Transactions of Nanjing University of Aeronautics & Astronautics
General Solutions of Thermoelastic Plane Problems of Two-Dimensional Quasicrystals
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Abstract:
The thermoelastic plane problems of two-dimensional decagonal quasicrystals (QCs) are systematically investigated. By introducing a displacement function, the problem of thermoelastic plane problems can be simplified to an eighth-order partial differential governing equation, and then general solutions are presented through an operator method. By virtue of the Almansi′s theorem, the general solutions are further established, and all expressions for the phonon, phason and thermal fields are described in terms of the potential functions. As an application of the general solution, for a steady point heat source in a semi-infinite quasicrystal plane, the closed form solutions are presented by four newly induced harmonic functions.
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This work was supported by the National Natural Science Foundation of China (11172319); the Chinese Universities Scientific Fund (2011JS046,2013BH008); the Opening Fund of State Key Laboratory of Nonlinear Mechanics; the Program for New Century Excellent Talents in University (NCET-13-0552); the National Science Foundation for Post-doctoral Scientists of China (2013M541086).
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