Finite element analysis of transient dynamic viscoelastic problems in time domain

In this paper, the simplified and stable finite element method is presented for the time domain analysis of the transient dynamic viscoelastic problems, for which the weak form is obtained by applying the Galerkin's method to the equations of motion in time integral which do not contain the inertia terms explicitly, but the inertia effect is taken into account, and discretized spatially to obtain the semidiscrete equations in time integral. In the temporal approximation, only the time interpolation functions are used for approximating the dependent variables on the divided time axis, while the time integration schemes such as the Newmark and Houbolt methods are not necessary in contrary to the conventional approach. To show the validity and applicability, two-dimensional examples are given and solved for the displacements and stresses, especially for the dynamic stress concentrations by the wave diffraction, which are discussed in detail at the aspect of the viscoelastic damping. To the authors' knowledge, no previous results except for the test example exist in the literature.