Dynamic analyses of viscoelastic three-dimensional structures with advanced one-dimensional finite elements

This paper presents mechanical responses of viscoelastic structures with complicated geometries. The structures are discretized with finite beam elements, whose kinematic theories are derived according to the Carrera Unified Formulation. The governing equations are solved in the Laplace domain to avoid the computation of the convolution integral, which mathematically simulates the viscoelastic constitutive law. The three-dimensional displacement, strain, and stress fields are transformed in the time domain through a numerical inversion algorithm. The numerical simulations are performed on a beam with a hole at the center of its cross-section and on a thick-walled cylindrical shell subjected to various loading and boundary conditions. The comparisons between the present results, analytical predictions, and three-dimensional finite element solutions demonstrate the accuracy of the formulation.