170
I. P. Markov and M. V. Markina
multipliers and a perturbation solution. International Journal of Solids and Structures, 81, 1–12.
https://doi.org/10.1016/j.ijsolstr.2015.08.029.
dell’Isola, F., Giorgio, I., Pawlikowski, M., & Rizzi, N. (2016c). Large deformations of planar
extensible beams and pantographic lattices: Heuristic homogenization, experimental and numerical examples of equilibrium. Proceedings of the Royal Society A: Mathematical, Physical and
Engineering Sciences, 472, 20150790. https://doi.org/10.1098/rspa.2015.0790.
dell’Isola, F., Igumnov, L., Litvinchuk, S., Ipatov, A., Petrov, A., & Modin, I. (2019a). Surface waves
in dissipative poroviscoelastic layered half space: Boundary element analyses. In H. Altenbach,
A. Belyaev, V. Eremeyev, A. Krivtsov, & A. Porubov (Eds.), Advanced Structured Materials.
Dynamical processes in generalized continua and structures (Vol. 103). Cham: Springer.
dell’Isola, F., Seppecher, P., Alibert, J., Lekszycki, T., Grygoruk, R., Pawlikowski, M., et al. (2019b).
Pantographic metamaterials: An example of mathematically driven design and of its technological challenges. Continuum Mechanics and Thermodynamics, 31(4), 851–884. https://doi.org/10.
1007/s00161-018-0689-8.
dell’Isola, F., Seppecher, P., & Madeo, A. (2012). How contact interactions may depend on the shape
of Cauchy cuts in Nth gradient continua: Approach “à la D’Alembert.” Zeitschrift für Angewandte
Mathematik und Physik, 63(6), 1119–1141. https://doi.org/10.1007/s00033-012-0197-9.
dell’Isola, F., Seppecher, P., Spagnuolo, M., Barchiesi, E., Hils, F., Lekszycki, T., et al. (2019c).
Advances in pantographic structures: Design, manufacturing, models, experiments and image
analyses. Continuum Mechanics and Thermodynamics, 31(4), 1231–1282. https://doi.org/10.
1007/s00161-019-00806-x.
Dineva, P., Manolis, G., & Wuttke, F. (2019). Fundamental solutions in 3D elastodynamics for the
BEM: A review. Engineering Analysis with Boundary Elements, 105, 47–69. https://doi.org/10.
1016/j.enganabound.2019.04.003.
Dravinski, M., & Niu, Y. (2001). Three-dimensional time-harmonic Green’s functions for a triclinic
full-space using a symbolic computation system. International Journal for Numerical Methods
in Engineering, 53, 445–472. https://doi.org/10.1002/nme.292.
Dravinski, M., & Zheng, T. (2000). Numerical evaluation of three-dimensional time-harmonic
Green’s functions for a nonisotropic full-space. Wave Motion, 32, 141–151. https://doi.org/10.
1016/s0165-2125(00)00034-2.
Evans, G., & Webster, J. (1997). A high order, progressive method for the evaluation of irregular oscillatory integrals. Applied Numerical Mathematics, 23, 205–218. https://doi.org/10.1016/
s0168-9274(96)00058-x.
Fooladi, S., & Kundu, T. (2019a). An improved technique for elastodynamic Green’s function
computation for transversely isotropic solids. Journal of Nondestructive Evaluation, Diagnostics
and Prognostics of Engineering Systems, 2, 021005. https://doi.org/10.1115/1.4043605.
Fooladi, S., & Kundu, T. (2019b). Distributed point source modeling of the scattering of elastic
waves by a circular cavity in an anisotropic half-space. Ultrasonics, 94, 264–280. https://doi.org/
10.1016/j.ultras.2018.09.002.
Fredholm, I. (1900). Sur les équations de l’équilibre d’un corps solide élastique. Acta Mathematica,
23, 1–42. https://doi.org/10.1007/bf02418668.
Iserles, A., Nørsett, S., & Olver, S. (2006) Highly oscillatory quadrature: The story so far. Numerical Mathematics and Advanced Applications, 97–118. https://doi.org/10.1007/978-3-540-342
88-5_6.
Lee, V. (2009). Derivatives of the three-dimensional Green’s functions for anisotropic materials.
International Journal of Solids and Structures, 46, 3471–3479. https://doi.org/10.1016/j.ijsolstr.
2009.06.002.
Levin, D. (1982). Procedures for computing one- and two-dimensional integrals of functions with
rapid irregular oscillations. Mathematics of Computation, 38, 531. https://doi.org/10.2307/200
7287.
Lifshitz, I., & Rozenzweig, L. (1947). Construction of the Green tensor for the fundamental
equation of elasticity theory in the case of unbounded elastically anisotropic medium. Zhurnal
Eksperimental’noi i Teoreticheskoi Fiziki, 17, 783–791.
I. P. Markov and M. V. Markina
multipliers and a perturbation solution. International Journal of Solids and Structures, 81, 1–12.
https://doi.org/10.1016/j.ijsolstr.2015.08.029.
dell’Isola, F., Giorgio, I., Pawlikowski, M., & Rizzi, N. (2016c). Large deformations of planar
extensible beams and pantographic lattices: Heuristic homogenization, experimental and numerical examples of equilibrium. Proceedings of the Royal Society A: Mathematical, Physical and
Engineering Sciences, 472, 20150790. https://doi.org/10.1098/rspa.2015.0790.
dell’Isola, F., Igumnov, L., Litvinchuk, S., Ipatov, A., Petrov, A., & Modin, I. (2019a). Surface waves
in dissipative poroviscoelastic layered half space: Boundary element analyses. In H. Altenbach,
A. Belyaev, V. Eremeyev, A. Krivtsov, & A. Porubov (Eds.), Advanced Structured Materials.
Dynamical processes in generalized continua and structures (Vol. 103). Cham: Springer.
dell’Isola, F., Seppecher, P., Alibert, J., Lekszycki, T., Grygoruk, R., Pawlikowski, M., et al. (2019b).
Pantographic metamaterials: An example of mathematically driven design and of its technological challenges. Continuum Mechanics and Thermodynamics, 31(4), 851–884. https://doi.org/10.
1007/s00161-018-0689-8.
dell’Isola, F., Seppecher, P., & Madeo, A. (2012). How contact interactions may depend on the shape
of Cauchy cuts in Nth gradient continua: Approach “à la D’Alembert.” Zeitschrift für Angewandte
Mathematik und Physik, 63(6), 1119–1141. https://doi.org/10.1007/s00033-012-0197-9.
dell’Isola, F., Seppecher, P., Spagnuolo, M., Barchiesi, E., Hils, F., Lekszycki, T., et al. (2019c).
Advances in pantographic structures: Design, manufacturing, models, experiments and image
analyses. Continuum Mechanics and Thermodynamics, 31(4), 1231–1282. https://doi.org/10.
1007/s00161-019-00806-x.
Dineva, P., Manolis, G., & Wuttke, F. (2019). Fundamental solutions in 3D elastodynamics for the
BEM: A review. Engineering Analysis with Boundary Elements, 105, 47–69. https://doi.org/10.
1016/j.enganabound.2019.04.003.
Dravinski, M., & Niu, Y. (2001). Three-dimensional time-harmonic Green’s functions for a triclinic
full-space using a symbolic computation system. International Journal for Numerical Methods
in Engineering, 53, 445–472. https://doi.org/10.1002/nme.292.
Dravinski, M., & Zheng, T. (2000). Numerical evaluation of three-dimensional time-harmonic
Green’s functions for a nonisotropic full-space. Wave Motion, 32, 141–151. https://doi.org/10.
1016/s0165-2125(00)00034-2.
Evans, G., & Webster, J. (1997). A high order, progressive method for the evaluation of irregular oscillatory integrals. Applied Numerical Mathematics, 23, 205–218. https://doi.org/10.1016/
s0168-9274(96)00058-x.
Fooladi, S., & Kundu, T. (2019a). An improved technique for elastodynamic Green’s function
computation for transversely isotropic solids. Journal of Nondestructive Evaluation, Diagnostics
and Prognostics of Engineering Systems, 2, 021005. https://doi.org/10.1115/1.4043605.
Fooladi, S., & Kundu, T. (2019b). Distributed point source modeling of the scattering of elastic
waves by a circular cavity in an anisotropic half-space. Ultrasonics, 94, 264–280. https://doi.org/
10.1016/j.ultras.2018.09.002.
Fredholm, I. (1900). Sur les équations de l’équilibre d’un corps solide élastique. Acta Mathematica,
23, 1–42. https://doi.org/10.1007/bf02418668.
Iserles, A., Nørsett, S., & Olver, S. (2006) Highly oscillatory quadrature: The story so far. Numerical Mathematics and Advanced Applications, 97–118. https://doi.org/10.1007/978-3-540-342
88-5_6.
Lee, V. (2009). Derivatives of the three-dimensional Green’s functions for anisotropic materials.
International Journal of Solids and Structures, 46, 3471–3479. https://doi.org/10.1016/j.ijsolstr.
2009.06.002.
Levin, D. (1982). Procedures for computing one- and two-dimensional integrals of functions with
rapid irregular oscillations. Mathematics of Computation, 38, 531. https://doi.org/10.2307/200
7287.
Lifshitz, I., & Rozenzweig, L. (1947). Construction of the Green tensor for the fundamental
equation of elasticity theory in the case of unbounded elastically anisotropic medium. Zhurnal
Eksperimental’noi i Teoreticheskoi Fiziki, 17, 783–791.