基于邊界面法的CAE與CAD一體化研究
發(fā)布時(shí)間：2019-06-19 13:06
【摘要】：CAD與CAE一體化已成為工程及科學(xué)計(jì)算領(lǐng)域中的一大研究熱點(diǎn)。目前商業(yè)CAE分析軟件普遍采用有限單元法,其分析模型是通過網(wǎng)格生成模塊對(duì)CAD模型離散而獲得的。CAD與CAE對(duì)應(yīng)模型表達(dá)方式不同,前者是連續(xù)的參數(shù)模型,后者為近似的離散網(wǎng)格模型。因此,雖然很多CAD軟件中添加了CAE分析功能,但還不能從根本上實(shí)現(xiàn)兩者的無縫集成。基于邊界積分方程的邊界面法具有許多優(yōu)點(diǎn),例如一般只需要離散問題域的表面且可采用不連續(xù)單元。在邊界面法中,對(duì)邊界的數(shù)值積分和場(chǎng)變量的插值都是在幾何模型邊界曲面的二維參數(shù)空間里進(jìn)行的。其幾何數(shù)據(jù)直接由參數(shù)曲面計(jì)算得到,而不是通過分段多項(xiàng)式插值近似,從而能夠避免幾何誤差,有利于實(shí)現(xiàn)CAD\CAE的一體化。本文基于邊界面法,在CAD\CAE一體化的程序設(shè)計(jì)實(shí)現(xiàn)和理論方面做出一系列的探索。主要完成了以下研究工作:(1)為實(shí)現(xiàn)對(duì)復(fù)雜三維實(shí)體的表面網(wǎng)格自動(dòng)生成,本文利用C++語言構(gòu)建了一個(gè)實(shí)體表面網(wǎng)格自動(dòng)生成框架。該框架分為公共幾何接口模塊、拓?fù)湫迯?fù)、網(wǎng)格尺寸場(chǎng)、曲線離散、網(wǎng)格數(shù)據(jù)管理和網(wǎng)格生成方法六個(gè)部分。本文設(shè)計(jì)了一個(gè)統(tǒng)一的網(wǎng)格數(shù)據(jù)管理器,以便于程序的調(diào)整、維護(hù)及擴(kuò)充。在該框架中可方便地添加和實(shí)現(xiàn)各種二維網(wǎng)格生成方法,可將所得的網(wǎng)格單元轉(zhuǎn)換為計(jì)算單元,且可導(dǎo)出到其他模塊(比如體網(wǎng)格生成模塊)。(2)為實(shí)現(xiàn)對(duì)復(fù)雜三維實(shí)體的表面三角形網(wǎng)格自動(dòng)生成,本文提出了一種將推進(jìn)波前法與Delaunay方法相結(jié)合的方式來生成網(wǎng)格。該方法利用推進(jìn)波前法生成面內(nèi)點(diǎn),之后采用Delaunay內(nèi)核插點(diǎn)算法將該點(diǎn)加入到網(wǎng)格中。本文添加了對(duì)前沿的識(shí)別,將前沿分為活動(dòng)前沿及非活動(dòng)前沿,只對(duì)滿足要求的活動(dòng)前沿插入新點(diǎn)。創(chuàng)建了基于曲面鄰近特征的自適應(yīng)尺寸場(chǎng),并將其作為背景網(wǎng)格,使得所生成的網(wǎng)格能較好地反映曲面鄰近特征。該方法能夠生成較高質(zhì)量的表面網(wǎng)格,且可以保證網(wǎng)格生成的收斂。同時(shí),實(shí)現(xiàn)了柵格法,使得對(duì)于幾類曲面特征的網(wǎng)格生成規(guī)模大大降低。(3)為實(shí)現(xiàn)對(duì)具有焊縫的鋼架結(jié)構(gòu)的曲面網(wǎng)格生成,鑒于邊界面法的特點(diǎn),本文首先直接基于連續(xù)曲面模型,完成了短邊、窄面和不光滑邊界等3類曲面缺陷幾何特征的拓?fù)湫迯?fù)。拓?fù)湫迯?fù)中涉及的所有操作皆為虛操作,不改變?cè)心Ｐ偷膸缀味x。并且提出了基于柵格法的混合網(wǎng)格生成方式,對(duì)不同的子區(qū)域采用不同的網(wǎng)格生成方法,最后將子區(qū)域上的網(wǎng)格合并得到最終的曲面網(wǎng)格。與傳統(tǒng)的網(wǎng)格生成方式對(duì)比,大大降低了網(wǎng)格規(guī)模。(4)為求解邊界積分方程中的弱奇異及近奇異積分,提出了一種通用的自適應(yīng)單元細(xì)分方法。該算法通過一系列以源點(diǎn)為球心且半徑不斷減小的球與單元相交來細(xì)分單元,能夠?qū)拷袋c(diǎn)的積分片進(jìn)行自動(dòng)加密細(xì)分,并在生成積分片的過程中額外添加點(diǎn)的遷移算法來保證每個(gè)積分片具有較“好”的形狀及大小。該算法適用于任意形狀的單元,而且源點(diǎn)可以在任意位置。使用本文的方法所獲得的計(jì)算精度有顯著的提高。而且,在要求獲得相同數(shù)量級(jí)計(jì)算精度的情況下,該算法需要少得多的高斯積分點(diǎn),因而大大提高了計(jì)算效率。(5)在多域邊界面法實(shí)現(xiàn)中,提出了一個(gè)域編號(hào)序列優(yōu)化算法來減小總體組裝矩陣的帶寬。由于矩陣的稀疏結(jié)構(gòu)與未知量在整體方程組系統(tǒng)中的順序直接相關(guān),因此采用了一種排序策略來獲得最佳的塊結(jié)構(gòu)。該域序號(hào)優(yōu)化算法的優(yōu)點(diǎn)是使得矩陣中非零塊盡可能地靠近主對(duì)角線。在該算法中,首先通過考慮域的自由度及連通性產(chǎn)生一個(gè)或者多個(gè)層次結(jié)構(gòu)。其次,對(duì)于每個(gè)連續(xù)的層次結(jié)構(gòu),分別計(jì)算這些層次結(jié)構(gòu)的帶寬。最后,根據(jù)具有最小帶寬的層次結(jié)構(gòu)對(duì)域進(jìn)行重新排序。數(shù)值算例表明采用該算法對(duì)整體矩陣進(jìn)行LU分解的時(shí)間顯著減少,同時(shí)內(nèi)存開銷也顯著降低。
[Abstract]:The integration of CAD and CAE has become a hot topic in engineering and scientific computing. At present, the finite element method is widely used in commercial CAE analysis software, and the analysis model is obtained by the discrete of the grid generation module to the CAD model. The former is a continuous parameter model, and the latter is the approximate discrete grid model. Therefore, although the CAE analysis function is added to many CAD software, it is not possible to fundamentally realize the seamless integration of the two. The boundary surface method based on the boundary integral equation has many advantages, for example, it generally requires only the surface of the discrete problem domain and may employ discrete units. In the boundary surface method, the numerical integration of the boundary and the interpolation of the field variable are carried out in the two-dimensional parameter space of the boundary surface of the geometric model. The geometric data is directly calculated by the parametric surface, rather than the piecewise polynomial interpolation approximation, so that the geometric error can be avoided, and the integration of the CADCAE can be facilitated. In this paper, based on the boundary surface method, a series of exploration is made in the design and theory of the integration of CAD and CAE. The following research work is mainly done: (1) In order to realize the automatic generation of the surface mesh of the complex three-dimensional entity, this paper constructs a solid surface mesh automatic generation framework using the C ++ language. The framework is divided into six parts: common geometric interface module, topology repair, mesh size field, curve dispersion, grid data management and grid generation method. In this paper, a unified grid data manager is designed to facilitate the adjustment, maintenance and expansion of the program. In the framework, various two-dimensional grid generation methods can be conveniently added and implemented, and the obtained grid cells can be converted into a calculation unit and can be exported to other modules (such as a body grid generation module). (2) In order to realize the automatic generation of the surface triangle mesh of the complex three-dimensional entity, this paper presents a method of combining the advance wave front method and the Delaunay method to generate the grid. The method uses the advance wave front method to generate the inner point of the plane, and then the point is added into the grid by using the delaunay kernel interpolation point algorithm. In this paper, the recognition of the leading edge is added, the leading edge is divided into the front of the active and the non-active front, and the new point is only inserted into the leading edge of the activity. The adaptive dimension field based on the adjacent feature of the surface is created and used as the background mesh, so that the generated mesh can better reflect the adjacent features of the curved surface. The method can generate a high-quality surface mesh, and can ensure the convergence of grid generation. At the same time, the grid method is realized, so that the grid generation scale for several types of surface features is greatly reduced. (3) In order to realize the surface mesh generation of the steel frame structure with the welding seam, in view of the characteristics of the boundary surface method, the topological repair of three surface defect geometric features such as the short side, the narrow surface and the non-smooth boundary is completed directly based on the continuous surface model. All operations involved in the topology repair are virtual operations and do not change the geometry of the original model. And a hybrid mesh generation method based on the grid method is proposed, different grid generation methods are adopted for different sub-regions, and finally, the mesh in the sub-region is combined to obtain a final curved surface mesh. Compared with the traditional grid generation method, the grid scale is greatly reduced. (4) In order to solve the weak singular and near singular integral in the boundary integral equation, a general adaptive unit subdivision method is proposed. The method comprises the following steps of: dividing a unit by a series of balls with a source point as a ball center and a constant radius, and enabling the integration piece close to the source point to be automatically encrypted and subdivided, And the migration algorithm of the additional points is added in the process of generating the integral piece to ensure that each integral piece has a higher "-Okay." shape and size. The algorithm is suitable for any shape of cell and the source point can be in any position. The accuracy of the calculation obtained by using the method provided by the method is remarkably improved. Moreover, in the case where the calculation accuracy of the same order of magnitude is required, a much less Gaussian integration point is required for the algorithm, and thus the calculation efficiency is greatly improved. (5) In the multi-domain boundary surface method, a domain number sequence optimization algorithm is proposed to reduce the bandwidth of the overall assembly matrix. Since the sparse structure of the matrix is directly related to the order of unknowns in the system of the integral equations, a sort of sort strategy is used to obtain the best block structure. The advantage of the domain sequence number optimization algorithm is that the non-zero blocks in the matrix are as close as possible to the main diagonal. In this algorithm, one or more hierarchies are first generated by considering the degree of freedom and connectivity of the domain. Second, for each successive hierarchy, calculate the bandwidth for these hierarchies, respectively. Finally, the domain is re-ordered according to the hierarchy with the minimum bandwidth. The numerical example shows that the time of LU decomposition of the whole matrix is significantly reduced by using the algorithm, and the memory overhead is also significantly reduced.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TP391.7
本文編號(hào)：2502363
[Abstract]:The integration of CAD and CAE has become a hot topic in engineering and scientific computing. At present, the finite element method is widely used in commercial CAE analysis software, and the analysis model is obtained by the discrete of the grid generation module to the CAD model. The former is a continuous parameter model, and the latter is the approximate discrete grid model. Therefore, although the CAE analysis function is added to many CAD software, it is not possible to fundamentally realize the seamless integration of the two. The boundary surface method based on the boundary integral equation has many advantages, for example, it generally requires only the surface of the discrete problem domain and may employ discrete units. In the boundary surface method, the numerical integration of the boundary and the interpolation of the field variable are carried out in the two-dimensional parameter space of the boundary surface of the geometric model. The geometric data is directly calculated by the parametric surface, rather than the piecewise polynomial interpolation approximation, so that the geometric error can be avoided, and the integration of the CADCAE can be facilitated. In this paper, based on the boundary surface method, a series of exploration is made in the design and theory of the integration of CAD and CAE. The following research work is mainly done: (1) In order to realize the automatic generation of the surface mesh of the complex three-dimensional entity, this paper constructs a solid surface mesh automatic generation framework using the C ++ language. The framework is divided into six parts: common geometric interface module, topology repair, mesh size field, curve dispersion, grid data management and grid generation method. In this paper, a unified grid data manager is designed to facilitate the adjustment, maintenance and expansion of the program. In the framework, various two-dimensional grid generation methods can be conveniently added and implemented, and the obtained grid cells can be converted into a calculation unit and can be exported to other modules (such as a body grid generation module). (2) In order to realize the automatic generation of the surface triangle mesh of the complex three-dimensional entity, this paper presents a method of combining the advance wave front method and the Delaunay method to generate the grid. The method uses the advance wave front method to generate the inner point of the plane, and then the point is added into the grid by using the delaunay kernel interpolation point algorithm. In this paper, the recognition of the leading edge is added, the leading edge is divided into the front of the active and the non-active front, and the new point is only inserted into the leading edge of the activity. The adaptive dimension field based on the adjacent feature of the surface is created and used as the background mesh, so that the generated mesh can better reflect the adjacent features of the curved surface. The method can generate a high-quality surface mesh, and can ensure the convergence of grid generation. At the same time, the grid method is realized, so that the grid generation scale for several types of surface features is greatly reduced. (3) In order to realize the surface mesh generation of the steel frame structure with the welding seam, in view of the characteristics of the boundary surface method, the topological repair of three surface defect geometric features such as the short side, the narrow surface and the non-smooth boundary is completed directly based on the continuous surface model. All operations involved in the topology repair are virtual operations and do not change the geometry of the original model. And a hybrid mesh generation method based on the grid method is proposed, different grid generation methods are adopted for different sub-regions, and finally, the mesh in the sub-region is combined to obtain a final curved surface mesh. Compared with the traditional grid generation method, the grid scale is greatly reduced. (4) In order to solve the weak singular and near singular integral in the boundary integral equation, a general adaptive unit subdivision method is proposed. The method comprises the following steps of: dividing a unit by a series of balls with a source point as a ball center and a constant radius, and enabling the integration piece close to the source point to be automatically encrypted and subdivided, And the migration algorithm of the additional points is added in the process of generating the integral piece to ensure that each integral piece has a higher "-Okay." shape and size. The algorithm is suitable for any shape of cell and the source point can be in any position. The accuracy of the calculation obtained by using the method provided by the method is remarkably improved. Moreover, in the case where the calculation accuracy of the same order of magnitude is required, a much less Gaussian integration point is required for the algorithm, and thus the calculation efficiency is greatly improved. (5) In the multi-domain boundary surface method, a domain number sequence optimization algorithm is proposed to reduce the bandwidth of the overall assembly matrix. Since the sparse structure of the matrix is directly related to the order of unknowns in the system of the integral equations, a sort of sort strategy is used to obtain the best block structure. The advantage of the domain sequence number optimization algorithm is that the non-zero blocks in the matrix are as close as possible to the main diagonal. In this algorithm, one or more hierarchies are first generated by considering the degree of freedom and connectivity of the domain. Second, for each successive hierarchy, calculate the bandwidth for these hierarchies, respectively. Finally, the domain is re-ordered according to the hierarchy with the minimum bandwidth. The numerical example shows that the time of LU decomposition of the whole matrix is significantly reduced by using the algorithm, and the memory overhead is also significantly reduced.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TP391.7
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