基于有限元法的曲面变形技术研究

发布时间：2018-04-07 15:49

本文选题：计算机辅助几何设计　切入点：曲面造型　出处：《南京航空航天大学》2013年博士论文

【摘要】：飞机、汽车等复杂产品的数字化设计是一个反复编辑、不断修改的过程。因此，灵活精确、自然高效的曲面变形技术一直是该领域的研究热点。本文基于有限元法，针对不同的曲面模型和变形需求，对曲面变形技术进行了研究，主要研究内容和成果如下：借鉴骨架驱动生物运动的机制，提出了一种骨架-刚架模型驱动网格曲面变形算法。算法采用光线求交法求取由直线段组成的骨架，通过将直线段定义为梁单元创建骨架-刚架模型，建立网格顶点与骨架-刚架模型的映射，基于有限元法分别建立载荷作用下和几何约束下的骨架-刚架模型变形控制方程，求解该方程获得骨架-刚架模型的变形，进而带动附着在骨架上的网格曲面发生变形；通过梁单元形函数插值创建旋转场进一步修正计算结果。该算法适用于具有明显骨架语义的网格变形设计，与已有的物理变形技术相比，无需将变形过程划分多步，提高了使用方便性。为实现由网格曲面描述的产品表面的变形设计，提出了一种网格-刚架模型驱动网格曲面保特征变形算法。算法通过对初始网格进行一定程度的简化得到相应的基网格，将基网格顶点定义为网格-刚架模型节点，确立初始网格顶点与网格-刚架模型之间的映射关系，基于有限元法分别建立载荷作用下和几何约束下的网格-刚架模型的变形控制方程，求解该方程获得网格-刚架模型的变形，根据映射关系计算初始网格的变形。在变形计算中，通过增大网格曲面特征区域所关联单元体材料的弹性模量，达到整体变形中局部形状特征的保持。该算法兼有载荷作用下的自由变形和满足几何约束的精确设计功能，同时，采用基网格创建网格-刚架模型，保证了曲面变形计算的高效性。以有限元六面体单元变形理论为基础，提出了一种六面体栅格模型驱动网格曲面变形算法。该算法采用栅格法剖分网格曲面的包围盒创建六面体栅格模型，建立网格顶点与六面体栅格模型之间的映射关系，基于有限元法建立载荷作用下六面体栅格模型的变形控制方程，进而采用“变形累加法”计算六面体栅格模型的变形，根据映射关系计算网格曲面变形。该算法适用于载荷作用下的网格曲面保特征自由变形设计。针对由多张B-Spline曲面拼接构成的几何变形设计问题，提出了刚架模型驱动多张B-Spline曲面变形算法。通过合并曲面片的控制顶点建立刚架模型，将曲面片之间的光滑拼接条件抽象为刚架模型节点间的位置约束，结合点约束、法矢约束共同组成约束条件，基于有限元法建立刚架模型的变形控制方程，求解方程获得刚架模型的变形，进而计算曲面变形。变形后的多张B样条曲面不仅满足给定的几何约束，而且保持变形前的光滑拼接状态。
[Abstract]:The digital design of complex products, such as aircraft and automobile, is a process of repeated editing and constant modification.Therefore, flexible, accurate, natural and efficient surface deformation technology has been a research hotspot in this field.In this paper, based on finite element method, the surface deformation technology is studied according to different surface models and deformation requirements. The main research contents and results are as follows:Based on the mechanism of skeleton driving biological movement, a skeleton-rigid frame model driven mesh surface deformation algorithm is proposed.The algorithm uses the ray intersection method to obtain the skeleton composed of straight line segments. By defining the straight line segment as the beam element, the skeleton rigid frame model is created, and the mapping between the mesh vertex and the skeleton rigid frame model is established.Based on the finite element method, the deformation control equations of the skeleton rigid frame model under load and geometric constraints are established, and the deformation of the skeleton rigid frame model is obtained by solving the equation, which leads to the deformation of the mesh surface attached to the skeleton.The rotation field is created by the interpolation of the beam element form function to further modify the calculation results.The algorithm is suitable for mesh deformation design with obvious skeleton semantics. Compared with the existing physical deformation technology, the algorithm does not need to divide the deformation process into multiple steps and improves the ease of use.In order to realize the deformation design of the product surface described by the mesh surface, a grid-rigid frame model driven feature preserving deformation algorithm for the mesh surface is proposed.By simplifying the initial grid to a certain extent, the algorithm defines the vertex of the base grid as a grid-rigid frame model node, and establishes the mapping relationship between the initial grid vertex and the grid-rigid frame model.Based on the finite element method, the deformation control equations of the mesh-rigid frame model under load and geometric constraints are established, and the deformation of the grid-rigid frame model is obtained by solving the equation. The deformation of the initial grid is calculated according to the mapping relationship.In the deformation calculation, the local shape characteristics of the whole deformation can be preserved by increasing the elastic modulus of the materials associated with the characteristic region of the mesh surface.The algorithm has the functions of free deformation under load and precise design to satisfy geometric constraints. At the same time, the grid-rigid frame model is created by using basic mesh, which ensures the high efficiency of surface deformation calculation.Based on the finite element theory of hexahedron element deformation, a hexahedron grid model driven mesh surface deformation algorithm is proposed.In this algorithm, the hexahedron raster model is created by dividing the bounding box of the mesh surface, and the mapping relationship between the vertex of the grid and the hexahedron grid model is established.Based on the finite element method, the deformation control equation of hexahedron grid model under load is established, and the deformation of hexahedron grid model is calculated by "deformation cumulative addition method", and the deformation of mesh surface is calculated according to the mapping relation.This algorithm is suitable for the free deformation design of mesh surfaces under load.In order to solve the problem of geometric deformation design which is composed of multiple B-Spline surfaces, a deformation algorithm driven by rigid frame model for multiple B-Spline surfaces is proposed.A rigid frame model is established by combining the control vertices of a curved surface slice, and the smooth joint condition between the surfaces is abstracted into the position constraint, the joint point constraint and the normal vector constraint between the nodes of the rigid frame model.Based on the finite element method, the deformation control equation of the rigid frame model is established, and the deformation of the rigid frame model is obtained by solving the equation, and then the deformation of the curved surface is calculated.The deformed B-spline surfaces not only satisfy the given geometric constraints, but also maintain the smooth splicing state before deformation.
【学位授予单位】：南京航空航天大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TH122;TP391.72

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