Isogeometric analysis of plane stress structure

Abstract

Differential equations are derived to describe the physical phenomena in engineering system. In this project, differential equations of simple rectangular plane stress problem were first derived and solved using Isogeometric Analysis (IGA) and Finite Element Method (FEM). The root idea of IGA is to use a single basis to represent the geometry and the analysis fields in order to overcome the bottleneck in Computer Aided Design (CAD) and Computer Aided Engineering (CAE). The aim is to investigate the performance of IGA as compared to FEM. It is realized that the main difference between the two numerical techniques adopted is the formulation of shape functions. Therefore, emphasis is put on the formulation of IGA using Non-Uniform Rational B-Splines (NURBS) as the basis function where the results obtained are compared against finite element formulation which uses polynomial functions for the shape functions. Besides that, the results by both formulations are verified against exact solution and commercial software. Although only the shape function differs, IGA uses a global shape function over the domain while FEM uses the same local shape functions over the elements in the domain. Performance study on IGA was also carried out. It has been found that the convergence of IGA is comparable to conventional FEM and the error is small against the exact solution. Despite more time is needed to compute the shape functions in IGA, there are various refinement mechanisms in IGA where knot insertion shows the best performance in this study. In short, IGA is worthwhile to be used as an analysis tool to initiate the communication between computer aided design (CAD) and computer aided engineering (CAE).