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Structural Engineering and Mechanics Volume 26, Number 1, May10 2007 , pages 31-42 DOI: https://doi.org/10.12989/sem.2007.26.1.031 |
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The unsymmetric finite element formulation and variational incorrectness |
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G. Prathap, S. Manju and V. Senthilkumar
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| Abstract | ||
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The unsymmetric finite element formulation has been proposed recently to improve predictions from distorted finite elements. Studies have also shown that this special formulation using parametric functions for the test functions and metric functions for the trial functions works surprisingly well because the former satisfy the continuity conditions while the latter 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, a question that remained was whether the unsymmetric formulation was variationally correct. Here we determine that it is not, using the simplest possible element to amplify the principles. | ||
| Key Words | ||
| mesh distortion; unsymmetric formulation; best-fit paradigm; parametric-metric element; projection theorem; three-node bar element. | ||
| Address | ||
| G. Prathap: CSIR Centre for Mathematical Modelling and Computer Simulation, Bangalore 560 037, India S. Manju: National Aerospace Laboratories, Bangalore 560 017, India V. Senthilkumar: CSIR Centre for Mathematical Modelling and Computer Simulation, Bangalore 560 037, India | ||