Stress analyses of viscoelastic three-dimensional beam-like structures with low- and high-order one-dimensional finite elements

The mechanical responses of viscoelastic structures are evaluated by using finite beam elements based on different kinematical assumptions. The governing equations related to the structural theories are obtained with the Carrera Unified Formulation. The viscoelastic constitutive law is expressed in an integral form, which relates the viscous moduli with the strain rate. The solution of the governing equations is obtained in the Laplace domain and then transformed in the time domain through a numerical inversion procedure. The numerical simulations are performed on slender, squat, isotropic, and orthotropic beams in order to examine the actual differences between the results obtained with low-order theories and the refined models. The current results are validated with classical and higher-order solutions available in the literature. Moreover, comparisons between the equivalent-single layer and the layer-wise approach are reported and discussed.