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Exact solutions for elastic half-space problems

Hi all

I am looking for exact solutions of deflection & stresses for the following problems:

1.    Elastic half-space loaded by a circular uniformly distributed load
2.    Elastic half-space subjected to a concentrated ring load

I found few journal papers, where reference was given to Timoshenko & Goodier.  But I could not trace the explicit equations for exact solutions of deflection & stresses for the above problems.

I would appreciate if some body could direct me to the correct REFERENCE where the explicit equations for exact solutions of deflection & stresses for the above problems are given.


ruogang zhao's picture

Hi Arun,

This article discussed the analytical solution of an elastic half-space subjected to a circular uniformly distributed load with a concentrated ring boundary. It is not exactly what you looking for, but maybe you can do some derivation based on this.

Theret, D. P., Levesque, M. J., Sato, M., Nerem, R. M., and Wheeler, L. T., 1988, ‘‘The Application of a Homogeneous Half-Space Model in the Analysis of Endothelial Cell Micropipette Measurements,’’ ASME J. Biomech. Eng., 110, pp. 190–199.



Haimin Yao's picture

Try to look up book "Contact Mechanics" by K.L. Johnson.

I believe the answers are documented in detail in

Elastic Solutions for Soil and Rock Mechanics (Soil Engineering) (Hardcover)

by Harry G. Poulos (Author), Edward H. Davis (Author)


the book is probably out of print. Ask your librarian to get a copy for you


P/S: are you looking for normal load or horizontal load?


m_rahman's picture


There are several ways you can derive the solutions to these axisymmetric Boussinesq problems. In fact, if you can derive the solution for the ring load only, you can use it a Green's function (influence function) to develop the solution for any axisymmetric load. Give me your e-mail address and I will send you something.

Mujibur Rahman

Dear Mujibur Rahman

 Thank you very much for your time and suggestions.


I am not sure, maybe you can refer to "Theory of elasticity" by Landau and Lifshitz (Page 25), or "Fourier transforms" by Sneddon.

Ying-Song Yu

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