关键词: NURBS, 参数化, 等几何分析, 结构优化

Abstract: 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.

Key words: isogeometric analysis, NURBS, parameterization, structural optimization