Vol. 4, No. 1, 2009

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 4, 541–649
Issue 4, 541–572
Issue 3, 303–540
Issue 2, 157–302
Issue 1, 1–156

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN (electronic): 1559-3959
ISSN (print): 1559-3959
Author index
To appear
Other MSP journals
Viscoelastic state of a semi-infinite medium with multiple circular elastic inhomogeneities

Andrey V. Pyatigorets and Sofia G. Mogilevskaya

Vol. 4 (2009), No. 1, 57–87

This paper is concerned with the problem of an isotropic, linear viscoelastic half-plane containing multiple, isotropic, circular elastic inhomogeneities. Three types of loading conditions are allowed at the boundary of the half-plane: a point force, a force uniformly distributed over a segment, and a force uniformly distributed over the whole boundary of the half-plane. The half-plane is subjected to far-field stress that acts parallel to its boundary. The inhomogeneities are perfectly bonded to the material matrix. An inhomogeneity with zero elastic properties is treated as a hole; its boundary can be either traction free or subjected to uniform pressure. The analysis is based on the use of the elastic-viscoelastic correspondence principle. The problem in the Laplace space is reduced to the complementary problems for the bulk material of the perforated half-plane and the bulk material of each circular disc. Each problem is described by the transformed complex Somigliana’s traction identity. The transformed complex boundary parameters at each circular boundary are approximated by a truncated complex Fourier series. Numerical inversion of the Laplace transform is used to obtain the time domain solutions everywhere in the half-plane and inside the inhomogeneities. The method allows one to adopt a variety of viscoelastic models. A number of numerical examples demonstrate the accuracy and efficiency of the method.

viscoelastic half-plane, multiple circular elastic inhomogeneities, correspondence principle, direct boundary integral method, numerical Laplace inversion
Received: 2 September 2008
Accepted: 20 November 2008
Published: 8 April 2009
Andrey V. Pyatigorets
Department of Civil Engineering
University of Minnesota
500 Pillsbury Drive SE
Minneapolis, MN 55455
United States
Sofia G. Mogilevskaya
Department of Civil Engineering
University of Minnesota
500 Pillsbury Drive SE
Minneapolis, MN 55455
United States