Direct and inverse problems for an inhomogeneous medium


  • Luciana Majercsik Transilvania University of Brasov, Romania
  • Ligia Munteanu Institute of Solid Mechanics of the Romanian Academy, Romania


inhomogeneous medium, direct and inverse problems, shallow shell


The plane problem for an inhomogeneous medium is analyzed in this paper by using the cnoidal representation of the material inhomogeneity. This representation approximates the distribution of elastic properties in the material. Direct problem is finding the stress distribution in an inhomogeneous body when the elastic moduli of the material are known, and the inverse problem is searching for the elastic moduli of the inhomogeneous material for a given state of stress. The inverse problem is exercised to an inhomogeneous shallow shell subjected to uniformly distributed external load.


ELLABIB, A., NACHAOUI, A., An iterative approach to the solution of an inverse problem in linear elasticity, Mathematics and Computers in Simulation, 77, 2–3, pp. 189-201, 2008.

AMMARI, H., KANG, H. Reconstruction of small inhomogeneities from boundary measurements, Springer-Verlag, 2004.

TARDIEU, N., CONSTANTINESCU, A., On the determination of elastic coefficients from indentation experiments, Inverse Problems, 16, 3, pp. 577-588, 2000.

TIKHONOV, A.N., ARSENIN, V.Y., Solutions to ill-posed problems, Winston-Wiley, New York, 1977.

SOKOLOWSKI, J., ZOCHOWSKI, A., On the topological derivative in shape optimization, SIAM J. Control Optim., 37, pp. 1251–1272, 1999.

SOKOLOWSKI, J., ZOLESIO, J.P., Introduction to shape optimization. Shape sensitivity analysis, Springer series in Computational Mathematics, vol. 16, Springer-Verlag, 1992.

NINTCHEU FATA, S., GUZINA, B.B., A linear sampling method for near-field inverse problems in elastodynamics, Inverse Problems, 20, 3, pp. 713-736, 2004.

NINTCHEU FATA, S., GUZINA, B.B., BONNET, M., A computational basis for elastodynamic cavity identification in a semi-infinite solid, Comp. Mech., 32, pp. 370–380, 2003.

JADAMBA, B., KHAN, A.A., RACITI, F., On the inverse problem of identifying Lamé coefficients in linear elasticity, Computers & Mathematics with Applications, 56, 2, pp. 431-443, 2008.

GOCKENBACH, M.S., KHAN, A., A convex objective functional for elliptic inverse problems, in: Mathematical Models and Methods for Real World Systems (eds. K.M. Furuti, M.Z. Nashed, A.H. Siddiqi), pp. 389-419, Chapman & Hall/CRC, 2005.

HU, G., LI, P., LIU, X., ZHAO, Y., Inverse source problems in electrodynamics, Inverse Problems and Imaging, 12, pp. 1411-1428, 2018.

CHIROIU, V., CHIROIU, C., Inverse problems in mechanics (in Romanian), 2003.

MUNTEANU, L., DONESCU, St., Introduction to soliton theory: Applications to mechanics, Book Series Fundamental Theories of Physics, Vol. 143, Kluwer Academic Publishers, Dordrecht, Boston (Springer Netherlands), 2004.

TORLIN, V.N., Direct and inverse problem of the plane theory of elasticity of a inhomogeneous body, Prikladnaya Mekhanika, 12, 8, pp. 49-52, August, 1976.

BILLINGTON, DAVID P., Thin shell concrete structures, McGraw-Hill, New York, 1965.

MIHAILESCU, M., CHIROIU, V., Advanced mechanics on shells and intelligent structures, Edit. Academiei Române, 2004.

GHEBRESELASIE, M.H., Structural Analysis of Thin Concrete shells, Master Thesis, Trondheim Norwegian University of Science and Technology, 2015.



Most read articles by the same author(s)

1 2 3 > >>