The mixed finite element method for the quasi-static and dynamic analysis of viscoelastic timoshenko beams

Abstract

Summary: The quasi-static and dynamic responses of a linear viscoelastic Timoshenko beam on Winkler foundation are studied numerically by using the hybrid Laplace-Carson and finite element method. In this analysis we use the field equation for viscoelastic material. In the transformed Laplace-Carson space, two new functionals have been constructed for viscoelastic Timoshenko beams through a systematic procedure based on the Gâteaux differential. These functionals have six and two independent variables, respectively. We obtain two mixed finite element formulations: TB12 and TB4. For the inverse transform, Schapery and Fourier methods are used. Numerical results for quasi-static and dynamic responses of several viscoelastic models illustrate the approach.