A finite element model for linear viscoelastic behaviour of pultruded thin-walled beams under general loadings

A finite element model for orthotropic thin-walled beams subject to long-term loadings is presented. The hypothesis, rather usual for thin-walled beams, of cross-sections remaining undistorted in their own planes after deformation is introduced, so reducing the number of d.o.f.’s and, consequently, the computational effort of the analysis. The model is used to perform linear viscoelastic analysis of prismatic beams with general cross-sections, i.e., open, closed or multi-cell. As far as the constitutive viscoelastic law is concerned, a generalized linear Maxwell model is adopted. Making use of the exponential algorithm, differential equations are written in incremental form and integration is performed adopting time intervals of variable length. Numerical examples are finally presented, concerning glass-fibre pultruded shapes under long-term loadings. Displacement evolution with time and stress redistribution adopting different creep laws are presented. Convergence features of the proposed finite element and time integration procedure are also shown.