A Coupling Approach for Linear Elasticity Problems with Spatially Noncoincident Interfaces
This work provides a consistent coupling method for nonconforming interfaces in linear elasticity, addressing a known bottleneck in computational mechanics.
The paper introduces a new Dirichlet-Neumann formulation for coupling linear elasticity problems with noncoincident interfaces, achieving piecewise linear finite element error bounds for domain decomposition and problems with differing Lamé parameters.
We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we derive a new set of interface conditions that allow our formulation to pass the linear consistency test. In addition, we propose an iterative method to determine the solution of our formulation. We demonstrate in our numerical results that we may achieve the desired piecewise linear finite element error bounds for both nonoverlapping domain decomposition problems as well as for interface coupling problems where the Lamé parameters of the structures differ.