面向生物医学结构设计的non-Newtonian流体流动拓扑优化方法研究

项目名称： 面向生物医学结构设计的non-Newtonian流体流动拓扑优化方法研究

项目编号： No.11272251

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 刘小民

作者单位： 西安交通大学

项目金额： 82万元

中文摘要： 基于生物器官内流体流动原理和数学的最优化理论进行生物医学结构拓扑优化，是解决目前生物医学结构设计中存在的难题、发展新颖的生物医学结构的重要途径。本项目将拓扑导数方法引入到水平集拓扑优化中，着重发展一种面向生物医学结构设计的non-Newtonian流体流动拓扑优化方法。首先针对血管或者胆管旁路搭桥等具体的生物医学结构设计，以最小能量耗散和最大剪切应力为目标，建立non-Newtonian流体流动拓扑优化问题的数学模型。然后对此拓扑优化问题进行形状灵敏度分析和拓扑灵敏度分析，在非结构化网格上采用有限元方法数值求解物理场，在结构化网格上采用有限差分法求解水平集类方程，基于无样条重新网格划分方法实现水平集类方程求解与物理场求解的结合，进而完成水平集拓扑优化及其全局性研究。集成拓扑优化程序，并将其扩展到一般意义上的生物医学结构设计中。最后分别从数值模拟计算和实验的角度验证优化设计方法的有效性。

中文关键词： 非牛顿流体流动；生物医学结构设计；拓扑优化；水平集方法；血管架桥

英文摘要： Biomedical structural topology optimization, based on the principle of fluid flow in biological organs and mathematical optimization theory, is an important way to solve the problems in the biomedical structural design and develop novel biomedical structure. The topological derivative method is introduced to the level set topology optimization method to achieve the global optimization. In the project, a new topology optimization method and theoretical basis is developed for the non-Newtonian fluid flow in the biomedical structural design. Firstly, to obtain the minimum energy dissipation and the maximum shear stress, a mathematical model of topology optimization for non-Newtonian fluid flow is established for the specific biomedical structural design such as the bypass design of blood vessels or bile ducts. Secondly, the shape and topology sensitivity analysis for the established topology optimization problem are completed. The physical systems including the state equation and the conjugate equation are solved numerically using the finite element method in the unstructured grid. The numerical solutions of the level set equations are obtained using the finite difference method in the structured grid. Based on the spline-free re-meshing method, the combination of the level set function evolution and numerical anal

英文关键词： non-Newtonian flows；biomedical structural design；topology optimization；level set method；arterial bypass