isogeometrikus

Isogeometric analysis (IGA) is a computational method that uses the same basis functions used for describing the geometry of a design to perform the analysis of that design. This means that the curves and surfaces used in computer-aided design (CAD) are directly employed in the finite element method (FEM) or other numerical simulation techniques. This approach aims to bridge the gap between design and analysis, eliminating the need for mesh generation, which is often a time-consuming and error-prone step in traditional FEM.

The core idea of IGA is to leverage the properties of spline-based representations, such as Non-Uniform Rational B-Splines (NURBS) or T-splines, which are commonly used in CAD. These basis functions offer several advantages over the polynomial basis functions typically used in FEM, including higher continuity and the ability to represent complex geometries exactly. By using these same functions for analysis, IGA can achieve higher accuracy with fewer degrees of freedom compared to traditional methods for the same geometry.

Key benefits of isogeometric analysis include improved accuracy, reduced pre-processing time, and a more seamless workflow from design to analysis. It is particularly well-suited for problems involving complex geometries, such as those found in aerospace, automotive, and biomedical engineering. While IGA offers significant advantages, it also presents challenges, including the development of suitable solvers and the integration with existing software tools. Research in this area continues to focus on expanding its applicability and addressing these challenges.