Two methods of solving dynamic response by discretization of Gurtin variational principle

Based on the Gurtin variational principle and the finite element method two recurrence formulae of solving dynamic response are derived in this paper. The first recurrence formula which is conditionally stable is obtained by adopting “dual temporal finite element” to discretize the Gurtin variational principle and then making use of convolution, while the second, an unconditionally stable one derived by discritizing the variational principle in each time step and taking approprlate integration parameter θ. The paper had been accepted by the XVIth International Congress of IUTAM, Lyngby, Denmark, August, 1984.