Time integration in the context of energy control and locking free finite elements

SummaryIn the present paper two main research areas of computational mechanics, namely the finite element development and the design of time integration algorithms are reviewed and discussed with a special emphasis on their combination. The finite element techniques are designed to prevent locking and the time integration schemes to guarantee numerical stability in non-linear elastodynamics. If classical finite element techniques are used, their combination with time integration schemes allow to avoid any modifications on the element or algorithmic level. It is pointed out, that on the other hand Assumed Stress and Enhanced Assumed Strain elements have to be modified if they are combined with energy conserving or decaying time integration schemes, especially the Energy-Momentum Method in its original and generalized form. The paper focusses on the necessary algorithmic formulation of Enhanced Assumed Strain elements which will be developed by the reformulation of the Generalized Energy-Momentum Method based on a classical one-field functional, the extension to a modifiedHu-Washizu three-field functional including enhanced strains and a suitable time discretization of the additional strain terms. The proposed method is applied to non-linear shell dynamics using a shell element which allows for shear deformation and thickness change, and in which the Enhanced Assumed Strain Concept is introduced to avoid artificial thickness locking. Selected examples illustrate the locking free and numerically stable analysis.

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