Overview
This work introduces a new boundary integral equation formulation designed for solving elastostatic traction boundary value problems. This formulation is applicable in both two and three dimensions. The method employs novel layer potentials, termed 'string kernels,' which are derived from modifications of the Boussinesq-Cerruti family of half-space solutions.
Approach
The core of the methodology involves the development of new layer potentials, referred to as string kernels. These kernels are built upon existing Boussinesq-Cerruti half-space solutions, with modifications applied to their structure. The application of these string kernels leads to the establishment of integral equations. The researchers demonstrate that these resulting integral equations are classified as second-kind integral equations. Furthermore, the formulation's behavior under the condition of incompressibility was investigated, and it was shown to remain well-behaved in this incompressible limit. The performance of this method was assessed through the use of several numerical examples.
Findings
- A new boundary integral equation formulation has been developed for elastostatic traction boundary value problems.
- This formulation utilizes novel layer potentials, named string kernels.
- String kernels are based on modifications of the Boussinesq-Cerruti family of half-space solutions.
- The resulting integral equations are proven to be second-kind integral equations.
- The integral equations are shown to be well-behaved when subjected to the incompressible limit.
- Numerical examples illustrate the method's performance.