CAGD与CAD/CAE/AI深度融合的类B样条等几何方法研究

类B样条是CAGD中理论发展完善的样条工具，具有独特的建模与计算优势，本项目挖掘类B样条在CAD/CAE/AI中的应用潜力，运用并拓展等几何思想，提出新融合领域基于类B样条的等几何方法：.1.利用类B样条丰富的曲线曲面表示能力及可细分性，提出线弹性问题的建模、求解、细化、后处理及域外边界延拓方法，建立基于类B样条的高精度等几何边界元分析框架。.2.利用类B样条在柔性铰链精确建模及敏感性分析中的求导计算优势，结合物理与几何优化目标，建立基于类B样条的等几何形状优化方法，实现四种常用柔性铰链的弯曲柔度、轴向刚度物理性能及几何性能的提升。.3.利用类B样条在CAD边界表示模型中统一表示及属性精确计算能力，建立同时包含类B样条边界表示及三角网格表示的三维CAD模型数据集，以几何拓扑信息为输入、以可训练的类B样条关联函数为卷积核函数，创新提出等几何深度学习框架，并高效实现三维CAD模型形状分析任务。

B-like splines provide a rich set of spline tools with well-established theories in CAGD and with unique modeling and computing advantages. This project explores potential applications of B-like splines in CAD/CAE/AI, and further develops isogeometric methods based on B-like splines in new promising fields of applications:.1. B-like splines are capable of representation and subdivision of a rich class of curves and surfaces. In this project, we develop algorithms on B-like spline modeling and refinement and establish a general framework for isogeometric boundary element analysis of linear elasticity problems with relevant post-processing based on B-like splines..2. Taking advantages in accurate modeling of flexure hinges using B-like splines and relevant sensitivity analysis, we further develop isogeometric shape optimization methods for flexure hinges based on B-like splines. During the optimization process, objectives for both shape and performance optimization will be considered. Shape optimization experiments for four types of commonly used flexure hinges will be conducted to improve their flexibility, axial stiffness and geometric properties..3. Being a unified representation using B-like splines for B-rep modeling and accurate evaluation of geometric properties, we construct a large data set of CAD models including both B-like spline B-rep models and trigonometric meshes, and propose an isogeomtric deep learning network based on B-like splines. The input of this network is 3D geometric and topological information. Its convolution functions are trainable continuous functions. We also use the new deep learning network for efficient implementation and shape analysis of CAD models.