Fundamental solutions of penny-shaped and half-infinite plane cracks embedded in an infinite space of one-dimensional hexagonal quasi-crystal under thermal loading

An exact closed-form solution for a multilayered one-dimensional orthorhombic quasicrystal plate

“…Based on the general solutions of 1D QCs [24,25], Gao et al [26,27] solved exactly plane problems for both a QC beam and QC plate by introducing a refined theory. Recently, static and transient bending of 1D QC plates was studied by a mesh-free method [28], and an exact closed-form solution for a half-infinite plane crack in an infinite space of 1D hexagonal QC under thermal loading was derived by Li [29]. However, an exact closed-form solution for 3D static problems of 1D orthorhombic QCs in a finite domain has not been studied yet to the best of the authors' knowledge.…”

Fundamental elastic field in an infinite medium of two-dimensional hexagonal quasicrystal with a planar crack: 3D exact analysis

“…Then, the mode I problem for three common cracks (penny-shaped, external circular and half-infinite plane crack) embedded in 1D hexagonal QC was investigated by Li (2014), in a systematic manner. Recently, following the similar techniques in Li (2013Li ( , 2014, obtained the axisymmetric thermoelastic solutions for an infinite space of 2D hexagonal QC containing a penny-shaped under the action of uniform thermal loadings. However, the mode I crack problem, in the framework of elasticity of 2D hexagonal QCs, has not been studied yet to the best of the authors' knowledge.…”

“…Taking advantage of the general solutions in terms of quasi-harmonic functions conjugated with the generalized method of potential theory, Li (2013) presented the 3D non-axisymmetric fundamental thermo-elastic field in an infinite 1D hexagonal QC space, which is weakened by a penny-shaped/half-infinite plane crack submitted to a pair of point temperatures. Then, the mode I problem for three common cracks (penny-shaped, external circular and half-infinite plane crack) embedded in 1D hexagonal QC was investigated by Li (2014), in a systematic manner.…”

Defects in Static Elasticity of Quasicrystals

“…For example, Radi and Mariano focused their attention on the straight cracks and dislocations in two-dimensional quasicrystals, and described linear elasticity of quasicrystals and obtained some profound results for [39][40][41]. Li and his workers induced fundamental solutions for thermo-elasticity of one-dimensional hexagonal quasicrystals with half infinite plane cracks and obtained some solutions [42][43][44]. Of course, elastic theory of quasicrystals has been developed by some researchers (for example, Li and Chai [45] and Sladek et al [46]).…”