Isogeometric analysis: an overview and computer implementation aspects

TL;DR

This paper provides an overview of isogeometric analysis (IGA), highlighting its integration with CAD, practical implementation in MATLAB, and extensions for fracture mechanics, demonstrating its efficiency and versatility in computational mechanics.

Contribution

It introduces a MATLAB implementation of IGA, including extended methods with enrichment functions and Bezier extraction, and discusses recent developments in the field.

Findings

MATLAB code supports 2D and 3D problems in elasticity and fracture mechanics

IGA reduces analysis time by integrating CAD and analysis

Efficient analysis on T-spline geometries using Bezier extraction

Abstract

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The implications to practical engineering design scenarios are profound, since the time taken from design to analysis is greatly reduced, leading to dramatic gains in efficiency. The tight coupling of CAD and analysis within IGA requires knowledge from both fields and it is one of the goals of the present paper to outline much of the commonly used notation. In this manuscript, through a clear and simple Matlab implementation, we present an introduction to IGA applied to the Finite Element (FE) method and related computer implementation aspects. Furthermore, implemen- tation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several examples for both two-dimensional and three-dimensional fracture are illustrated. The open source Matlab code which accompanies the present paper can be applied to one, two and three-dimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. The Bezier extraction concept that allows FE analysis to be performed efficiently on T-spline geometries is also incorporated. The article includes a summary of recent trends and developments within the field of IGA.