String kernel representations in elastostatics
Provides a novel method for solving elastostatic boundary value problems, particularly beneficial for applications requiring stable solutions near incompressibility.
The paper introduces a new boundary integral equation formulation for elastostatic traction problems using string kernels, achieving second-kind integral equations that remain well-behaved in the incompressible limit, with numerical examples demonstrating performance.
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.