Elastic Layer Pressed Against a Half Space

1974 ◽  
Vol 41 (3) ◽  
pp. 703-707 ◽  
Author(s):  
K. C. Tsai ◽  
J. Dundurs ◽  
L. M. Keer
Keyword(s):  
Eigenvalue Problem ◽  
Integral Equations ◽  
Half Space ◽  
Elastic Layer ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Auxiliary Functions ◽  
Receding Contact ◽  
Two Bodies

The paper considers the elastic layer which is pressed against a half space by loads that are not necessarily symmetric about the center of the loaded region. It is shown that the receding contact between the two bodies can be treated by means of superposition, leading to two homogeneous Fredholm integral equations for auxiliary functions that are directly related to the contact tractions. The determination of the extent of contact and the shift between the load and contact intervals can be viewed as an eigenvalue problem of the homogeneous integral equations. Specific numerical results are given for two types of triangular loads, and a comparison is made with certain symmetric loads.

On the Torsion of Elastic Half Spaces With Embedded Penny-Shaped Flaws

1972 ◽  
Vol 39 (3) ◽  
pp. 786-790 ◽  
Author(s):  
R. D. Low
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Rigid Inclusion ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Graphical Displays ◽  
Penny Shaped Crack ◽  
Shaped Crack

The investigation is concerned with some of the effects of embedded flaws in an elastic half space subjected to torsional deformations. Specifically two types of flaws are considered: (a) a penny-shaped rigid inclusion, and (b) a penny-shaped crack. In each case the problem is reduced to a system of Fredholm integral equations. Graphical displays of the numerical results are included.

scholarly journals Dynamic Behavior of an Embedded Foundation under Horizontal Vibration in a Poroelastic Half-Space

2019 ◽  
Vol 9 (4) ◽  
pp. 740 ◽  
Author(s):  
Yang Chen ◽  
Wen Zhao ◽  
Pengjiao Jia ◽  
Jianyong Han ◽  
Yongping Guan
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Mixed Boundary ◽  
Fredholm Integral Equations ◽  
Wave Forces ◽  
Dual Integral Equations ◽  
Horizontal Vibration ◽  
Embedded Foundation ◽  
Embedded Foundations ◽  
Caisson Foundations

More and more huge embedded foundations are used in large-span bridges, such as caisson foundations and anchorage open caisson foundations. Most of the embedded foundations are undergoing horizontal vibration forces, that is, wind and wave forces or other types of dynamic forces. The embedded foundations are regarded as rigid due to its high stiffness and small deformation during the forcing process. The performance of a rigid, massive, cylindrical foundation embedded in a poroelastic half-space is investigated by an analytical method developed in this paper. The mixed boundary problem is solved by reducing the dual integral equations to a pair of Fredholm integral equations of the second kind. The numerical results are compared with existing solutions in order to assess the accuracy of the presented method. To further demonstrate the applicability of this method, parametric studies are performed to evaluate the dynamic response of the embedded foundation under horizontal vibration. The horizontal dynamic impedance and response factor of the embedded foundation are examined based on different embedment ratio, foundation mass ratio, relative stiffness, and poroelastic material properties versus nondimensional frequency. The results of this study can be adapted to investigate the horizontal vibration responses of a foundation embedded in poroelastic half-space.

Problems Involving a Receding Contact Between a Layer and a Half Space

1972 ◽  
Vol 39 (4) ◽  
pp. 1115-1120 ◽  
Author(s):  
L. M. Keer ◽  
J. Dundurs ◽  
K. C. Tsai
Keyword(s):  
Integral Equation ◽  
Half Space ◽  
Contact Pressure ◽  
Auxiliary Function ◽  
Unexpected Result ◽  
Wide Range ◽  
Receding Contact ◽  
Axisymmetric Problems ◽  
Uniformly Distributed Loads ◽  
Two Bodies

The work reconsiders the smooth receding contact between an elastic layer and a half space when the two bodies are pressed together. The analysis leads to a Fredholm integral equation of the second kind for an auxiliary function that is directly related to the contact pressure. An unexpected result is that the integral equation is homogeneous, and that finding the extent of contact can be viewed as an eigenvalue problem. The integral equation can be solved numerically to any required degree of accuracy, and the extent of contact and the contact pressure are computed for concentrated and uniformly distributed loads in both plane and axisymmetric problems. The present analysis confirms the results of Weitsman rather than Pu and Hussain over a wide range of mismatch in the elastic constants.

Vibration Isolation Using Pile Rows in a Layered Poroelastic Half-Space Against the Vibration Due to Harmonic Loads

2010 ◽  
Author(s):  
Jian-Fei Lu ◽  
Bin Xu ◽  
Jian-Hua Wang
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Vibration Isolation ◽  
Dynamic Interaction ◽  
Isolation Effect ◽  
Fredholm Integral Equations ◽  
Vertical Load ◽  
Large Length ◽  
Patch Load ◽  
Transmission And Reflection

The isolation of the vibration due to a harmonic vertical load using pile rows embedded in a layered poroelastic half-space is investigated in this study. Based on Biot’s theory, the frequency domain fundamental solution for a vertical circular patch load applied in a layered poroelastic half-space is derived via the transmission and reflection matrices (TRM) method. Utilizing Muki and Sternberg’s method, the second kind of Fredholm integral equations describing the dynamic interaction between the pile rows and the layered poroelastic half-space subjected to a harmonic vertical load is constructed. The isolation effect of piles rows for the vibration due to the harmonic vertical load is investigated via numerical solution of the integral equations. Numerical results of this study show that a stiffer upper layer overlying a softer bottom half-space will worsen the vibration isolation effect of pile rows and vice versa. Also, pile rows with large length are preferable for a better vibration isolation effect.

Dynamic Response of a Rigid Foundation Subjected to a Distance Blast

2012 ◽  
Author(s):  
Deji Ojetola ◽  
Hamid R. Hamidzadeh
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Integral Transform ◽  
Numerical Technique ◽  
Formal Solution ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Rigid Foundation ◽  
Transform Method

Blasts and explosions occur in many activities that are either man-made or nature induced. The effect of the blasts could have a residual or devastating effect on the buildings at some distance within the vicinity of the explosion. In this investigation, an analytical solution for the time response of a rigid foundation subjected to a distant blast is considered. The medium is considered to be an elastic half space. A formal solution to the wave propagations on the medium is obtained by the integral transform method. To achieve numerical results for this case, an effective numerical technique has been developed for calculation of the integrals represented in the inversion of the transformed relations. Time functions for the vertical and radial displacements of the surface of the elastic half space due to a distant blast load are determined. Mathematical procedures for determination of the dynamic response of the surface of an elastic half-space subjected to the blast along with numerical results for displacements of a rigid foundation are provided.

The Vibration of Pile Groups Embedded in a Layered Poroelastic Half Space Subjected to Harmonic Axial Loads by Using Integral Equations Method

2012 ◽  
Vol 204-208 ◽  
pp. 1170-1173
Author(s):  
Chun Bo Cheng ◽  
Man Qing Xu ◽  
Bin Xu
Keyword(s):  
Dynamic Response ◽  
Layer Thickness ◽  
Integral Equations ◽  
Half Space ◽  
Pile Group ◽  
Dynamic Interaction ◽  
Fredholm Integral Equations ◽  
Pile Groups ◽  
Axial Loads ◽  
Layered Half Space

The dynamic response of a pile group embedded in a layered poroelastic half space subjected to axial harmonic loads is investigated in this study. Based on Biot's theory and utilizing Muki's method, the second kind of Fredholm integral equations describing the dynamic interaction between the layered half space and the pile group is constructed. Numerical results show that in a two-layered half space, for the closely populated pile group with a rigid cap, the upper softer layer thickness has considerably different influence on the center pile and the corner piles, while for sparsely populated pile group, it has almost the same influence on all the piles.

The Singularity at the Apex of a Bonded Wedge-Shaped Stamp

1979 ◽  
Vol 46 (3) ◽  
pp. 577-580 ◽  
Author(s):  
K. S. Parihar ◽  
L. M. Keer
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Solution ◽  
Integral Equations ◽  
Half Space ◽  
Singular Integral ◽  
Green's Functions ◽  
Green’S Functions ◽  
Singular Integral Equations ◽  
Elastic Half Space

The problem of determining the singularity at the apex of a rigid wedge bonded to an elastic half space is formulated by considerations of Green’s functions for the loaded half space. The eigenvalue problem is reduced to finding the solution of a coupled pair of singular integral equations. A numerical solution for small wedge angles is given.

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