基于桁架变形原理的复杂曲面变形设计方法研究

项目名称： 基于桁架变形原理的复杂曲面变形设计方法研究

项目编号： No.50805075

项目类型： 青年科学基金项目

立项/批准年度： 2009

项目学科： 无线电电子学、电信技术

项目作者： 王志国

作者单位： 南京航空航天大学

项目金额： 15万元

中文摘要： 曲面变形是CAD模型快速设计和创新设计中需解决的关键问题。本项目研究基于桁架变形原理的复杂曲面变形设计,包括：对复杂曲面控制顶点网格的拓扑合并与断裂，"提取"桁架结构的节点和杆件；曲面变形中节点上载荷的优化反算，实现基于约束的曲面变形设计；三角网格模型变形过程中的细节特征保持等。本项研究的特色是避免了复杂曲面变形过程中曲面片之间光滑拼接的可解性问题，实现复杂曲面的光滑协调变形。变形后的曲面不仅满足给定的约束条件，且保证了曲面片之间在变形中始终G1连续。通过调整桁架中杆件的材料参数如弹性模量，亦可实现三角网格模型的保特征变形。本项目研究的变形方法属于物理变形范畴，但与传统的物理变形不同，本方法是线性的，无需求解非线性动力学偏微分方程，也无需计算曲面的变形能，因此简单、快速，适于交互式变形设计。项目成果将为计算机辅助设计及相关学科提供高性能的变形造型理论，建立新的变形技术与方法。

中文关键词： 自由变形；桁架；形状优化；物理变形；有限元

英文摘要： Surface deformaiton is a key problem in the field of rapid design and innovation design of CAD model. truss based shape modificatioin is researched in this project, and main research contents include:1)nodes and bar elements are extraced by merging and spliting control point mesh of complicated surfaces; 2)constraint based deformable surface design is developed using inverse computation of external node loads optimization; 3)feature-preserving deformaition of triangle model is researched and so on. The characteristic of this project is that smooth and compatible deformation of complicated surface can be achieved without considering the problem of smooth joint between surface patches. The deformed surfaces not only satisfy the giving geometric constraints but also preserving G1 connectivity between surface patches. By means of adjusting meterial parameters such as elastic modulus, feature-preserving deformation of triangle model also can be obtained. This research is different from traditional physically based deformation. We need not to solve non-linear partial differential equations and compute deformaiton energy of surfaces. The proposed method is simple, fast and applicable to interactive deformable design. Research achievements will present novel theory and method of geometric modelling with high performance in the field of computer aided design and related discipline.

英文关键词： free-form deformation; truss; shape optimizatioin; physically based deformation; finite element method