• Stress and mixed boundary conditions for two-dimensional dodecagonal quasi-crystal plates

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    • Keywords


      Boundary conditions; plates; axisymmetric deformation; two-dimensional dodecagonal quasi-crystals; decaying states.

    • Abstract


      For plate bending and stretching problems in two-dimensional (2D) dodecagonal quasi-crystal (QC) media, the reciprocal theorem and the general solution for QCs are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order. The method developed by Gregory and Wan is used to generate necessary conditions which the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate; these decaying state conditions are obtained explicitly for axisymmetric bending and stretching of a circular plate when stress or mixed conditions are imposed on the plate edge. They are then used for the correct formulation of boundary conditions for the interior solution. For the stress data, our boundary conditions coincide with those obtained in conventional forms of plate theories. More importantly, appropriate boundary conditions with a set of mixed edge-data are obtained for the first time. Furthermore, the corresponding necessary conditions for transversely isotropic elastic plate are obtained directly, and their isotropic elastic counterparts are also obtained.

    • Author Affiliations


      Yan Gao1 Si-Peng Xu2 Bao-Sheng Zhao3

      1. College of Science, China Agricultural University, P.O. Box 74, Beijing 100083, People’s Republic of China
      2. College of Engineering, Ocean University of China, Qingdao 266071, People’s Republic of China
      3. School of Mechanical Engineering, University of Science and Technology Liaoning, Anshan 114044, People’s Republic of China
    • Dates

  • Pramana – Journal of Physics | News

© 2017 Indian Academy of Sciences, Bengaluru.