Institute of Mathematics

References:
[1] M. Altunkaynak: An analytical method for solving elastic system in inhomogeneous orthotropic media. Math. Methods Appl. Sci. 42 (2019), 2324-2333. DOI 10.1002/mma.5510 | MR 3936402 | Zbl 1420.35154
[2] N. B. Andersen: Real Paley-Wiener theorems for the inverse Fourier transform on a Riemannian symmetric space. Pac. J. Math. 213 (2004), 1-13. DOI 10.2140/pjm.2004.213.1 | MR 2040247 | Zbl 1049.43004
[3] J. Chen, Z. Liu, Z. Zou: Transient internal crack problem for a nonhomogeneous orthotropic strip (Mode I). Int. J. Eng. Sci. 40 (2002), 1761-1774. DOI 10.1016/S0020-7225(02)00038-1
[4] W. Q. Chen, Y. L. Ma, H. J. Ding: On three-dimensional elastic problems of one-dimensional hexagonal quasicrystal bodies. Mech. Res. Commun. 31 (2004), 633-641. DOI 10.1016/j.mechrescom.2004.03.007 | MR 2092970 | Zbl 1098.74554
[5] C. H. Daros: A fundamental solution for SH-waves in a class of inhomogeneous anisotropic media. Int. J. Eng. Sci. 46 (2008), 809-817. DOI 10.1016/j.ijengsci.2008.02.001 | MR 2427933 | Zbl 1213.74156
[6] C. H. Daros: A time-harmonic fundamental solution for a class of inhomogeneous transversely isotropic media. Wave Motion 46 (2009), 269-279. DOI 10.1016/j.wavemoti.2009.02.001 | MR 2568578 | Zbl 1231.74172
[7] P. De, R. A. Pelcovits: Linear elasticity theory of pentagonal quasicrystals. Phys. Rev. B 35 (1987), Article ID 8609, 12 pages. DOI 10.1103/PhysRevB.35.8609
[8] D.-H. Ding, R. Wang, W. Yang, C. Hu: General expressions for the elastic displacement fields induced by dislocations in quasicrystals. J. Phys., Conden. Matt. 7 (1995), Article ID 5423, 14 pages. DOI 10.1088/0953-8984/7/28/003
[9] D.-H. Ding, W. Yang, C. Hu, R. Wang: Generalized elasticity theory of quasicrystals. Phys. Rev. B 48 (1993), Article ID 7003, 8 pages. DOI 10.1103/PhysRevB.48.7003
[10] H. Ding, Chenbuo, Liangjian: General solutions for coupled equations for piezoelectric media. Int. J. Solids Struct. 33 (1996), 2283-2298. DOI 10.1016/0020-7683(95)00152-2 | Zbl 0899.73453
[11] T. Fan: Mathematical Theory of Elasticity of Quasicrystals and Its Applications. Springer, Berlin (2011). DOI 10.1007/978-3-642-14643-5 | MR 2847904 | Zbl 1222.74003
[12] T.-Y. Fan, Y.-W. Mai: Elasticity theory, fracture mechanics, and some relevant thermal properties of quasi-crystalline materials. Appl. Mech. Rev. 57 (2004), 325-343. DOI 10.1115/1.1763591
[13] Y. Gao: Governing equations and general solutions of plane elasticity of cubic quasicrystals. Phys. Lett., A 373 (2009), 885-889. DOI 10.1016/j.physleta.2009.01.002 | Zbl 1236.74048
[14] Y. Gao, S.-P. Xu, B.-S. Zhao: A theory of general solutions of 3D problems in 1D hexagonal quasicrystals. Phys. Scr. 77 (2008), Article ID 015601, 6 pages. DOI 10.1088/0031-8949/77/01/015601 | Zbl 1157.82395
[15] Y. Gao, B.-S. Zhao: A general treatment of three-dimensional elasticity of quasicrystals by an operator method. Phys. Status Solid., B 243 (2006), 4007-4019. DOI 10.1002/pssb.200541400
[16] Y. Gao, B.-S. Zhao: General solutions of three-dimensional problems for two-dimensional quasicrystals. Appl. Math. Modelling 33 (2009), 3382-3391. DOI 10.1016/j.apm.2008.11.001 | MR 2524125 | Zbl 1205.74023
[17] R. L. Holford: Elementary source-type solutions of the reduced wave equation. J. Acoust. Soc. Am. 70 (1981), 1427-1436. DOI 10.1121/1.387099 | MR 0634323 | Zbl 0478.35030
[18] J. F. Hook: Green's functions for axially symmetric elastic waves in unbounded inhomogeneous media having constant velocity gradients. J. Appl. Mech. 29 (1962), 293-298. DOI 10.1115/1.3640544 | MR 0138265 | Zbl 0107.41902
[19] C. Hu, R. Wang, D.-H. Ding: Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals. Rep. Progr. Phys. 63 (2000), Article ID 63, 39 pages. DOI 10.1088/0034-4885/63/1/201 | MR 1732137
[20] D. Levine, P. J. Steinhardt: Quasicrystals: A new class of ordered structures. Phys. Rev. Lett. 53 (1984), Article ID 2477, 4 pages. DOI 10.1103/PhysRevLett.53.2477
[21] L.-H. Li, T.-Y. Fan: Final governing equation of plane elasticity of icosahedral quasicrystals and general solution based on stress potential function. Chin. Phys. Lett. 23 (2006), Article ID 2519, 3 pages. DOI 10.1088/0256-307X/23/9/047
[22] G. T. Liu, T. Y. Fan, R. P. Guo: Governing equations and general solutions of plane elasticity of one-dimensional quasicrystals. Int. J. Solids Struct. 41 (2004), 3949-3959. DOI 10.1016/j.ijsolstr.2004.02.028 | Zbl 1079.74524
[23] G. D. Manolis, R. P. Shaw: Fundamental solutions for variable density two-dimensional elastodynamic problems. Eng. Anal. Bound. Elem. 24 (2000), 739-750. DOI 10.1016/S0955-7997(00)00056-4 | Zbl 0971.74046
[24] I. A. Ovid'ko: Plastic deformation and decay of dislocations in quasi-crystals. Mater. Sci. Eng., A 154 (1992), 29-33. DOI 10.1016/0921-5093(92)90359-9
[25] Y.-Z. Peng, T.-Y Fan: Perturbation theory of 2D decagonal quasicrystals. Physica B 311 (2002), 326-330. DOI 10.1016/S0921-4526(01)00611-1
[26] T. V. Rangelov, G. D. Manolis, P. S. Dineva: Elastodynamic fundamental solutions for certain families of 2D inhomogeneous anisotropic domains: Basic derivations. Eur. J. Mech., A, Solids 24 (2005), 820-836. DOI 10.1016/j.euromechsol.2005.05.002  | MR 2174322 | Zbl 1125.74344
[27] S. B. Rochal, I. V. Lebedyuk, Y. A. Kozinkina: Linear continuous inhomogeneous strains in octagonal and decagonal quasicrystals. Phys. Rev., B 60 (1999), Article ID 865, 9 pages. DOI 10.1103/PhysRevB.60.865
[28] D. Shechtman, I. Blech, D. Gratias, J. W. Cahn: Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53 (1984), Article ID 1951, 3 pages. DOI 10.1103/PhysRevLett.53.1951
[29] M. A. Slawinski: Waves and Rays in Elastic Continua. World Scientific, Hackensack (2021). DOI 10.1142/11994 | Zbl 1459.74002
[30] J. E. S. Socolar, T. C. Lubensky, P. J. Steinhardt: Phonons, phasons, and dislocations in quasicrystals. Phys. Rev., B 34 (1986), Article ID 3345, 16 pages. DOI 10.1103/PhysRevB.34.3345
[31] X. Wang: The general solution of one-dimensional hexagonal quasicrystal. Mech. Res. Commun. 33 (2006), 576-580. DOI 10.1016/j.mechrescom.2005.02.022 | MR 2215812 | Zbl 1192.74069
[32] K. Watanabe: Transient response of an inhomogeneous elastic solid to an impulsive SH-source: Variable SH-wave velocity. Bull. JSME 25 (1982), 315-320. DOI 10.1299/jsme1958.25.315
[33] K. Watanabe, R. G. Payton: Green's function and its non-wave nature for SH-wave in inhomogeneous elastic solid. Int. J. Eng. Sci. 42 (2004), 2087-2106. DOI 10.1016/j.ijengsci.2004.08.001 | MR 2102742 | Zbl 1211.74123
[34] V. Yakhno: A new method of solving equations of elasticity in inhomogeneous quasicrystals by means of symmetric hyperbolic systems. Math. Methods Appl. Sci. 44 (2021), 9487-9506. DOI 10.1002/mma.7373 | MR 4279862 | Zbl 1475.35338
[35] V. G. Yakhno, A. Sevimlican: Solving an initial value problem in inhomogeneous electrically and magnetically anisotropic uniaxial media. Appl. Math. Comput. 215 (2010), 3839-3850. DOI 10.1016/j.amc.2009.11.027 | MR 2578849 | Zbl 1188.78003
[36] V. Yakhno, A. Sevimlican: An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media. Appl. Math., Praha 56 (2011), 315-339. DOI 10.1007/s10492-011-0019-y | MR 2800581 | Zbl 1224.35392
[37] V. G. Yakhno, H. Ç Yaslan: Three dimensional elastodynamics of 2D quasicrystals: The derivation of the time-dependent fundamental solution. Appl. Math. Modelling 35 (2011), 3092-3110. DOI 10.1016/j.apm.2010.12.019 | MR 2776264 | Zbl 1219.74010
[38] L. Z. Yang, L. L. Zhang, Y. Gao: General solutions of plane problem in one-dimensional hexagonal quasicrystals. Appl. Mech. Mater. 275-277 (2013), 101-104. DOI 10.4028/www.scientific.net/AMM.275-277.101
[39] L. Zhang, Y. Zhang, Y. Gao: General solutions of plane elasticity of one-dimensional orthorhombic quasicrystals with piezoelectric effect. Phys. Lett., A 378 (2014), 2768-2776. DOI 10.1016/j.physleta.2014.07.027 | MR 3250390 | Zbl 1298.74027
[40] W.-M. Zhou, T.-Y. Fan: Axisymmetric elasticity problem of cubic quasicrystal. Chin. Phys. 9 (2000), Article ID 294, 10 pages. DOI 10.1088/1009-1963/9/4/009