提出等几何分析(Isogeometric analysis, IGA)是一种新的物理场数值求解方法，它可实现CAE数值分析与CAD建模工具的集成，给出一条使设计、分析和优化紧密结合的新途径。以等几何分析方法的计算框架为基础，详细介绍等几何分析方法中样条几何模型的描述方式和建模方法；并以NURBS为例，阐述了IGA中的分析模型的参数化表示以及网格模型的细化方法；结合现有的经典有限元的分析过程，简单介绍IGA的离散方法、边界条件和积分方法；系统总结等几何分析在热、流体、接触和优化方面的应用，并给出了一个简单的二维问题的IGA求解实例。

Isogeometric analysis (IGA) is a novel numerical method for solving equations of physical fields, which is motivated by improving the integration between numerical simulations of physical phenomena and the computer-aided design tools, and provides a new way to associate product design with analysis and optimization via a common mathematical platform. The method of geometric modeling and its mathematical description are introduced in detail based on the computational framework of IGA. Taking NURBS as an example, the parametric representation in an analysis model and the mesh refinement method are analyzed, and the discretization methods, boundary conditions and quadrature in the parametric domain of IGA are discussed as well by comparing them with those in the standard finite element analysis. Applications of IGA in thermal analysis, fluid-structure interaction, contact problems and structural optimization are summarized and a simple example of 2D problem is provided.