Application of generalized images method to contact problems for a transversely isotropic elastic layer on a smooth half-space

2010 ◽  
Vol 81 (7) ◽  
pp. 957-974 ◽  
Author(s):  
Valery I. Fabrikant
Keyword(s):  
Half Space ◽  
Elastic Layer ◽  
Transversely Isotropic ◽  
Contact Problems ◽  
Generalized Images Method

Solution of contact problems for a transversely isotropic elastic layer bonded to an elastic half-space

2009 ◽  
Vol 223 (11) ◽  
pp. 2487-2499 ◽  
Author(s):  
V I Fabrikant
Keyword(s):  
Half Space ◽  
Elastic Layer ◽  
Integral Transform ◽  
Transversely Isotropic ◽  
Contact Problems ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Electrostatic Problem ◽  
Crack Problems ◽  
New Interpretation

The idea, first used by the author for the case of crack problems, is applied here to solve a contact problem for a transversely isotropic elastic layer bonded to an elastic halfspace, made of a different transversely isotropic material. A rigid punch of arbitrary shape is pressed against the layer's free surface. The governing integral equation is derived; it is mathematically equivalent to that of an electrostatic problem of an infinite row of coaxial charged discs in the shape of the domain of contact. As a comparison, the method of integral transforms is also used to solve the problem. The main difference of our integral transform approach with the existing ones is in separating of our half-space solution from the integral transform terms. It is shown that both methods lead to the same results, thus giving a new interpretation to the integral transform as a sum of an infinite series of generalized images.

Love Waves in a Piezoelectric Half-Space with an Anisotropic Elastic Layer

2011 ◽  
Vol 117-119 ◽  
pp. 1160-1163 ◽  
Author(s):  
Qian Yang ◽  
Yan Ping Kong ◽  
Jin Xi Liu
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Orthotropic Material ◽  
Elastic Layer ◽  
Transversely Isotropic ◽  
Love Waves ◽  
Dispersion Characteristics ◽  
Material Anisotropy ◽  
Symmetric Plane ◽  
Anisotropic Elastic

This work is concerned with the dispersion characteristics of Love waves propagating in a layered structure consisting of an anisotropic elastic layer and a piezoelectric half-space. The layer processes one symmetric plane, while the half-space is transversely isotropic. The explicit dispersion equation is derived. As an example, an inclined orthotropic material is chosen as an elastic layer to reveal the effect of material anisotropy on the dispersion behaviors. The numerical results show that the phase velocity is strongly influenced by the anisotropic degree.

Analysis of a Transversely Isotropic Half Space Under Normal and Tangential Loadings

1991 ◽  
Vol 113 (2) ◽  
pp. 335-338 ◽  
Author(s):  
W. Lin ◽  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Transversely Isotropic ◽  
Contact Problems ◽  
Contact Stresses ◽  
Hertzian Contact ◽  
Stress Fields ◽  
Tangential Contact ◽  
Rectangular Patch

This paper analyzes the response of a transversely isotropic half space subjected to various distributions of normal and tangential contact stresses on its surface. Both the interior displacement and stress fields are given in closed form. Among them, rectangular patch solutions are constructed for application to solutions to non-Hertzian contact problems.

Sign in / Sign up

Export Citation Format

Share Document