Dynamic Green׳s function for a three-dimensional concentrated load in the interior of a poroelastic layered half-space using a modified stiffness matrix method

2015 ◽  
Vol 60 ◽  
pp. 51-66 ◽  
Author(s):  
Zhongxian Liu ◽  
Jianwen Liang ◽  
Chengqing Wu
Keyword(s):  
Half Space ◽  
Stiffness Matrix ◽  
Matrix Method ◽  
Three Dimensional ◽  
Concentrated Load ◽  
Layered Half Space

scholarly journals The dispersion of Rayleigh waves in orthotropic layered half-space using matrix method

2016 ◽  
Vol 38 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Tran Thanh Tuan ◽  
Tran Ngoc Trung
Keyword(s):  
Numerical Calculation ◽  
Half Space ◽  
Rayleigh Waves ◽  
Matrix Method ◽  
Secular Equation ◽  
Material Parameters ◽  
Rayleigh Surface Waves ◽  
The Matrix ◽  
Dimensionless Variables ◽  
Layered Half Space

In this paper, the secular equation of Rayleigh surface waves propagating in an orthotropic layered half-space is derived by the matrix method.  All the layers and the half-space are assumed to have identical principle axes. The explicit form of the matrizant for each layer is obtained by the Sylvester's theorem. The derived secular equation takes only real values and depends only on the dimensionless variables and dimensionless material parameters. Hence, it is convenient in numerical calculation.

A Numerical Solution for Layered Solid Contact Problems With Application to Bearings

1983 ◽  
Vol 105 (4) ◽  
pp. 585-590 ◽  
Author(s):  
Y. P. Chiu ◽  
M. J. Hartnett
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Contact Problems ◽  
Steel Rolling ◽  
Rolling Element ◽  
Method Of Solution ◽  
Rectangular Area ◽  
Layered Solid ◽  
Boussinesq Solution ◽  
Layered Half Space

Presented herein is a method of solution for three dimensional counterformal contact problems involving layered solids. Based on the generalized Boussinesq solution for a layered half space, displacement and stress coefficients are formulated for a uniformly distributed load applied over a rectangular area on the surface of a layered half space. A precise analytical solution has been developed to find the surface pressure, contact area, approach and subsurface stresses for contact of arbitrary surface shapes. Numerical results have been obtained for the indentation of a second order surface with a layered solid for the case the layer to substrate shear modulus ratio equal to 3, which simulates the contact of a steel rolling element with a steel bearing ring supported by aluminum substrate (or housing) in a transmission system.

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