Recovery of consistent stresses for compatible finite elements |
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| Affiliation: | 1. School of Mathematics, Sichuan University, Chengdu, 610064, China;2. Department of Mathematics, University of Houston, Houston, TX 77204, USA;3. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong;4. Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China;2. Department of Chemical & Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta T2N 1N4, Canada;3. School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China;1. Lawrence Livermore National Laboratory, AX Division, M/S L-38, P.O. Box 808, Livermore, CA 94550, United States;2. Los Alamos National Laboratory, XCP-4: Methods and Algorithms, M/S F644, Los Alamos, NM 87545, Unites States;1. Department of Computer Sciences, University of Wisconsin, Madison, WI 53705, USA;2. Department of Mechanical Engineering, University of Wisconsin, Madison, WI 53705, USA |
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| Abstract: | In displacement based finite element models, stresses deduced directly from the constitutive relationship can show local erratic behaviour. This occurs in problems involving initial stresses or strains, or varying rigidities over the element domain, when local stresses do not meet a specific consistency requirement. In this context, an integrated procedure for recovering consistent stresses, that is stresses ridded of spurious outcomes, is proposed. The procedure is developed within a general weighted residual approach, suitably specialized for the purpose. The relationship between the proposed procedure and those based on the Hu–Washizu formulation is also elucidated. For illustration purpose, some numerical tests are included. |
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