A shape‐free 8‐node plane element unsymmetric analytical trial function method |
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Authors: | Song Cen Guo‐Hua Zhou Xiang‐Rong Fu |
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Affiliation: | 1. Department of Engineering Mechanics, School of Aerospace, Tsinghua University, , Beijing, 100084, China;2. High Performance Computing Center, School of Aerospace, Tsinghua University, , Beijing, 100084 China;3. Key Laboratory of Applied Mechanics, School of Aerospace, Tsinghua University, , Beijing, 100084 China;4. College of Water Conservancy & Civil Engineering, China Agricultural University, , Beijing, 100083 China |
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Abstract: | The unsymmetric FEM is one of the effective techniques for developing finite element models immune to various mesh distortions. However, because of the inherent limitation of the metric shape functions, the resulting element models exhibit rotational frame dependence and interpolation failure under certain conditions. In this paper, by introducing the analytical trial function method used in the hybrid stress‐function element method, an effort was made to naturally eliminate these defects and improve accuracy. The key point of the new strategy is that the monomial terms (the trial functions) in the assumed metric displacement fields are replaced by the fundamental analytical solutions of plane problems. Furthermore, some rational conditions are imposed on the trial functions so that the assumed displacement fields possess fourth‐order completeness in Cartesian coordinates. The resulting element model, denoted by US‐ATFQ8, can still work well when interpolation failure modes for original unsymmetric element occur, and provide the invariance for the coordinate rotation. Numerical results show that the exact solutions for constant strain/stress, pure bending and linear bending problems can be obtained by the new element US‐ATFQ8 using arbitrary severely distorted meshes, and produce more accurate results for other more complicated problems. Copyright © 2012 John Wiley & Sons, Ltd. |
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Keywords: | finite element unsymmetric finite element method 8‐node plane quadrilateral element fundamental analytical solution analytical trial function severely distorted mesh |
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