﻿ Isogeometric Analysis (IA)

## DEFINITION

Isogeometric Analysis is characterized by use of common spline basis for geometric modelling and finite element analysis of a given object.

## INTRODUCTION

The engineering process starts with designers encapsulating their perception using Computer Aided Design (CAD) tools. Thus, the geometry described in CAD systems is to be considered exact in the sense that it represents the projection from the designers perception of the desired object onto an electronic description. Today most CAD systems use spline basis function and often Non-Uniform Rational B-Splines (NURBS) of different polynomial order.

During and after the design stages different levels of numerical solid and fluid simulations are performed on the object. Very often this involves using the Finite Element Method (FEM) where the geometry is represented by piecewise low order polynomials. This practise introduce either significant approximation errors or fine FEM models with a large number of finite elements that make the numerical simulation computational costly. Furthermore, a huge amount of man-hours (in some applications about 80% of total time is spent on mesh generation, see Hughes et al. 2005) have to be spent in order to remodel the object into a suitable finite element mesh. This information transfer between models suitable for design (CAD) and analysis (FEM) is considered being a severe bottleneck in industry today.

To address this issue Hughes et al. (2005) introduced a analysis framework which is based on NURBS (Non-Uniform Rational B-Splines), which is standard technology employed in CAD systems. They propose to match the exact CAD geometry by NURBS surfaces, then construct a coarse mesh of Spline Elements. Throughout, the isoparametric philosophy is invoked, that is, the solution space for dependent variables is represented in terms of the same functions which represent the geometry. For this reason, they denote it isogeometric analysis.

## CHALLENGES

1. Analysis suitable parametrization