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String kernel representations in elastostatics
Abstract
In this paper we present a new boundary integral equation formulation for the solution of the elastostatic traction boundary value problem in two and three dimensions. The approach relies on the introduction of new layer potentials, called string kernels, which are based on modifications of the Boussinesq-Cerruti family of half-space solutions. We prove that the resulting integral equations are second-kind integral equations, and show that they are well-behaved in the incompressible limit. We illustrate the performance of the method with several numerical examples.
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BibTeX
@misc{hoskins2026string,
title = {{String kernel representations in elastostatics}},
author = {Jeremy G. Hoskins and Alan E. Lindsay and Manas Rachh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.24827},
eprint = {2605.24827},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.24827},
}
RIS
TY - UNPB
TI - String kernel representations in elastostatics
AU - Jeremy G. Hoskins
AU - Alan E. Lindsay
AU - Manas Rachh
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2605.24827
UR - https://arxiv.org/abs/2605.24827
AB - In this paper we present a new boundary integral equation formulation for the solution of the elastostatic traction boundary value problem in two and three dimensions. The approach relies on the introduction of new layer potentials, called string kernels, which are based on modifications of the Boussinesq-Cerruti family of half-space solutions. We prove that the resulting integral equations are second-kind integral equations, and show that they are well-behaved in the incompressible limit. We illustrate the performance of the method with several numerical examples.
ER -