Completeness of general solutions for three-dimensional transversely isotropic piezoelectricity |
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Authors: | Si-peng Xu Yang Gao Wei Wang |
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Institution: | aCollege of Engineering, Ocean University of China, Qingdao 266100, China;bCollege of Science, China Agricultural University, Beijing 100083, China;cDepartment of Mechanics and Engineering Science, Peking University, Beijing 100871, China |
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Abstract: | In this paper, a general solution for three-dimensional transversely isotropic piezoelectricity in terms of four quasi-quadri-harmonic functions is established first. Owing to complexity of the higher-order equation, it is difficult to obtain rigorous analytic solutions and in most cases this general solution is not applicable. By virtue of the generalized Almansi’s Theorem, the simplified generalized LHN solution and E–L solution expressed by lower order functions are achieved, respectively, by taking a decomposition and superposition technique. In the absence of piezoelectric coupling, these two simplified general solutions can be degenerated into those for transversely isotropic elasticity, i.e. LHN and E–L solutions. More importantly, the completeness of these two generalized solutions is proved if the domain is z-convex, no matter whether the characteristic roots are distinct or possibly equal to each other. |
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Keywords: | Transversely isotropic Piezoelectricity General solution Completeness |
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