The elastic field induced by a hemispherical inclusion in the half-space

2003 ◽  
Vol 19 (3) ◽  
pp. 253-262 ◽  
Author(s):  
Wu Linzhi
Keyword(s):  
Half Space ◽  
Elastic Field

Elastic Half Space under Axisymmetric Surface Loading and Influence of Couple Stresses

2020 ◽  
Vol 897 ◽  
pp. 129-133
Author(s):  
Jintara Lawongkerd ◽  
Toan Minh Le ◽  
Suraparb Keawsawasvong ◽  
Suchart Limkatanyu ◽  
Jaroon Rungamornrat
Keyword(s):  
Half Space ◽  
Integral Transform ◽  
Couple Stress Theory ◽  
Elastic Field ◽  
Elastic Half Space ◽  
Small Scale ◽  
Internal Length ◽  
Stress Theory ◽  
Axisymmetric Surface ◽  
Small Scale Effect

This paper presents the complete elastic field of a half space under axisymmetric surface loads by taking the influence of material microstructures into account. A well-known couple stress theory is adopted to handle such small scale effect and the resulting governing equations are solved by the method of Hankel integral transform. A selected numerical quadrature is then applied to efficiently evaluate all involved integrals. A set of results is also reported to not only confirm the validity of established solutions but also demonstrate the capability of the selected mathematical model to simulate the size-dependent characteristic of the predicted response when the external and internal length scales are comparable.

Arbitrary Load Distribution on a Layered Half Space

2000 ◽  
Vol 122 (4) ◽  
pp. 672-681 ◽  
Author(s):  
N. Schwarzer
Keyword(s):  
Half Space ◽  
Load Distribution ◽  
Elastic Field ◽  
Stress Fields ◽  
Method Of Images ◽  
Elementary Functions ◽  
Homogeneous Case ◽  
Arbitrary Load ◽  
Homogeneous Half Space ◽  
Layered Half Space

This paper develops a method which allows one to calculate the complete elastic field (stress field and displacements) of layered materials of transverse and complete isotropy under given load conditions. It is assumed that the layered body consists of an infinite half-space and various infinite planes which are all ideally bonded to each other. Thus, the interfaces are parallel to the surface of the resulting “coated half space.” The approach is based on the method of images in classical electrostatics. The final solution for an arbitrary load problem can be presented as a series of potential functions, where corresponding functions may be interpreted as “image loads” the analogous to “image charges.” The solution for the elastic field for any arbitrary stress distribution on the surface of the coated half space can be obtained in a relatively straightforward manner by using the method described here as long as the corresponding solution for the homogeneous half space is known. Further, if this solution of the homogeneous case may be expressed in terms of elementary functions, then the solution for the coated half space is elementary, too. Explicit formulas for the stress fields for some particular examples are given. [S0742-4787(00)01204-2]

The Elastic Field Resulting From Elliptical Hertzian Contact of Transversely Isotropic Bodies: Closed-Form Solutions for Normal and Shear Loading

1997 ◽  
Vol 64 (3) ◽  
pp. 457-465 ◽  
Author(s):  
M. T. Hanson ◽  
I. W. Puja
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Elastic Field ◽  
Transversely Isotropic ◽  
Normal Pressure ◽  
Shear Loading ◽  
Potential Functions ◽  
Hertzian Contact ◽  
Elementary Functions ◽  
Shear Traction

This analysis presents the elastic field in a half-space caused by an ellipsoidal variation of normal traction on the surface. Coulomb friction is assumed and thus the shear traction on the surface is taken as a friction coefficient multiplied by the normal pressure. Hence the shear traction is also of an ellipsoidal variation. The half-space is transversely isotropic, where the planes of isotropy are parallel to the surface. A potential function method is used where the elastic field is written in three harmonic functions. The known point force potential functions are utilized to find the solution for ellipsoidal loading by quadrature. The integrals for the derivatives of the potential functions resulting from ellipsoidal loading are evaluated in terms of elementary functions and incomplete elliptic integrals of the first and second kinds. The elastic field is given in closed-form expressions for both normal and shear loading.

Elastic Fields due to Eigenstrains in a Half-Space

2005 ◽  
Vol 72 (6) ◽  
pp. 871-878 ◽  
Author(s):  
Shuangbiao Liu ◽  
Qian Wang
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Half Space ◽  
Numerical Algorithms ◽  
Elastic Field ◽  
Contact Problems ◽  
Fast Fourier Transform Algorithm ◽  
Elastic Fields ◽  
Influence Coefficients ◽  
Residual Strains

Engineering components inevitably encounter various eigenstrains, such as thermal expansion strains, residual strains, and plastic strains. In this paper, a set of formulas for the analytical solutions to cases of uniform eigenstrains in a cuboidal region-influence coefficients, is presented in terms of derivatives of four key integrals. The linear elastic field caused by arbitrarily distributed eigenstrains in a half-space is thus evaluated by the discrete correlation and fast Fourier transform algorithm, along with the discrete convolution and fast Fourier transform algorithm. By taking advantage of both the convolution and correlation characteristics of the problem, the formulas of influence coefficients and the numerical algorithms are expected to enable efficient and accurate numerical analyses for problems having nonuniform distribution of eigenstrains and for contact problems.

The Elastic Field in a Half-Space With a Circular Cylindrical Inclusion

1996 ◽  
Vol 63 (4) ◽  
pp. 925-932 ◽  
Author(s):  
L. Z. Wu ◽  
S. Y. Du
Keyword(s):  
Half Space ◽  
Elastic Field ◽  
Elastic Half Space ◽  
Elliptic Integrals ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Function Technique ◽  
Explicit Solutions ◽  
Elastic Fields ◽  
Complete Elliptic Integrals

The problem of a circular cylindrical inclusion with uniform eigenstrain in an elastic half-space is studied by using the Green’s function technique. Explicit solutions are obtained for the displacement and stress fields. It is shown that the present elastic fields can be expressed as functions of the complete elliptic integrals of the first, second, and third kind. Finally, numerical results are shown for the displacement and stress fields.

Sign in / Sign up

Export Citation Format

Share Document