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

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 the field equation for viscoelastic material is used. 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. Two mixed finite element formulations are obtained; TB12 and TB4. For the inverse transform Schapery and Fourier methods are used. The numerical results for quasi-static and dynamic responses of several visco-elastic models are presented.