LIU Xingwei, LI Xing, WANG Wenshuai. The Anti-Plane Problem of Regular n-Polygon Holes With Radial Edge Cracks in 1D Hexagonal Piezoelectric Quasicrystals[J]. Applied Mathematics and Mechanics, 2020, 41(7): 713-724. doi: 10.21656/1000-0887.400334
Citation: LIU Xingwei, LI Xing, WANG Wenshuai. The Anti-Plane Problem of Regular n-Polygon Holes With Radial Edge Cracks in 1D Hexagonal Piezoelectric Quasicrystals[J]. Applied Mathematics and Mechanics, 2020, 41(7): 713-724. doi: 10.21656/1000-0887.400334

The Anti-Plane Problem of Regular n-Polygon Holes With Radial Edge Cracks in 1D Hexagonal Piezoelectric Quasicrystals

doi: 10.21656/1000-0887.400334
Funds:  The National Natural Science Foundation of China(11561055;11762017;11762016)
  • Received Date: 2019-11-06
  • Rev Recd Date: 2020-05-12
  • Publish Date: 2020-07-01
  • The heat conduction is a common problem in engineering practice. Compared with those of isotropic materials, the heat conduction problem of anisotropic materials is more complicated, so it is of great significance to accurately predict the internal temperature distribution. The numerical manifold method (NMM) was developed to solve typical continuous and discontinuous heat conduction problems in anisotropic materials. According to the governing differential equation, boundary conditions and variational principles, the NMM discrete equations for such problems were derived. Several representative examples involving continuous and discontinuous situations were analyzed with the uniform mathematical cover independent of all physical boundaries. The results prove the feasibility and accuracy of the method and indicate that the NMM can simulate the heat conduction problem of anisotropic materials well. Besides, the influences of the material properties and crack configurations on the temperatures were also investigated.
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