A new incompatible mode element with selective mass scaling for saturated soil dynamics
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It is a well-known fact that addressing hydromechanical problems in saturated soils with the finite element method and equal-order interpolation formulations in displacements and pore pressures produces unstable results. Classically, stabilization has been achieved by increasing the interpolation degree of displacement with respect to pore pressure, hence fulfilling the Babuska–Brezzi condition. However, the use of quadratic elements involves high computational costs. From that point of view, the use of stabilized low-order elements is a more desirable option. Much research has been carried out in different directions in the stabilization of low-order formulations for saturated soils in quasistatic conditions, among others with the technique based on strain field enhancement through internal degrees of freedom. This article presents an alternative displacement–pore pressure formulation for saturated soil dynamics based on the enhancement of the displacement field through incompatible modes.
KeywordsDynamics Finite elements Incompatible modes Mass scaling Saturated soil
The present work has been supported by research Grant BES-2010-036691 associated with research project BIA2009-14225-C02-02 Granted by Secretaría de Estado de Investigación of the Spanish Government.
- 5.Brezzi F, Pitkaranta J (1984) On the stabilization of finite element approximation of the Stokes problem. En: Vieweg, ed. Efficient solutions of elliptic problems, notes on numerical fluid mechanics. s.l.:Wiesbaden, pp 11–19Google Scholar
- 6.Cuéllar P (2011) Behaviour of pile foundations for offshore wind turbines under cyclic lateral loading. Berlin: ThesisGoogle Scholar
- 9.Huang MS, Liu M, Zienkiewicz OC (2007) Stabilized procedures for finite element analysis in saturated soils under cyclic loading. Eds:Shi, Y; Dongarra, J; Sloot, PMA. Computational Science - ICCS 2007, PT 3, PROCEEDINGS. Lecture Notes in Computer Science. Volumen 4489 pp 1105Google Scholar
- 10.Hughes TJ, Franca LP, Balestra M (1986) A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuzka–Bressi condition: a stable Petrov–Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput Methods Appl Mech Eng 59(1):85–99CrossRefzbMATHGoogle Scholar
- 16.Mira P (2002) Análisis por elementos finitos de problemas de rotura de geomateriales. Universidad Politécnica de Madrid, Ph.d. ThesisGoogle Scholar
- 18.Mira P, Pastor M, Li T, Liu X (2004) Failure problems in soils—an enhanced strain coupled formulation with application to localization problems. Revue Française de Génie Civil 8:735–759Google Scholar
- 26.Wilson EL, Taylor RL, Doherty WP, Ghaboussi J (1973) Incompatible displacement models. In: Proceedings, ONR symposium on numerical and computer method in structural mechanics. University of Illinois, Urbana. September. 1971. Also published in Numerical and Computational Mechanics (ed. S. T. Fenves). Academic PressGoogle Scholar