A locking-free finite element formulation for a non-uniform linear viscoelastic Timoshenko beam

摘要

In this paper we use a modified constitutive law in a hereditary integral form to analyze the response of an isotropic non-uniform linear viscoelastic Timoshenko beam. A mixed method framework is used to provide stability and semi-discrete error estimates that do not deteriorate as the thickness parameter becomes small. Numerical experiments for both quasi-static and transient cases are presented.