Exact solution of external tangential contact problem for a transversely isotropic elastic half-space

2001 ◽  
Vol 71 (6-7) ◽  
pp. 371-388 ◽  
Author(s):  
V. I. Fabrikant
Keyword(s):  
Exact Solution ◽  
Contact Problem ◽  
Half Space ◽  
Transversely Isotropic ◽  
Elastic Half Space ◽  
Tangential Contact

Solution of the Contact Problem of a Rigid Conical Frustum Indenting a Transversely Isotropic Elastic Half-Space

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
X.-L. Gao ◽  
C. L. Mao
Keyword(s):  
Contact Problem ◽  
Closed Form ◽  
Half Space ◽  
Cone Angle ◽  
Closed Form Solution ◽  
Transversely Isotropic ◽  
Elastic Half Space ◽  
Form Solution ◽  
Potential Functions ◽  
Displacement Method

The contact problem of a rigid conical frustum indenting a transversely isotropic elastic half-space is analytically solved using a displacement method and a stress method, respectively. The displacement method makes use of two potential functions, while the stress method employs one potential function. In both the methods, Hankel's transforms are applied to construct potential functions, and the associated dual integral equations of Titchmarsh's type are analytically solved. The solution obtained using each method gives analytical expressions of the stress and displacement components on the surface of the half-space. These two sets of expressions are seen to be equivalent, thereby confirming the uniqueness of the elasticity solution. The newly derived solution is reduced to the closed-form solution for the contact problem of a conical punch indenting a transversely isotropic elastic half-space. In addition, the closed-form solution for the problem of a flat-end cylindrical indenter punching a transversely isotropic elastic half-space is obtained as a special case. To illustrate the new solution, numerical results are provided for different half-space materials and punch parameters and are compared to those based on the two specific solutions for the conical and cylindrical indentation problems. It is found that the indentation deformation increases with the decrease of the cone angle of the frustum indenter. Moreover, the largest deformation in the half-space is seen to be induced by a conical indenter, followed by a cylindrical indenter and then by a frustum indenter. In addition, the axial force–indentation depth relation is shown to be linear for the frustum indentation, which is similar to that exhibited by both the conical and cylindrical indentations—two limiting cases of the former.

scholarly journals Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 505-515 ◽  
Author(s):  
D. C. Gakenheimer ◽  
J. Miklowitz
Keyword(s):  
Exact Solution ◽  
Free Surface ◽  
Steady State ◽  
Wave Front ◽  
Half Space ◽  
Displacement Field ◽  
Elastic Half Space ◽  
Point Load ◽  
Limit Case ◽  
Transient Waves

The propagation of transient waves in a homogeneous, isotropic, linearly elastic half space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are derived for the interior of the half space and for all load speeds. Wave-front expansions are obtained from the exact solution, in addition to results pertaining to the steady-state displacement field. The limit case of zero load speed is considered, yielding new results for Lamb’s point load problem.

Contact Stress Analysis of a Layered Transversely Isotropic Half-Space

1992 ◽  
Vol 114 (2) ◽  
pp. 253-261 ◽  
Author(s):  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Region ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Stress Components ◽  
Contact Failure

The three-dimensional problem of contact between a spherical indenter and a multi-layered structure bonded to an elastic half-space is investigated. The layers and half-space are assumed to be composed of transversely isotropic materials. By the use of Hankel transforms, the mixed boundary value problem is reduced to an integral equation, which is solved numerically to determine the contact stresses and contact region. The interior displacement and stress fields in both the layer and half-space can be calculated from the inverse Hankel transform used with the solved contact stresses prescribed over the contact region. The stress components, which may be related to the contact failure of coatings, are discussed for various coating thicknesses.

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