基于体参数化的产品设计基础理论研究

项目名称： 基于体参数化的产品设计基础理论研究

项目编号： No.51475309

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 机械、仪表工业

项目作者： 陈龙

作者单位： 上海理工大学

项目金额： 80万元

中文摘要： 工业中出现几何、拓扑、材料俱复杂产品，3D打印技术使该类产品制造成为可能，但是几何设计与性能分析分离、过多人工交互干预、不共享设计各阶段模型等特点的传统设计方法迫切需要改进。本项目提出体参数化模型统一表达几何和性能数据，等几何分析作为分析和优化手段的方法。针对拓扑复杂模型，提取模型表面或体域拓扑关键点，构建Morse-Smale复形，进行体分解得到零亏格子域，利用优化算法得到体参数化模型。设计基于区域分解理论的等几何分析算法，通过局部细化提高分析精度，按照拼接模式对边界特殊处理，按顺序完成基元体装配，实现复杂拓扑模型的性能分析。设计域作为物理域，体参数化背景网格作为参数域，构建域转换与相互设计机制，将几何变量、材料密度作为体参数化背景网格的设计变量，实现拓扑优化设计，消除网格依赖。赋予体参数化模型材料信息，完成非均质产品模型构建。项目预期为几何、拓扑、材料俱复杂产品提供设计与分析新方法。

中文关键词： 体参数化；拓扑识别；等几何分析；优化设计；非均质产品

英文摘要： There have been emerged many products complex in geometry, topology and material. The 3D printing technology makes it possible for manufacutring of these products.But the conventional design method，with the properties of separation of geometric design and performance analysis，too much manual intervention and no share of the model in different design stages has urgent need to improvement.This proposal put up that Volume parameterization model represents uniformly the geometrical and performance data and Isogeometric analysis is the means of analysis and optimization. For the models with complex topology,extract the topology critical points from surface or body domain, construct Morse-of Smale complex, and then subdomains with zero genus are acquired after volume decomposition. Optimization algorithms are utilized to acquire volume parametric primitive bodies. Isogeometric analysis algorithm are implemented based on the theory of domain decomposition. The accuracy of analysis can be improved further by refining the primitive body. Some special treatments are applied for the boundary of the primitive bodies according to the merging mode, assembly the primitives in order, then complete the performance analysis for the complex products. Taking design domain as physical domain, parametric volume background grid as parameter domain, construct the mechanism for converting and cross-referrence designing.Exploiting the geometric variables， density of materials as design variables of parametric volume background grid, topology optimization design can achieved through controlling density, as well as eliminating mesh dependence. Material information is input into the volume parametric primitives and heterogeneous product are created. It is can be expected that this project will provide a new method for the design, analysis and optimization of the products with complex geometry, topology and materials.

英文关键词： Volume parameterization;topology recognition;isogeometric analysis;optimization design;heterogeneous product