An Isogeometric Boundary Element Method for elastostatic analysis: 2D implementation aspects

TL;DR

This paper presents a 2D isogeometric boundary element method for elastostatic analysis that directly uses CAD geometry, reducing meshing efforts and bridging the gap between design and analysis.

Contribution

It introduces an implementation of 2D IGABEM that relies solely on CAD boundary representation, simplifying the analysis process and integrating design and analysis workflows.

Findings

The method reduces the need for boundary meshing.

Implementation details are provided with MATLAB code examples.

The approach enhances integration of CAD and analysis in elastostatics.

Abstract

The concept of isogeometric analysis, whereby the parametric func- tions that are used to describe CAD geometry are also used to approx- imate the unknown fields in a numerical discretisation, has progressed rapidly in recent years. This paper advances the field further by outlin- ing an isogeometric Boundary Element Method (IGABEM) that only re- quires a representation of the geometry of the domain for analysis, fitting neatly with the boundary representation provided completely by CAD. The method circumvents the requirement to generate a boundary mesh representing a significant step in reducing the gap between engineering design and analysis. The current paper focuses on implementation details of 2D IGABEM for elastostatic analysis with particular attention paid towards the differences over conventional boundary element implementa- tions. Examples of Matlab R{\deg} code are given whenever possible to aid understanding of the techniques used.