基于细分曲面造型的边界元法及后处理开发研究
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摘要
CAD/CAE技术，凭借其在产品设计和分析中的强大功能，能够显著地提高产品质量，缩短开发周期，降低开发成本，已经成为当前产品设计开发的强有力的辅助工具。然而，由于在传统的CAD/CAE各自系统中模型的表示方式不同，前者是连续的参数模型，后者则是离散的网格模型，数据模型在两种系统间的传递与转换所带来的问题逐渐受到人们的关注。如何实现数据模型在CAD/CAE系统间的自动转换，或者为CAD/CAE系统提供一个统一的模型表示，即CAD/CAE一体化，成了CAD/CAE研究领域的热点问题。本文将细分曲面和边界元法结合起来，自然地将CAD和CAE融为一体，实现了基于细分曲面造型的边界元法，并应用该方法求解三维位势和线弹性问题。同时，为了分析和研究该方法的结果数据，本文基于ExodusII和ParaView提出了一个科学计算可视化解决方案，与基于细分曲面造型的边界元法一起搭建了一个包含CAD造型（细分曲面造型）、CAE分析（边界元法数值计算）和可视化后处理（ParaView科学可视化方案）的完备的CAD/CAE一体化平台。此外，在实际工程问题中，本文应用上述可视化方案模拟混凝土坝浇筑过程并为其热传导分析提供可视化后处理解决方案。
基于细分曲面造型的边界元法具有以下特点：（1）细分网格既用于表达几何模型，又作为边界元法的离散分析网格，为CAD设计与CAE分析提供了一个一般的模型和统一的表示，避免了数据模型在不同系统间的转换。（2）由于细分网格为边界元分析提供了一个自动的和自适应的网格划分方案，该方法避免了传统边界元法模型离散引入的人为误差，同时可以通过细分层次控制模型表达和数值计算的精度，以满足不同的设计与分析要求。（3）基于细分曲面造型的边界元法，在几何设计中，具有细分曲面造型的不受几何拓扑限制可以构建整体光滑的任意复杂模型的特点，在数值分析中，又继承了边界元法只需边界离散、降维以及高精度的优点。
在细分曲面建模中，本文提供了均匀细分曲面建模和自适应细分曲面建模两种建模方案。由于在每一次细分过程中每一个网格面片都参与细分，均匀细分曲面建模的细分网格均匀且成倍增长，其整体质量提高较快。但是，均匀细分曲面建模容易引起细分不足和细分过度。由于在每一次迭代细分中网格面片根据自适应准则决定是否参与细分过程，自适应细分曲面建模能够在局部平坦区域减少细分次数，在局部复杂区域增加细分次数。因此，自适应细分曲面建模可以用相对较少的细分网格模拟几何模型，同时避免了细分网格过度生长。
在数值分析中，本文将基于细分曲面造型的边界元法应用于求解三维位势问题和线弹性问题，考察了该方法的收敛性、精度以及优越性，并讨论了均匀细分曲面和自适应细分曲面在建模和分析上的各自特点。从建模和分析结果来看，随着细分层次的增加，细分曲面模型的网格数量增多，其质量也不断提高；同时，针对细分曲面模型的边界元分析精度也越来越好。其中，针对均匀细分曲面建模的边界元分析的收敛性和精度都较高。两种细分建模方案都能够获得较好的几何模型和满足精度要求的分析结果。
在结果后处理中，本文基于ExodusII和ParaView提出了一个功能丰富的边界元分析可视化后处理方案。该方案借助ExodusII生成包含模型信息和分析结果的二进制数据文件。该数据文件可以储存时间不变的静态数据或者含有时间步的动态数据。该方案利用ParaView的各种可视化功能实现对边界元分析结果数据的定性和定量的分析。同时，根据实际需要和习惯操作，本文对ParaView做了一些二次开发工作，包含界面简化、颜色条随时间步更新、放大操作优化以及注释文字自动添加等。为了在处理大规模数据时获得高效的处理性能和稳定性，并满足硬件升级的需要，本文编译了64位版本的ParaView应用程序。
最后，本文基于多块数据集的概念，提出了一个针对含时间步的多域数据模型的特殊的可视化后处理方案，并将其应用到混凝土坝热传导问题分析的科学计算可视化中。通过ExodusII编写含有特殊标识的数据文件并借助ParaView的二次开发，该方案实现了在ParaView中模拟混凝土坝的浇筑过程；同时，针对包含混凝土坝完整模型信息和热传导问题分析结果的数据模型，该方案提供了一个有效的动画演示功能，使得在某一时间步中只显示当前时间步含有分析结果的混凝土坝层，以真实地反映混凝土坝浇筑过程以及浇筑完成后一定时间段里温度分布情况。该方案也适用于其他类似的含时间步的多域模型的分析结果可视化后处理。
CAD/CAE techno lo gies, re lying o n the ir powerful functio na lities in des ign a ndana lys is of product, enab ling to dramatica lly improve the qua lity o f product, shorte nthe deve lop ment cyc le a nd lower the develop me nt cost, have become strong tools forcurrent product design and deve lop me nt.Howe ver, the representatio ns of mode l intraditio na l CAD syste ms, in whic h parametric continuous model is used, and that inCAE syste ms, in which a discrete mode l is invo lved, are d iffere nt. Prob le msintroduced by data model’s transfer and transition between the two systems havearoused people’s concern. How to perform an automatic conversion of the datamode l between the two syste ms, or provide a unified model representatio n for thetwo syste ms, na me ly CAD/CAE inte gration, has beco me a hot researching iss ue inthe CAD/CAE fie ld. This dissertatio n coup ling s ubdiv is io n surface modeling andboundary e le me nt method, success fully realizes boundary e le me nt method based onsubdivis io n s urface mode ling, natura lly integrating CAD and CAE. And the n severa lnumerica l comp utations re lated to the3D potentia l and linear elast ic proble ms areperformed with the method. In order to provide a better way to eva luate thecomputation res ults, a sc ientific co mputatio n vis ua lizatio n solutio n based onExod usII and ParaView is proposed. A comp lete p latform conta ining CAD mode ling(subd ivis io n s urface), CAE ana lys is (boundary e le me nt method nume rica lcomputation) a nd vis ua lizatio n postprocessor (ParaView scie ntific vis ua lizatio nsolutio n) is constructed. Additio na lly, in practica l e ngineering, the vis ua lizatio nproject is applied to s imulate concrete da m pouring process and provide avis ua lizatio n post-process ing so lution for its heat conductio n nume rica l ana lys is.
BEM based on s ubdivis io n s urface mode ling has the fo llo wing c haracteristics:
(1) In the BEM based on s ubdivis io n s urface modeling, subd ivis io n mes h is notonly used to represent geo metry, but a lso performed as the d iscrete model in theboundary e le me nt a na lys is. Subd ivis ion mes h provides a co mmon mode l and unifiedrepresenta tion for CAD design and CAE ana lys is, avo id ing the trans i tion o f datamode l between the two differe nt syste ms.(2) Subdivis io n mesh, d irectly used asboundary e le me nt mes h in BEM, provides an a uto matic a nd adaptive mes hgeneratio n sche me for boundary e le me nt ana lys is. Artific ia l errors, introd uced in thetraditio na l BEM d iscretization, can be minimized. In addition, the accurac y of geo metric representation and numerica l ana lys is can be contro lled by subdivis io nle ve l, according to d iffere nt des ign and a na lys is require me nts.(3) BEM based onsubdivis io n s urface mode ling inherits the ad vanta ges of both the subd ivis ion s urfacemethod and the BEM. It can represent structures o f arb itrary topolo gy withouttrimming and patc hing. Moreo ver, it req uires o nly d iscretization of the bo undary,reduc ing the dime ns io na lity o f a prob le m by one, and has high acc uracy.
In the subd ivis io n surface mode ling, this d issertatio n presents two subd ivis ionmode ling sche mes, conta ining uniform s ubdivis io n s urface modeling a nd adaptivesurface mode ling. As each mesh facet is invo lved in each s ubd ivis ion le ve l,subdivis io n mesh of uniform s ubdivis io n surface mode ling grows uniformly andexpone ntia lly. And its overa ll q ua lity improves rap id ly. Howeve r, this sc he me isprone to lead to ins uffic ient subd ivis io n and e xcess ive s ubd ivis ion. S ince only mes hfacets, whic h meet the adaptive criteria, partic ipate the current subd ivis io n process,adaptive s ubd ivis ion enab les to red uce subd ivis io n in loca l flat re gio ns and increasesubdivis io n in loca l comp le x areas. Hence, adaptive subd ivis io n sche me canrepresent geo metry mode ls with less s ubd ivis ion meshes, a nd avo id the excess ivegrowth of the mes h quantity.
In the numerica l ana lys is, BEM based on subdivis io n surface modeling isapp lied to solve3D potentia l and linear static e lastic prob le ms. Its convergence andaccuracy are investigated. Moreover, d ifferent c haracteristics of uniform subd ivis io nsurface and adaptive s ubdivis io n s urface in mode ling a nd ana lys is are s tud ied.Results demo nstrated that, as the s ubdivis io n le ve l increases, subd ivis io n mes hgrows, and its o vera ll qua lity improves; the accuracy o f the BEA for the subd ivis io nsurface mode ls become better and better. The converge nce rate and accurac y ofnumerica l a na lys is for the uniform s ubd ivis io n are higher. Howe ver, both theuniform subd ivis io n sche me a nd adaptive s ubd ivis ion sc he me can achie ve goodgeo metric models a nd high accuracy.
In the post-processing, a scie ntific comp utatio n vis ua lizatio n so lution, whic h isbased on Exod usII and ParaView, for BEA is presented. Using ExodusII, a binarydata file whic h conta ins mode l informatio n and ana lys is results is writte n. Static dataat a comp utatio n time step or d yna mic data for severa l time steps is inc luded in thatfile. With vario us vis ua lization functio na lities pro vided by ParaView, users ca nqua litative ly and q uantitative ly ana lyze the ir data. Simulta neous ly, according toactua l needs and accusto med operatio ns, severa l ParaVie w secondary deve lop me ntsinc lud ing interface s imp lificatio n, color le ge nd updating a long with time steps, enlarging operation optimizatio n, annotatio n texts auto matic addition and so on,have been co mp leted. In order to obtain effic ient processing performa nce andstability in dealing with large-sca le data as we ll as to meet hardware upgraderequire ments, a64-bit vers io n ParaVie w applicatio n is comp lied.
Fina lly, based on the concept o f multi-block dataset, a spec ia l visua liza tionpost-processing sche me is prese nted for multi-do ma in data mode ls, and then app liedto a practica l e ngineering prob le m o f co ncrete da m heat cond uction ana lys is. Withdata files conta ining specia l mark ing written by Exod usII and secondarydevelop me nts o f ParaView, the pouring process of concrete da m is s imulated.Simulta neous ly, for the specia l data set, in whic h comp lete mode l informatio n andwho le a na lys is results are conta ined, an e ffic ie nt a nimatio n sc he me is provided. Inthe animatio n sche me, only concrete da m la yers conta ining ana lys is res ults areshown in the current time step, in order to factua lly re flect the temperaturedistrib utio n of concrete dam in its the pouring and cooling process. Add itiona lly, thissche me is suited to the vis ua lizatio n post-processing for other ana lo gous multip ledoma in mode ls with time steps.
基于细分曲面造型的边界元法具有以下特点：（1）细分网格既用于表达几何模型，又作为边界元法的离散分析网格，为CAD设计与CAE分析提供了一个一般的模型和统一的表示，避免了数据模型在不同系统间的转换。（2）由于细分网格为边界元分析提供了一个自动的和自适应的网格划分方案，该方法避免了传统边界元法模型离散引入的人为误差，同时可以通过细分层次控制模型表达和数值计算的精度，以满足不同的设计与分析要求。（3）基于细分曲面造型的边界元法，在几何设计中，具有细分曲面造型的不受几何拓扑限制可以构建整体光滑的任意复杂模型的特点，在数值分析中，又继承了边界元法只需边界离散、降维以及高精度的优点。
在细分曲面建模中，本文提供了均匀细分曲面建模和自适应细分曲面建模两种建模方案。由于在每一次细分过程中每一个网格面片都参与细分，均匀细分曲面建模的细分网格均匀且成倍增长，其整体质量提高较快。但是，均匀细分曲面建模容易引起细分不足和细分过度。由于在每一次迭代细分中网格面片根据自适应准则决定是否参与细分过程，自适应细分曲面建模能够在局部平坦区域减少细分次数，在局部复杂区域增加细分次数。因此，自适应细分曲面建模可以用相对较少的细分网格模拟几何模型，同时避免了细分网格过度生长。
在数值分析中，本文将基于细分曲面造型的边界元法应用于求解三维位势问题和线弹性问题，考察了该方法的收敛性、精度以及优越性，并讨论了均匀细分曲面和自适应细分曲面在建模和分析上的各自特点。从建模和分析结果来看，随着细分层次的增加，细分曲面模型的网格数量增多，其质量也不断提高；同时，针对细分曲面模型的边界元分析精度也越来越好。其中，针对均匀细分曲面建模的边界元分析的收敛性和精度都较高。两种细分建模方案都能够获得较好的几何模型和满足精度要求的分析结果。
在结果后处理中，本文基于ExodusII和ParaView提出了一个功能丰富的边界元分析可视化后处理方案。该方案借助ExodusII生成包含模型信息和分析结果的二进制数据文件。该数据文件可以储存时间不变的静态数据或者含有时间步的动态数据。该方案利用ParaView的各种可视化功能实现对边界元分析结果数据的定性和定量的分析。同时，根据实际需要和习惯操作，本文对ParaView做了一些二次开发工作，包含界面简化、颜色条随时间步更新、放大操作优化以及注释文字自动添加等。为了在处理大规模数据时获得高效的处理性能和稳定性，并满足硬件升级的需要，本文编译了64位版本的ParaView应用程序。
最后，本文基于多块数据集的概念，提出了一个针对含时间步的多域数据模型的特殊的可视化后处理方案，并将其应用到混凝土坝热传导问题分析的科学计算可视化中。通过ExodusII编写含有特殊标识的数据文件并借助ParaView的二次开发，该方案实现了在ParaView中模拟混凝土坝的浇筑过程；同时，针对包含混凝土坝完整模型信息和热传导问题分析结果的数据模型，该方案提供了一个有效的动画演示功能，使得在某一时间步中只显示当前时间步含有分析结果的混凝土坝层，以真实地反映混凝土坝浇筑过程以及浇筑完成后一定时间段里温度分布情况。该方案也适用于其他类似的含时间步的多域模型的分析结果可视化后处理。
CAD/CAE techno lo gies, re lying o n the ir powerful functio na lities in des ign a ndana lys is of product, enab ling to dramatica lly improve the qua lity o f product, shorte nthe deve lop ment cyc le a nd lower the develop me nt cost, have become strong tools forcurrent product design and deve lop me nt.Howe ver, the representatio ns of mode l intraditio na l CAD syste ms, in whic h parametric continuous model is used, and that inCAE syste ms, in which a discrete mode l is invo lved, are d iffere nt. Prob le msintroduced by data model’s transfer and transition between the two systems havearoused people’s concern. How to perform an automatic conversion of the datamode l between the two syste ms, or provide a unified model representatio n for thetwo syste ms, na me ly CAD/CAE inte gration, has beco me a hot researching iss ue inthe CAD/CAE fie ld. This dissertatio n coup ling s ubdiv is io n surface modeling andboundary e le me nt method, success fully realizes boundary e le me nt method based onsubdivis io n s urface mode ling, natura lly integrating CAD and CAE. And the n severa lnumerica l comp utations re lated to the3D potentia l and linear elast ic proble ms areperformed with the method. In order to provide a better way to eva luate thecomputation res ults, a sc ientific co mputatio n vis ua lizatio n solutio n based onExod usII and ParaView is proposed. A comp lete p latform conta ining CAD mode ling(subd ivis io n s urface), CAE ana lys is (boundary e le me nt method nume rica lcomputation) a nd vis ua lizatio n postprocessor (ParaView scie ntific vis ua lizatio nsolutio n) is constructed. Additio na lly, in practica l e ngineering, the vis ua lizatio nproject is applied to s imulate concrete da m pouring process and provide avis ua lizatio n post-process ing so lution for its heat conductio n nume rica l ana lys is.
BEM based on s ubdivis io n s urface mode ling has the fo llo wing c haracteristics:
(1) In the BEM based on s ubdivis io n s urface modeling, subd ivis io n mes h is notonly used to represent geo metry, but a lso performed as the d iscrete model in theboundary e le me nt a na lys is. Subd ivis ion mes h provides a co mmon mode l and unifiedrepresenta tion for CAD design and CAE ana lys is, avo id ing the trans i tion o f datamode l between the two differe nt syste ms.(2) Subdivis io n mesh, d irectly used asboundary e le me nt mes h in BEM, provides an a uto matic a nd adaptive mes hgeneratio n sche me for boundary e le me nt ana lys is. Artific ia l errors, introd uced in thetraditio na l BEM d iscretization, can be minimized. In addition, the accurac y of geo metric representation and numerica l ana lys is can be contro lled by subdivis io nle ve l, according to d iffere nt des ign and a na lys is require me nts.(3) BEM based onsubdivis io n s urface mode ling inherits the ad vanta ges of both the subd ivis ion s urfacemethod and the BEM. It can represent structures o f arb itrary topolo gy withouttrimming and patc hing. Moreo ver, it req uires o nly d iscretization of the bo undary,reduc ing the dime ns io na lity o f a prob le m by one, and has high acc uracy.
In the subd ivis io n surface mode ling, this d issertatio n presents two subd ivis ionmode ling sche mes, conta ining uniform s ubdivis io n s urface modeling a nd adaptivesurface mode ling. As each mesh facet is invo lved in each s ubd ivis ion le ve l,subdivis io n mesh of uniform s ubdivis io n surface mode ling grows uniformly andexpone ntia lly. And its overa ll q ua lity improves rap id ly. Howeve r, this sc he me isprone to lead to ins uffic ient subd ivis io n and e xcess ive s ubd ivis ion. S ince only mes hfacets, whic h meet the adaptive criteria, partic ipate the current subd ivis io n process,adaptive s ubd ivis ion enab les to red uce subd ivis io n in loca l flat re gio ns and increasesubdivis io n in loca l comp le x areas. Hence, adaptive subd ivis io n sche me canrepresent geo metry mode ls with less s ubd ivis ion meshes, a nd avo id the excess ivegrowth of the mes h quantity.
In the numerica l ana lys is, BEM based on subdivis io n surface modeling isapp lied to solve3D potentia l and linear static e lastic prob le ms. Its convergence andaccuracy are investigated. Moreover, d ifferent c haracteristics of uniform subd ivis io nsurface and adaptive s ubdivis io n s urface in mode ling a nd ana lys is are s tud ied.Results demo nstrated that, as the s ubdivis io n le ve l increases, subd ivis io n mes hgrows, and its o vera ll qua lity improves; the accuracy o f the BEA for the subd ivis io nsurface mode ls become better and better. The converge nce rate and accurac y ofnumerica l a na lys is for the uniform s ubd ivis io n are higher. Howe ver, both theuniform subd ivis io n sche me a nd adaptive s ubd ivis ion sc he me can achie ve goodgeo metric models a nd high accuracy.
In the post-processing, a scie ntific comp utatio n vis ua lizatio n so lution, whic h isbased on Exod usII and ParaView, for BEA is presented. Using ExodusII, a binarydata file whic h conta ins mode l informatio n and ana lys is results is writte n. Static dataat a comp utatio n time step or d yna mic data for severa l time steps is inc luded in thatfile. With vario us vis ua lization functio na lities pro vided by ParaView, users ca nqua litative ly and q uantitative ly ana lyze the ir data. Simulta neous ly, according toactua l needs and accusto med operatio ns, severa l ParaVie w secondary deve lop me ntsinc lud ing interface s imp lificatio n, color le ge nd updating a long with time steps, enlarging operation optimizatio n, annotatio n texts auto matic addition and so on,have been co mp leted. In order to obtain effic ient processing performa nce andstability in dealing with large-sca le data as we ll as to meet hardware upgraderequire ments, a64-bit vers io n ParaVie w applicatio n is comp lied.
Fina lly, based on the concept o f multi-block dataset, a spec ia l visua liza tionpost-processing sche me is prese nted for multi-do ma in data mode ls, and then app liedto a practica l e ngineering prob le m o f co ncrete da m heat cond uction ana lys is. Withdata files conta ining specia l mark ing written by Exod usII and secondarydevelop me nts o f ParaView, the pouring process of concrete da m is s imulated.Simulta neous ly, for the specia l data set, in whic h comp lete mode l informatio n andwho le a na lys is results are conta ined, an e ffic ie nt a nimatio n sc he me is provided. Inthe animatio n sche me, only concrete da m la yers conta ining ana lys is res ults areshown in the current time step, in order to factua lly re flect the temperaturedistrib utio n of concrete dam in its the pouring and cooling process. Add itiona lly, thissche me is suited to the vis ua lizatio n post-processing for other ana lo gous multip ledoma in mode ls with time steps.
引文
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