Two-dimensional version of Sternberg and Al-Khozaie fundamental solution for viscoelastic analysis using the boundary element method

In this work a general and concise two-dimensional fundamental solution is obtained for quasi-static linear viscoelastic problems using the boundary element method. For this purpose, the three-dimensional fundamental displacement, derived by Sternberg and Al-Khozaie from the generalization of Navier...

Full description

Saved in:
Bibliographic Details
Published in:Engineering analysis with boundary elements 2011-06, Vol.35 (6), p.836-844
Main Authors: Cezario, F., Santiago, J.A.F., Oliveira, R.F.
Format: Article
Language:English
Subjects:
Aluminum
Bolts
Boundaries
Boundary element method
Boundary elements
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Fundamental solutions
Integrals
Linear viscoelasticity
Mathematical analysis
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
Physics
Sciences and techniques of general use
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Two dimensional
Viscoelasticity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this work a general and concise two-dimensional fundamental solution is obtained for quasi-static linear viscoelastic problems using the boundary element method. For this purpose, the three-dimensional fundamental displacement, derived by Sternberg and Al-Khozaie from the generalization of Navier equation, is integrated with respect to z-coordinate. A time formulation is constructed from the viscoelastic Reciprocity Principle, defined in terms of the Stieltjes integral and the material functions are acquired by means of Boltzmann's rheological model. The collocation method and a semi-analytical procedure for the singular boundary integral are employed to the numerical analysis of the boundary integral. The Gaussian quadrature, the analytical method and an incremental approach are used to deal with the convolution integral. As the latter has presented the best performance, it is employed in most analyses of the examples. Finally, numerical results of problems, found in the literature, are presented in order to validate the formulation and the two-dimensional fundamental solution.
ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2011.01.006