计算机辅助设计与分析的无缝融合是先进制造领域亟需解决的核心问题之一，对我国在先进制造、计算力学软件行业的国际竞争力有重要影响。近10年多在等几何分析概念的影响下成果丰硕，但主要局限于二维结构，而且在自适应分析、精确CAD网格生成等方面还存在困难。本项目针对等几何分析目前存在的困难展开四方面的研究并基于这些成果及申请人的前期相关研究成果开发计算力学软件：（1）把CAD模型的边界表示与构造实体几何和有限元胞方法结合起来研究稀疏的、能够精确表示CAD几何的曲面和实体单元的自动生成；（2）把微分求积升阶谱有限元方法与精确的CAD曲面和实体单元结合起来做自适应分析，并解决裁剪曲面之间的匹配问题；（3）解决张量积形式的任意三角形和四面体单元汇聚点的奇异性；（4）基于申请人提出的非均匀有理Hermite函数研究C1连续问题的等几何分析。研究成果可望为解决计算机辅助设计与分析无缝融合这一瓶颈问题奠定基础。

Seamless integration of computer aided design (CAD) and analysis is one of the core issues to be addressed for advanced manufacture. It has significant influence on the international competitiveness of China on advanced manufacturing and computational mechanics software industries. There are great achievements in recent 10 more years due to the influence of the iso-geometric analysis (IGA) concepts. However, these achievements mainly limited in two-dimensional structures and there are some difficulties in self-adaptive analysis, exact CAD mesh generation, etc. This project carries out researches on four aspects that IGA met with difficulties and will develop computational mechanics software based on these achievements and related previous achievements of the applicant: (1) Combining the boundary representation (B-Rep) and constructive solid geometry (CSG) of CAD models with the finite cell method to study the automatic generation of coarse surface and solid elements that can match the exact CAD geometry. (2) To carry out self-adaptive analysis and solve the matching problem of trimmed surfaces by combining the exact CAD surface and solid elements with the differential quadrature hierarchical finite element method. (3) To solve the singularity problem of the degenerated point of tensor product arbitrary triangular and tetrahedral elements. (4) To study iso-geometric analysis of C1 continuity problem based on non-uniform rational Hermite functions proposed by the applicant. The achievements of this project are expected to provide a basis of solving the bottle neck problem of seamless integration of computer aided design and analysis.