A general Love solution for the inhomogeneous linear isotropic theory of elasticity with the elastic constants dependent on the coordinate r is proposed. The axisymmetric case is analyzed and cylindrical coordinates are used. This is the fourth publication in the series on general solutions in the inhomogeneous theory of elasticity. The new results are promising for the modern theory of functionally graded materials. The key steps of deriving the Love solutions are described for further use of the derivation procedure. The procedure of generalizing the Love solutions to the inhomogeneous theory of elasticity is detailed. The results obtained are discussed
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M. Yu. Kashtalyan and J. J. Rushchitsky, “General Hoyle–Youngdahl and Love solutions in the linear inhomogeneous theory of elasticity,” Int. Appl. Mech., 46, No. 1, 1–17 (2010).
M. Yu. Kashtalyan and J. J. Rushchitsky, “Love solutions in the linear inhomogeneous transversely isotropic theory of elasticity,” Int. Appl. Mech., 46, No. 2, 121–129 (2010).
M. A. Koltunov, Yu. N. Vasil’ev, and V. A. Chernykh, Elasticity and Strength of Cylindrical Bodies [in Russian], Vysshaya Shkola, Moscow (1975).
V. A. Lomakin, Theory of Elasticity of Inhomogeneous Bodies [in Russian], Izd. Mosk. Univ., Moscow (1976).
A. I. Lurie, Theory of Elasticity, Springer, Berlin (1999).
V. Birman and L. W. Bird, “Modeling and analysis of FGM and structures,” Appl. Mech. Rev., 60, 195–216 (2007).
C. Cattani and J. J. Rushchitsky, Wavelet and Wave Analysis as Applied to Materials with Micro or Nanostructures, World Scientific, Singapore–London (2007).
C. Cattani, J. J. Rushchitsky, and S. V. Sinchilo, “Physical constants for one type of nonlinearly elastic fibrous microand nanocomposites with hard and soft nonlinearities,” Int. Appl. Mech., 41, No. 12, 1368–1377 (2005).
N. Gupta, S. K. Gupta, and B. J. Mueller, “Analysis of a functionally graded particulate composite under flexural loading conditions,” Mater. Sci, Eng., A485, No. 1–2, 439–447 (2008).
A. N. Guz and J. J. Rushchitsky, “Nanomaterials: On the mechanics of nanomaterials,” Int. Apðl. Mech., 39, No. 11, 1271–1293 (2003).
A. N. Guz, J. J. Rushchitsky, and I. A. Guz, “Establishing fundamentals of the mechanics of nanocomposites,” Int. Appl. Mech., 43, No. 3, 247–271 (2007).
A. N. Guz, J. J. Rushchitsky, and I. A. Guz, “Comparative computer modeling of carbon-polymer composites with carbon or graphite microfibers or carbon nanotubes,” Comp. Model. Eng. Sci., 26, No. 3, 159–176 (2008).
I. A. Guz and J. J. Rushchitsky, “Comparing the evolution characteristics of waves in nonlinearly elastic micro- and nanocomposites with carbon fillers,” Int. Appl. Mech., 40, No. 7, 785–793 (2004).
I. A. Guz and J. J. Rushchitsky, “Theoretical description of a delamination mechanism in fibrous micro- and nano-composites,” Int. Appl. Mech., 40, No. 10, 1129–1136 (2004).
I. A. Guz, A. A. Rodger, A. N. Guz, and J. J. Rushchitsky, “Developing the mechanical models for nanomaterials,” Composites. Part A: Appl. Sci. Manufact., 38, No. 4, 1234–1250 (2007).
I. A. Guz and J. J. Rushchitsky, “Computational simulation of harmonic wave propagation in fibrous micro- and nanocomposites,” Compos. Sci. Technol., 67, No. 4, 861–866 (2007).
I. A. Guz, A. A. Rodger, A. N. Guz, and J. J. Rushchitsky, “Predicting the properties of micro and nanocomposites: from the microwhiskers to bristled nano-centipedes,” Philos. Trans. Royal Society, A: Math. Phys. Eng. Sci., 365, No. 1860, 3233–3239 (2008).
H. G. Hahn, Elastizitatstheorie. Grundlagen der linearen Theorie and Anwendungen auf eindimensionale, ebene und raumliche Probleme, B. G. Teubner, Stuttgart (1985).
M. Kashtalyan, “Three-dimensional elasticity solution for bending of functionally graded rectangular plates,” Europ. J. Mech. A/Solids, 23, No. 5, 853–864 (2004).
M. Kashtalyan and M. Menshykova, “Three-dimensional elastic deformation of a functionally graded coating/substrate system,” Int. J. Solids Struct., 44, No. 16, 5272–5288 (2007).
M. Kashtalyan and M. Menshykova, “Three-dimensional analysis of a functionally graded coating~/~substrate system of finite thickness,” Phil. Trans. Royal Society A, 336, No. 1871, 1821–1826 (2008).
M. Kashtalyan and M. Menshykova, “Three-dimensional elasticity solution for sandwich panels with a functionally graded core,” Compos. Struct., 74, No. 2, 326–336 (2009).
M. Kashtalyan and J. J. Rushchitsky, “Revisiting displacement functions in three-dimensional elasticity of inhomogeneous media,” Int. J. Solids Struct., 46, No. 19, 3654–3662 (2009).
W. A. Kayssen and B. Ilschner, “FGM research activities in Europe,” MRS Bull., 20, 22–26 (1995).
M. Koizumi, “Concept of FGM,” Ceramic Trans., 34, 3–10 (1993).
M. Koizumi, “FGM activities in Japan,” Composites B, B 28, 1–4 (1997).
X. Y. Li, H. J. Ding, and W. Q. Chen, “Elasticity solutions for a transversely isotropic FGM circular plate subject to an axisymmetric transverse load qr k,” Int. J. Solids Struct., 45, 191–210 (2008).
X. Y. Li, H. J. Ding, and W. Q. Chen, “Axisymmetric elasticity solutions for a uniformly loaded annular plate of transversely isotropic FGM,” Acta Mech., 196, 139–159 (2008).
A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Dover, New York (1944).
Y. Miyamoto, W. A. Kaysser, B. H. Rabin, A. Kawasaki, and R. G. Ford, FGM: Design, Processing and Applications, Kluwer, Dordrecht (1999).
W. Nowacki, Elasticity Theory [in Polish], PWN, Warsaw (1970).
M. J. Pindera, S. M. Arnold, J. Aboudi, and D. Hui, “Use of composites in FGM,” Compos. Eng., 4, 1–145 (1994).
V. P. Plevako, “On the theory of elasticity of inhomogeneous media,” J. Appl. Math. Mech., 35, No. 5, 806–813 (1971).
Y. N. Shabana and N. Noda, “Numerical evaluation of the thermomechanical effective properties of FGM using homogenization method,” Int. J. Solids Struct., 45, 3494–3506 (2008).
S. Suresh and A. Mortensen, Fundamentals of FGM, Maney, London (1998).
M. Yamanouchi, M. Koizumi, T. Hirai, and I. Shiota (eds.), Proc. 1st Symp. on FGM Forum and the Society of Non-Traditional Technology, Japan (1990).
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Translated from Prikladnaya Mekhanika, Vol. 46, No. 3, pp. 3–13, March 2010.
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Kashtalyan, M.Y., Rushchitsky, J.J. General love solution in the linear isotropic inhomogeneous theory of radius-dependent elasticity. Int Appl Mech 46, 245–254 (2010). https://doi.org/10.1007/s10778-010-0304-6
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DOI: https://doi.org/10.1007/s10778-010-0304-6