Alternative Kelvin viscoelastic procedure for finite elements

In this work, an alternative Kelvin viscoelastic formulation for the finite element method (FEM) is described. This formulation performs spatial approximations before considering time integration and makes use of differential viscoelastic relations. A matrix time differential equation arises from the proposed formulation. It is solved numerically by a time marching procedure. It is shown that, after a small simplification, this methodology can be employed together with existent dynamic FEM packages. The methodology is extended to dynamic analysis leading to a rheological explanation for the first order modal decomposition stiffness proportional damping matrix. Plates and shells applications are shown in order to demonstrate the proposed formulation accuracy and stability.