Variational principles of elastic-viscous dynamics in Laplace transformation form, FEM formulation and numerical method (Q1067859)

The author gives variational principles of elasto-viscous dynamics in spectral resolving form, extended to Laplace transformation form, mixed variational principle of shell dynamics and variational principle of dynamics of elasto-viscous-porous media; for the latter, a finite element method formulation has been worked out. Variational principles in Laplace transformation form have concise forms, for the sake of utilizing the finite element method conveniently it is necessary to find values of preliminary time function at some instants, when values of Laplace transformation at some points are known, but there are no efficient methods till now. In this paper, a numerical method for finding discrete values of preliminary functions is presented, from numerical examples we see such a method is efficient. By combining both methods stated above, variational principles in Laplace transformation form and numerical method, a quite wide range of solid dynamic problems can be solved with the aid of digital computers.