11 Numerical Evaluation of Integrals in Laplace Domain Anisotropic …
171
Malén, K. (1971). A unified six-dimensional treatment of elastic green’s functions and dislocations.
Physica Status Solidi (B), 44, 661–672. https://doi.org/10.1002/pssb.2220440224.
Mura, T., & Kinoshita, N. (1971). Green’s functions for anisotropic elasticity. Physica Status Solidi
(B), 47, 607–618. https://doi.org/10.1002/pssb.2220470226.
Nakamura, G., & Tanuma, K. (1997). A formula for the fundamental solution of anisotropic elasticity. The Quarterly Journal of Mechanics and Applied Mathematics, 50, 179–194. https://doi.
org/10.1093/qjmam/50.2.179.
Pan, E., & Chen, W. (2015). Static Green’s functions in anisotropic media. Cambridge: Cambridge
University Press.
Phan, A., Gray, L., & Kaplan, T. (2004). On the residue calculus evaluation of the 3-D anisotropic
elastic Green’s function. Communications in Numerical Methods in Engineering, 20, 335–341.
https://doi.org/10.1002/cnm.675.
Phan, A., Gray, L., & Kaplan, T. (2005). Residue approach for evaluating the 3D anisotropic elastic
Green’s function: Multiple roots. Engineering Analysis with Boundary Elements, 29, 570–576.
https://doi.org/10.1016/j.enganabound.2004.12.012.
Placidi, L., Andreaus, U., & Giorgio, I. (2017). Identification of two-dimensional pantographic
structure via a linear D4 orthotropic second gradient elastic model. Journal of Engineering
Mathematics, 103, 1–21. https://doi.org/10.1007/s10665-016-9856-8.
Placidi, L., Barchiesi, E., Turco, E., & Rizzi, N. (2016). A review on 2D models for the description
of pantographic fabrics. Zeitschrift für Angewandte Mathematik und Physik, 67, 121. https://doi.
org/10.1007/s00033-016-0716-1.
Rahali, Y., Giorgio, I., Ganghoffer, J.-F., & dell’Isola, F. (2015). Homogenization à la Piola produces
second gradient continuum models for linear pantographic lattices. International Journal of
Engineering Science, 97, 148–172. https://doi.org/10.1016/j.ijengsci.2015.10.003.
Sáez, A., & Dom´ ınguez, J. (1999). BEM analysis of wave scattering in transversely isotropic solids.
International Journal for Numerical Methods in Engineering, 44, 1283–1300. https://doi.org/10.
1002/(sici)1097-0207(19990330)44:9<1283::aid-nme544>3.0.co;2-o.
Sáez, A., & Dom´ ınguez, J. (2000). Far field dynamic Green’s functions for BEM in transversely
isotropic solids. Wave Motion, 32, 113–123. https://doi.org/10.1016/s0165-2125(00)00032-9.
Sales, M., & Gray, L. (1998). Evaluation of the anisotropic Green’s function and its derivatives.
Computers & Structures, 69, 247–254. https://doi.org/10.1016/s0045-7949(97)00115-6.
Sciarra, G., dell’Isola, F., & Coussy, O. (2007). Second gradient poromechanics. International
Journal of Solids and Structures, 44(20), 6607–6629. https://doi.org/10.1016/j.ijsolstr.2007.
03.003.
Shiah, Y., Tan, C., & Lee, R. (2010). Internal point solutions for displacements and stresses in 3D
anisotropic elastic solids using the boundary element method. Computer Modeling in Engineering
& Sciences, 69, 167–179. https://doi.org/10.3970/cmes.2010.069.167.
Shiah, Y., Tan, C., & Wang, C. (2012). Efficient computation of the Green’s function and its derivatives for three-dimensional anisotropic elasticity in BEM analysis. Engineering Analysis with
Boundary Elements, 36, 1746–1755. https://doi.org/10.1016/j.enganabound.2012.05.008.
Tan, C., Shiah, Y., & Wang, C. (2013). Boundary element elastic stress analysis of 3D generally
anisotropic solids using fundamental solutions based on Fourier series. International Journal of
Solids and Structures, 50, 2701–2711. https://doi.org/10.1016/j.ijsolstr.2013.04.026.
Ting, T. (1997). The three-dimensional elastostatic Green’s function for general anisotropic linear
elastic solids. The Quarterly Journal of Mechanics and Applied Mathematics, 50, 407–426.
https://doi.org/10.1093/qjmam/50.3.407.
Vavryˇ cuk, V. (2007). Asymptotic Green’s function in homogeneous anisotropic viscoelastic media.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463,
2689–2707. https://doi.org/10.1098/rspa.2007.1862.
Wang, C., & Achenbach, J. (1994). Elastodynamic fundamental solutions for anisotropic solids.
Geophysical Journal International, 118, 384–392. https://doi.org/10.1111/j.1365-246x.1994.tb0
3970.x.
171
Malén, K. (1971). A unified six-dimensional treatment of elastic green’s functions and dislocations.
Physica Status Solidi (B), 44, 661–672. https://doi.org/10.1002/pssb.2220440224.
Mura, T., & Kinoshita, N. (1971). Green’s functions for anisotropic elasticity. Physica Status Solidi
(B), 47, 607–618. https://doi.org/10.1002/pssb.2220470226.
Nakamura, G., & Tanuma, K. (1997). A formula for the fundamental solution of anisotropic elasticity. The Quarterly Journal of Mechanics and Applied Mathematics, 50, 179–194. https://doi.
org/10.1093/qjmam/50.2.179.
Pan, E., & Chen, W. (2015). Static Green’s functions in anisotropic media. Cambridge: Cambridge
University Press.
Phan, A., Gray, L., & Kaplan, T. (2004). On the residue calculus evaluation of the 3-D anisotropic
elastic Green’s function. Communications in Numerical Methods in Engineering, 20, 335–341.
https://doi.org/10.1002/cnm.675.
Phan, A., Gray, L., & Kaplan, T. (2005). Residue approach for evaluating the 3D anisotropic elastic
Green’s function: Multiple roots. Engineering Analysis with Boundary Elements, 29, 570–576.
https://doi.org/10.1016/j.enganabound.2004.12.012.
Placidi, L., Andreaus, U., & Giorgio, I. (2017). Identification of two-dimensional pantographic
structure via a linear D4 orthotropic second gradient elastic model. Journal of Engineering
Mathematics, 103, 1–21. https://doi.org/10.1007/s10665-016-9856-8.
Placidi, L., Barchiesi, E., Turco, E., & Rizzi, N. (2016). A review on 2D models for the description
of pantographic fabrics. Zeitschrift für Angewandte Mathematik und Physik, 67, 121. https://doi.
org/10.1007/s00033-016-0716-1.
Rahali, Y., Giorgio, I., Ganghoffer, J.-F., & dell’Isola, F. (2015). Homogenization à la Piola produces
second gradient continuum models for linear pantographic lattices. International Journal of
Engineering Science, 97, 148–172. https://doi.org/10.1016/j.ijengsci.2015.10.003.
Sáez, A., & Dom´ ınguez, J. (1999). BEM analysis of wave scattering in transversely isotropic solids.
International Journal for Numerical Methods in Engineering, 44, 1283–1300. https://doi.org/10.
1002/(sici)1097-0207(19990330)44:9<1283::aid-nme544>3.0.co;2-o.
Sáez, A., & Dom´ ınguez, J. (2000). Far field dynamic Green’s functions for BEM in transversely
isotropic solids. Wave Motion, 32, 113–123. https://doi.org/10.1016/s0165-2125(00)00032-9.
Sales, M., & Gray, L. (1998). Evaluation of the anisotropic Green’s function and its derivatives.
Computers & Structures, 69, 247–254. https://doi.org/10.1016/s0045-7949(97)00115-6.
Sciarra, G., dell’Isola, F., & Coussy, O. (2007). Second gradient poromechanics. International
Journal of Solids and Structures, 44(20), 6607–6629. https://doi.org/10.1016/j.ijsolstr.2007.
03.003.
Shiah, Y., Tan, C., & Lee, R. (2010). Internal point solutions for displacements and stresses in 3D
anisotropic elastic solids using the boundary element method. Computer Modeling in Engineering
& Sciences, 69, 167–179. https://doi.org/10.3970/cmes.2010.069.167.
Shiah, Y., Tan, C., & Wang, C. (2012). Efficient computation of the Green’s function and its derivatives for three-dimensional anisotropic elasticity in BEM analysis. Engineering Analysis with
Boundary Elements, 36, 1746–1755. https://doi.org/10.1016/j.enganabound.2012.05.008.
Tan, C., Shiah, Y., & Wang, C. (2013). Boundary element elastic stress analysis of 3D generally
anisotropic solids using fundamental solutions based on Fourier series. International Journal of
Solids and Structures, 50, 2701–2711. https://doi.org/10.1016/j.ijsolstr.2013.04.026.
Ting, T. (1997). The three-dimensional elastostatic Green’s function for general anisotropic linear
elastic solids. The Quarterly Journal of Mechanics and Applied Mathematics, 50, 407–426.
https://doi.org/10.1093/qjmam/50.3.407.
Vavryˇ cuk, V. (2007). Asymptotic Green’s function in homogeneous anisotropic viscoelastic media.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463,
2689–2707. https://doi.org/10.1098/rspa.2007.1862.
Wang, C., & Achenbach, J. (1994). Elastodynamic fundamental solutions for anisotropic solids.
Geophysical Journal International, 118, 384–392. https://doi.org/10.1111/j.1365-246x.1994.tb0
3970.x.