PACS 61.44. Br, 62.20.Dc By an operator method, the general solution of three-dimensional elasticity of quasicrystals is given constructively with some displacement functions, and its completeness is proved at the same time. Nonuniqueness and the scope of nonuniqueness of the general solution are also pointed out. The method used in the paper extends work from elasticity to quasicrystals elasticity. As two special cases, twodimensional dodecagonal quasicrystal and one-dimensional hexagonal QCs are considered, and the general solutions based on the operator method are presented.
By introducing four displacement functions, the governing equations of the threedimensional thermoelasticity of two-dimensional hexagonal quasicrystals are decoupled into two uncorrelated problems. Two higher-order displacement functions are introduced to represent the general solutions, which are eighth-order and fourth-order, respectively, for the two problems. By taking a decomposition and superposition procedure, the general solutions are further simplified in seven cases in terms of six quasi-harmonic displacement functions. To show the application of the general solutions obtained, a closed form solution is obtained for an infinite space containing a penny-shaped crack, subjected to a uniformly distributed temperature at the crack surface.
By using the reciprocal theorem of elasticity, the author obtained the appropriate stress boundary conditions for the Levy solution for plate bending accurate to all order for plates of general edge geometry and loading. Two special cases of k = 0 (axisymmetric deformation of a circular plate) and k P 2 (unsymmetric deformation of a circular plate) were discussed in detail in the paper.However, for the first case, the author indicated, ''However, they determine only the Fourier coefficient b 0 but not the rigid body transverse displacement component a 0 . Such a level of nonuniqueness is expected when all edge data are prescribed in terms of stresses.' ' (p. 4115, lines 20-22). To determine the Fourier coefficient a 0 , the second singular axisymmetric biharmonic function w 0 0 (r) = r 2 ln r in Eqs. (21) in Wan (2003) should be used. For this singular biharmonic function, the relevant displacement and stress components of the Levy solution are0020-7683/$ -see front matter Ó
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