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Structural Engineering and Mechanics
  Volume 29, Number 3, June20 2008, pages 289-300

Mesh distortion, locking and the use of metric trial functions for displacement type finite elements
Surendra Kumar and G. Prathap

    The use of metric trial functions to represent the real stress field in what is called the unsymmetric finite element formulation is an effective way to improve predictions from distorted finite elements. This approach works surprisingly well because the use of parametric functions for the test functions satisfies the continuity conditions while the use of metric (Cartesian) shape functions for the trial functions attempts to ensure that the stress representation during finite element computation can retrieve in a best-fit manner, the actual variation of stress in the metric space. However, the issue of how to handle situations where there is locking along with mesh distortion has never been addressed. In this paper, we show that the use of a consistent definition of the constrained strain field in the metric space can ensure a lock-free solution even when there is mesh distortion. The three-noded Timoshenko beam element is used to illustrate the principles. Some significant conclusions are drawn regarding the optimal strategy for finite element modelling where distortion effects and field-consistency requirements have to be reconciled simultaneously.
Key Words
    mesh distortion; locking; unsymmetric parametric-metric formulation; metric trial function; Timoshenko theory; three-node beam element.
Surendra Kumar: CSIR Centre for Mathematical Modelling and Computer Simulation, Bangalore 560 037, India
G. Prathap: CSIR Centre for Mathematical Modelling and Computer Simulation, Bangalore 560 037, India

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