Efficient isogeometric Boundary Element simulation of elastic domains containing thin inclusions

TL;DR

This paper presents an efficient isogeometric Boundary Element method for simulating elastic domains with thin, high-aspect-ratio inclusions, addressing numerical challenges and demonstrating high accuracy through various examples.

Contribution

The paper introduces novel numerical integration techniques specifically designed for thin inclusions with extreme aspect ratios in Boundary Element simulations.

Findings

Methods achieve high accuracy in simulating thin inclusions.

Numerical techniques effectively handle singular integrals.

Results align well with analytical and other numerical solutions.

Abstract

This paper is concerned with the Boundary Element simulation of elastic domains that contain thin inclusions that have elastic material properties, which are different to the domain. With thin inclusions we mean inclusions with extreme aspect ratios, i.e. where one dimension is much smaller than the other ones. Examples of this are reinforcements in civil/mechanical engineering or concrete linings in underground construction. The fact that an inclusion has an extreme aspect ratio poses a challenge to the numerical integration of the arising singular integrals and novel approaches are presented to deal with it. Several examples demonstrate the efficiency and accuracy of the proposed methods and show that the results are in good agreement with analytical and other numerical solutions.