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 LaplaceÐCarson and Þnite element method. In this analysis the Þeld equation for viscoelastic material is used. In the transformed LaplaceÐCarson space two new functionals have been constructed for viscoelastic Timoshenko beams through a systematic procedure based on the Gaöteaux di¤erential. These functionals have six and two independent variables respectively. Two mixed Þnite 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. Copyright