A Coupling Approach for Linear Elasticity Problems with Spatially Noncoincident Interfaces

TL;DR

This paper introduces a novel coupling formulation for linear elasticity problems with noncoincident interfaces, utilizing Taylor series expansions to improve interface condition accuracy and an iterative method for solution convergence.

Contribution

The paper develops a new interface coupling formulation based on Taylor expansions that passes linear consistency tests and is effective for problems with differing Lamé parameters.

Findings

Achieves piecewise linear finite element error bounds

Effective for nonoverlapping domain decomposition

Handles interfaces with differing material properties

Abstract

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 Lam\'e parameters of the structures differ.