An Isogeometric Boundary Element Method for elastostatic analysis: 2D implementation aspects
For engineers and researchers in computational mechanics, this work provides an incremental implementation of isogeometric analysis within the boundary element framework, focusing on 2D elastostatics.
This paper presents an isogeometric Boundary Element Method (IGABEM) for 2D elastostatic analysis that uses CAD geometry directly, eliminating the need for boundary mesh generation. The method is demonstrated with MATLAB code examples, showing a step toward reducing the gap between design and analysis.
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° code are given whenever possible to aid understanding of the techniques used.