Isogeometric analysis (IGA) is a computational approach that integrates geometric design and finite element analysis. It aims to bridge the gap between computer-aided design (CAD) and finite element analysis (FEA) by using the same basis functions to represent both the geometry and the solution fields.
In traditional FEA, the geometry is often simplified or approximated using piecewise polynomial basis functions like linear or quadratic elements. However, this can lead to inaccuracies, especially when dealing with complex geometries or when trying to maintain geometric fidelity.
IGA, on the other hand, uses basis functions derived from the same geometric description used in CAD systems, such as Non-Uniform Rational B-Splines (NURBS). These basis functions can exactly represent complex geometries with smooth curves and surfaces. By using the same basis functions for both geometry and analysis, IGA can provide more accurate results compared to traditional FEA methods.
Some advantages of IGA include:
- Accuracy: Since IGA uses exact geometric representations, it can provide more accurate results, especially for problems involving complex geometries.
- Integration with CAD: IGA allows seamless integration between CAD and analysis, reducing the need for geometry approximation or conversion.
- Reduced Preprocessing: With IGA, there’s often less preprocessing required compared to traditional FEA, as the geometry is already accurately represented.
- Higher Order Continuity: IGA supports higher order continuity between elements, which can be beneficial for problems requiring smooth solutions.
IGA has found applications in various engineering fields such as structural mechanics, fluid dynamics, electromagnetics, and acoustics. Its ability to handle complex geometries while maintaining accuracy makes it a valuable tool in computational modeling and simulation.