本文選題：計算機輔助幾何設計　切入點：曲面造型　出處：《南京航空航天大學》2013年博士論文

【摘要】：飛機、汽車等復雜產品的數字化設計是一個反復編輯、不斷修改的過程。因此，靈活精確、自然高效的曲面變形技術一直是該領域的研究熱點。本文基于有限元法，針對不同的曲面模型和變形需求，對曲面變形技術進行了研究，主要研究內容和成果如下： 借鑒骨架驅動生物運動的機制，提出了一種骨架-剛架模型驅動網格曲面變形算法。算法采用光線求交法求取由直線段組成的骨架，通過將直線段定義為梁單元創(chuàng)建骨架-剛架模型，建立網格頂點與骨架-剛架模型的映射，基于有限元法分別建立載荷作用下和幾何約束下的骨架-剛架模型變形控制方程，求解該方程獲得骨架-剛架模型的變形，進而帶動附著在骨架上的網格曲面發(fā)生變形；通過梁單元形函數插值創(chuàng)建旋轉場進一步修正計算結果。該算法適用于具有明顯骨架語義的網格變形設計，與已有的物理變形技術相比，無需將變形過程劃分多步，提高了使用方便性。 為實現由網格曲面描述的產品表面的變形設計，提出了一種網格-剛架模型驅動網格曲面保特征變形算法。算法通過對初始網格進行一定程度的簡化得到相應的基網格，將基網格頂點定義為網格-剛架模型節(jié)點，確立初始網格頂點與網格-剛架模型之間的映射關系，基于有限元法分別建立載荷作用下和幾何約束下的網格-剛架模型的變形控制方程，求解該方程獲得網格-剛架模型的變形，根據映射關系計算初始網格的變形。在變形計算中，通過增大網格曲面特征區(qū)域所關聯單元體材料的彈性模量，達到整體變形中局部形狀特征的保持。該算法兼有載荷作用下的自由變形和滿足幾何約束的精確設計功能，同時，采用基網格創(chuàng)建網格-剛架模型，保證了曲面變形計算的高效性。 以有限元六面體單元變形理論為基礎，提出了一種六面體柵格模型驅動網格曲面變形算法。該算法采用柵格法剖分網格曲面的包圍盒創(chuàng)建六面體柵格模型，建立網格頂點與六面體柵格模型之間的映射關系，基于有限元法建立載荷作用下六面體柵格模型的變形控制方程，進而采用“變形累加法”計算六面體柵格模型的變形，根據映射關系計算網格曲面變形。該算法適用于載荷作用下的網格曲面保特征自由變形設計。 針對由多張B-Spline曲面拼接構成的幾何變形設計問題，提出了剛架模型驅動多張B-Spline曲面變形算法。通過合并曲面片的控制頂點建立剛架模型，將曲面片之間的光滑拼接條件抽象為剛架模型節(jié)點間的位置約束，結合點約束、法矢約束共同組成約束條件，基于有限元法建立剛架模型的變形控制方程，求解方程獲得剛架模型的變形，進而計算曲面變形。變形后的多張B樣條曲面不僅滿足給定的幾何約束，而且保持變形前的光滑拼接狀態(tài)。
[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.
【學位授予單位】：南京航空航天大學
【學位級別】：博士
【學位授予年份】：2013
【分類號】：TH122;TP391.72

【參考文獻】

相關期刊論文 前10條

1 ;Shape Modification and Deformation of Parametric Surfaces[J];Computer Aided Drafting,Design and Manufacturing;2002年01期

2 李靜;陳健云;周晶;;改進的SSOR-PCG迭代法在接觸問題研究中應用[J];大連理工大學學報;2006年04期

3 成思源,張湘?zhèn)?可變形B樣條曲線曲面模型及其有限元求解[J];重慶大學學報(自然科學版);2003年02期

4 施法中,吳駿恒;Bézier作圖定理與三次Bézier曲線的幾何特征[J];航空學報;1982年03期

5 王志國;王小平;鮑益東;周來水;;基于有限元方法中粱模型的形狀修改算法(英文)[J];Chinese Journal of Aeronautics;2010年02期

6 李道倫;盧德唐;孔祥言;吳剛;;徑向基函數網絡的隱式曲面方法[J];計算機輔助設計與圖形學學報;2006年08期

7 王雋;張宏鑫;許棟;鮑虎軍;;勾畫式泊松網格編輯[J];計算機輔助設計與圖形學學報;2006年11期

8 許秋兒;譚光華;張三元;張引;;保持幾何特征的均值骨架子空間網格變形[J];計算機輔助設計與圖形學學報;2009年03期

9 張湘玉;廖文和;劉浩;;基于細分曲面的泊松網格編輯[J];計算機輔助設計與圖形學學報;2010年01期

10 張亞萍;熊華;姜曉紅;石教英;;大型網格模型簡化和多分辨率技術綜述[J];計算機輔助設計與圖形學學報;2010年04期

相關博士學位論文 前3條

1 莫X;基于隱式函數的曲面重構方法及其應用[D];華中科技大學;2010年

2 張湘玉;基于細分的曲線曲面變形技術研究[D];南京航空航天大學;2010年

3 許秋兒;網格變形技術研究[D];浙江大學;2009年

，

本文編號：1719842