Dual-mixed principles in elastodynamics - an application to cylindrical shells

Abstract eng:
The commercial finite elements suffer from several kind of numerical difficulties. These problems occur in such a way that the finite element solution for the unknowns deteriorates as the mesh become refined step by step, namely the convergence for the relative errors of variables is very slow. This is the numerical locking effect. These low-order, primal and primal-mixed structural finite elements suffer from the most serious convergence problems. One of the most efficient strategies, to avoid the numerical locking phenomenon, is the use of multi-field dual-mixed variational principles for development of finite element models. Accordingly three, new multi-field dual-mixed energy principles using non-symmetric stresses are presented for linear elastodynamic problems. One of them provides a theoretical basis for construction of a new hp-version cylindrical shell finite element which is tested through benchmark problems, and the numerical results are compared to computed ones by the models appearing in the literature.

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