Finite element method on fractional visco-elastic frames

Abstract

In this study the Finite Element Method (FEM) on viscoelastic frames is presented. It is assumed that the Creep function of the constituent material is of power law type, as a consequence the local constitutive law is ruled by fractional operators. The Euler Bernoulli beam and the FEM for the frames are introduced. It is shown that the whole system is ruled by a set of coupled fractional differential equations. In quasi static setting the coupled fractional differential equations may be decomposed into a set of fractional viscoelastic Kelvin-Voigt units whose solution may be obtained in a very easy way.