its influence in the results is analyzed, in both linear and non-linear problems. The Vlasov's theory describing the coupled flexural-torsional phenomenon and the implementation of the FSDT theory in thin-walled beams is discussed, as well as the strains, stress resultants and constitutive relationships for composites box beams. The application of the Mechanic of Laminated Beam theory (MLB) to the calculation of the shear correction factors considering more constitutive terms for computing the shear flow in flanges and webs than those ones used in the original theory is also debated. The Updated Lagrangian finite element model applied in this work for nonlinear analysis of box beams is described. A comparison of the numerical results with those obtained experimentally, analytically and by the numerical models proposed by other authors is done for both linear and non-linear problems. The assumptions made in this work and the formulation developed only applies to thin-walled beams that undergo large displacements, but small to moderate twist rotations.