Fundamental thermo‐electro‐elastic solutions for 1D hexagonal QC

Abstract

This paper is concerned with the fundamental solutions, in the framework of thermo‐electro‐elasticity, for an infinite/half‐infinite space of 1D hexagonal quasicrystals (QCs). To this end, three‐dimensional static general solutions, in terms of 5 quasi‐harmonic functions, are derived with the help of rigorous operator theory and generalized Almansi's theorem. For an infinite/half‐infinite space subjected to an external thermal load, corresponding problem is formulated by boundary value problems. Appropriate potential functions are set by a trail‐and‐error technique. Green functions for the problems in question are obtained explicitly in the closed forms. The present fundamental solutions can be employed to construct 3D analysis for crack, indentation and dislocation problems. Furthermore, these solutions also serve as benchmarks for various numerical simulations.

Thermo‐elastic analysis of functionally graded multilayered two‐dimensional decagonal quasicrystal plates

“…It can be observed from Figures 3(a)-(b) that the quite different responses of 33 and 23 are induced by different . 11 in Figure 3(c) and 12 in Figure 3(d) increase with increasing , and H 23 and H 11 (Figure 3(f)) follow the similar trend. The obvious influence of on H 23 is similar with the behavior of 33 and 23 .…”

“…used the extended displacement discontinuity method to analyze cracks in the periodical plane of one‐dimensional QCs with the heat effect and obtained the fundamental solutions. Li et al . derived a set of thermo‐electro‐elastic solutions for 1D QCs.…”

“…[10] Fan et al [11] used the extended displacement discontinuity method to analyze cracks in the periodical plane of one-dimensional QCs with the heat effect and obtained the fundamental solutions. Li et al [12] derived a set of thermoelectro-elastic solutions for 1D QCs. Guo et al [13] derived a general solution for the 2D thermoelastic QCs with a conductive elliptic hole in terms of the Stroh-type formalism.…”

Fundamental solutions and frictionless contact problem in a semi‐infinite space of 2D hexagonal piezoelectric QCs

“…We get a set of material properties of a particular 2D hexagonal piezoelectric QCs satisfying the positive definite condition from Refs. [14,20,27], whose material properties are tabulated in Table 1. Based on the material constants given in Table 1, we obtain the material parameters ( = 1, 2, 3, 4), ′ ( = 1, 2) of the 2D hexagonal piezoelectric QCs as follows, which are positive and different with each other:…”

“…[8][9][10] Chen [11] firstly obtained the fundamental solutions of one dimensional (1D) hexagonal QCs in the elastic field by means of potential theory and the generalized Almansi's theorem. Subsequently, some researchers obtained the 3D fundamental solutions of 1D hexagonal QCs in the thermo-elastic field, [12] in the piezoelectric field, [13] and in the thermo-electro-elastic field, [14] and the 3D fundamental solutions of 2D hexagonal QCs in the elastic field [15] and in the thermo-elastic field. [16] Because of the brittleness of the QCs, [5] the mechanical behavior of QCs with defects, such as crack, dislocation, void, inclusion, etc., has aroused the attention of many researchers'.…”