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On the assumptions of the generalized plane stress problem and the Filon average

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Abstract

In this article, we prove that the assumption of vanishing normal stress for the generalized plane stress problem can be further weakened, so that the normal stress is harmonic. The stress state under this harmonic assumption can also be decomposed into the plane stress state and the shear stress state. Finally, a necessary and sufficient condition is presented for the existence of the biharmonic Airy stress function for the Filon averaged in-plane stresses, which is shown to be weaker than the assumption of the harmonic normal stress.

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Authors and Affiliations

  1. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing, 100871, People’s Republic of China

    Min-Zhong Wang

  2. Department of Materials and Earth Science, Institute of Materials Science, TU Darmstadt, Jovanka-Bontschits-Strasse 2, 64287, Darmstadt, Germany

    Bai-Xiang Xu

  3. College of Science, China Agricultural University, P. O. Box 74, Beijing, 100083, People’s Republic of China

    Yang Gao

Authors
  1. Min-Zhong Wang
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  2. Bai-Xiang Xu
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  3. Yang Gao
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Correspondence to Bai-Xiang Xu.

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Wang, MZ., Xu, BX. & Gao, Y. On the assumptions of the generalized plane stress problem and the Filon average. Acta Mech 225, 1419–1427 (2014). https://doi.org/10.1007/s00707-013-1036-6

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  • DOI: https://doi.org/10.1007/s00707-013-1036-6

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