Unidimensional Inhomogeneous Isotropic Elastic Half-Space ()
Abstract
The homogeneous system of the equations of the linear theory of
elasticity for the isotropic environment with one-dimensional continuous
heterogeneity is considered. Bidimensional transformation Fourier is applied
and the problem for images is led to the ordinary differential equations.
Generally, the differential equations are transformed in integro-differential
and the algorithm of such transformation is resulted. Solutions of specific
problems are resulted.
Share and Cite:
Dobrovolsky, I. (2015) Unidimensional Inhomogeneous Isotropic Elastic Half-Space.
Open Access Library Journal,
2, 1-6. doi:
10.4236/oalib.1101670.
Conflicts of Interest
The authors declare no conflicts of interest.
References
|
[1]
|
Gibson, R.E. (1967) Some Results Concerning Displacements and Stresses in a Nonhomogeneous Elastic Half-Space. Geotechnique, 17, 58-67.
http://dx.doi.org/10.1680/geot.1967.17.1.58
|
|
[2]
|
Brown, P.T. and Gibson, R.E. (1979) Surface Settlement of a Finite Elastic Layer Whose Modulus Increases Linearly with Depth. International Journal for Numerical and Analytical Methods in Geomechanics, 3, 33-47.
http://dx.doi.org/10.1002/nag.1610030105
|
|
[3]
|
Guler, M.A. and Erdogan, F. (2004) Contact Mechanics of Graded Coatings. International Journal of Solids and Structures, 41, 3865-3889.
http://dx.doi.org/10.1016/j.ijsolstr.2004.02.025
|
|
[4]
|
Dobrovolsky, I.P. (2014) The Integral Equation, Corresponding to the Ordinary Differential Equation. Open Access Library Journal, 1, e1058.
http://dx.doi.org/10.4236/oalib.1101058
|
|
[5]
|
Lomakin, V.A. (1976) The Elasticity Theory of Inhomogeneous Solid. The Moscow Univercity, Moscow, 368 p.
|
|
[6]
|
Kamke, E. (1959) Differential Gleichungen. Lösungsmetohden und Losungen. Leipzig.
|