Evaluation of the Hypersingular Kernel for a Three-Dimensional Exponentially Graded Material
- ORNL
Martin et al. have shown that the fundamental displacement tensor for three dimensional exponentially graded elasticity can be expressed in terms of one and two dimensional finite integrals of Bessel functions. However, these formulas, and as well those for the corresponding traction kernel, are necessarily expensive to compute, and thus a boundary integral analysis based upon this approach borders on impractical. In this paper we derive new representations for the fundamental graded displacement kernel, given as a relatively simple analytic term, plus a well behaved remainder that can be rapidly obtained numerically. These new expressions are easily differentiated with respect to source and field points, leading to effective formulas for the traction and hypersingular kernels. Test calculations show that the new and old formulas for the displacement and traction kernels agree.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- DE-AC05-00OR22725
- OSTI ID:
- 979130
- Resource Relation:
- Conference: 12th International Conference on Fracture (ICF 12), Ottawa, Canada, 20090712, 20090717
- Country of Publication:
- United States
- Language:
- English
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