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1、Developing a Finite Element Analysis AgentPadmanabh DabkeIntroductionRecently there is a trend towards using it in the early stages of design. A designer may use FEA just to validate the structural integrity of a design or she may use it for structural optimization along with the parametrized design
2、 techniques.This paper examines the requirements of a structural analysis agent and proposes an architecture to facilitate FEA in a concurrent design environment. The next section briefly describes how FEA is used in a typical industrial set up.Section 3 presents a survey of existing FE tools. Secti
3、on 4 discusses some issues related to the development of an FEA agent. Section 5 proposes an architecture for the FEA agent that addresses the issues described in Section 4 and finally Section 6 presents the concluding remarks.Steps in Finite Element AnalysisThe process of FEA starts with identifica
4、tion of the region of interest and the formulation of the physical problem。1. The region of interest might be an assembly, a component or a portion of a component (or an assembly). The interaction of the rest of the assembly and the environmental conditions with the region of interest is captured in
5、 two ways. One way to represent this interaction is to idealize them as loads and displacement constraints on the region of interest. For example a spot weld fixing a component to a bigger structure will result in a constraining all the degrees of freedom at that point. The other commonly used metho
6、d is to use spring and/or gap elements. Analysts often draw a Free Body Diagram of the region of interest to clarify its interaction with the rest of the assembly and to gain more insight into its structural behavior.Required components and assemblies are then retrieved from the Solid Modeling syste
7、m into the finite element package.In recent years a number of commercial systems have started offering both: FEA and Solid Modeling capabilities.In this case, the data exchange may occur between two modules of the same package.The original design geometry is sometimes too complicated for the purpose
8、 of analysis. The analyst may choose to simplify it so that it is easier to mesh and incurs less computational cost.This task of simplifying the design geometry is referred to as Global Idealization.Global Idealization may involve deletion/modification of some of the geometric features. The analyst
9、may choose to take advantage of the symmetry and analyze only a portion of the model. If the problem is axi-symmetric, she may choose to reduce a 3D problem to 2D by analyzing the radial cross-section.If the analyst intends to make significant modifications in the geometry, she may choose to import
10、the geometry in a drafting package first and then read the modified geometry in the analysis package.Global Idealization is often followed by Element Idealization. Element Idealization consists of characterizing the finite element dimensionality of the globally idealized object. The original 3D geom
11、etry may be transformed into a collection of 1D, 2D and 3D entities depending on the characterization of various geometric parts as beams, plates/shells, and solid elements respectively. Element Idealization decisions are based on two factors: shape of the object and the boundary conditions.The next
12、 step in the modeling process is selection of type of elements and their material properties. Based on this decision, the user discretizes the idealized geometry into finite elements. This step is commonly referred to as Mesh Generation.Traditionally the loads and boundary conditions are applied to
13、the nodes and the element boundaries. In the proposed system they are applied to the geometry. Finally, he user has to select the type of analysis (static, modal,etc.) and the solution method and the finite element model is ready for analysis. The raw answers computed by the finite element solver ha
14、ve to be processed further. This includes calculation of derived quantities (such as stress and strain values), computing error estimates, creating创建 graphical displays showing deformed shapes , stress contour plots, etc. All these tasks are collectively referred to as post-processing. Based on the
15、post-processing results the user may modify the model at any stage of idealization (including the original design itself)and start the loop once again.An overview of the analysis process is shown in Figure 1.Figure 1 Steps in Finite Element AnalysisDevelopment of Finite Element ToolsDue to the obvio
16、us pay-offs associated with speeding up of the analysis process, there is almost an explosion of both research and commercial systems supporting FEA. The development of FEA tools has followed a path very similar to the development of Design Automation tools. The early software supporting FEA was pri
17、marily meant to automate tasks in the detailed analysis stage, namely Mesh Generation and Post-Processing. A survey of earlier work in automatic mesh generation methods can be found in references 2 and 3. Earlier mesh generator would simply discretize the analysis geometry into a bunch of elements w
18、ith almost no regard for the solution accuracy implied by the mesh.Adaptive meshing methods improved the reliability of mesh generation process.These methods use one of the several error estimation techniques 4,5 to estimate the discretization error for a trial mesh and improve the mesh quality eith
19、er by refining the mesh in certain areas (called h-refinement methods) 6, or increasing the order of element interpolation (called p-enrichment methods) 7 or a combination of both (called h-p methods) 7.The raw FE data is usually too difficult to interpret due to its large volume.Post-Processing too
20、ls aid visualization and facilitate easier interpretation of the data. Post-processing features provided by todays commercial packages include display of deformed shapes; calculation of useful engineering quantities such as Von Mises Stress, principal stresses, etc.; contour and shaded plotsshowing
21、distributionf numerical parameters over the analysis domain.The emergence of Expert Systems technology saw the development of a new generation of FEA tools. The researchers became interested in applying Expert Systems techniques to automate early stages of the finite element modeling process. These
22、systems try to capture the experiential and often subjective knowledge used by expert analysts and act as “modeling assistant” to a novice user. Fenves 8 suggested a framework for developing a knowledgebased system to assist FE analysis. Bennett et al. 9 developed a rule based system called SACON to
23、 suggest an analysis strategy to a novice user of MARC (a commercial FE code). Todays commercial systems have incorporated most of the research in Mesh Generation and Post Processing. Also,the trend is towards developing integrated Computer Aided Engineering (CAE) packages which offer a range of fac
24、ilities (solid modeling, drafting, analysis, etc.). This has greatly helped to ease the transition from a Solid Model of a design to its finite element model.Issues in Developing a Finite Element Analysis AgentAn FEA agent must surely support all the FE activities described in Section 2. But we pref
25、er to use a commercial package for Mesh Generation and Post-Processing because todays FE packages are fairly sophisticated in these areas and it seems pointless to duplicate this work. On the other hand, commercial codes are not suitable for合 the Model Preparation tasks in any specific domain and th
26、e proposed FEA agent is intended to fill this gap. As a result, the following discussion primarily focuses on the model preparation tasks in FEA. 1Exchanging Finite Element Modeling InformationThe FEA agent should facilitate exchange of an FE modeling problem at different levels of descriptions. A v
27、ery high level description would consist of the sketch of the part to be analyzed with a verbal description of the operating conditions and the analysis requirements. Another form of description may consist of a B-Rep of the part with a descriptionof the boundary conditions with reference to the B-r
28、ep entities of the part. An ontology for describing assemblies, components, boundary conditions, etc. will have to developed to provide a formal language for the data exchange.The agent should have the capability to read and write IGES and STEP files. Both the standards have the capability of handli
29、ng Constructive Solid Geometry (CSG) and Boundary Representation (B-Rep) formats. STEP is claimed to have the capability of exchanging FE entitiesas well. 2Representation of a Finite Element ModelA representation of an FE modeling problem would have to include the following information:1. Geometry2.
30、 Boundary Conditions3. Material Properties4. Geometric Properties5. Type of Analysis6. Accuracy DesiredThe geometry should be maintained at different levels of FE idealizations. This would require the use of a non-manifold geometric modeler since FE models are often composed of elements of different
31、 dimensionality (e.g. a model may consist of plates and beams). The geometric description also needs to be maintained in the b-rep form since all of the mesh generators require it in this form.Traditionally, the boundary conditions are applied to model after it has been meshed even though the analys
32、t knows what they are in the beginning and uses this knowledge in creating an appropriate FE mesh for the object. The Design Representation System (DRS) that we have developed allows us to prescribe boundary conditions along with the geometry and attachthem to the b-rep of the FE model.In practice,
33、the FE problem seldom involves a single mechanical component, therefore it is desirable to maintain a symbolic representation of the assemblies and connections. The representation of connections can also be used to automatically derive the boundary conditions due to the interaction of mating compone
34、nts. 3Geometry EditingAn analyst often wants to delete/modify certain geometric features of the model to simplify analysis procedure. This has been referred to as Global Idealization.Therefore the FE agent should provide feature-editing facility and quickly compute the b-rep of the resulting object.
35、 Certain higher level commands that convert one FE model into another should be provided (E.g. building a 2-D model by extracting the radial cross section of an axi-symmetric model).Geometric properties such as feature volumes, centroids, etc. should be automatically calculated. Direct addition/ del
36、etion of FE entities such as beams, plates, etc. should also be possible for a quick what-if analysis in structural design. 4 Interface with Commercial Finite Element PackagesThe proposed agent would use a commercial code for Mesh Generation, Analysis and Post-Processing. Therefore, the interface wi
37、th this package may not be limited to just IGES or STEP files. The FEA agent must incorporate the knowledge needed for the effective use of the chosen FE package. This knowledge can then be used to write “program files” that will direct the above mentionedactivities in the FE code. 5Knowledge-based
38、AssistanceThe FE modeling decisions are primarily based on the two factors: shape of the components being analyzed and the boundary conditions. Since the geometry is maintained in terms of its boundary representation, the b-rep informationcan be used to infer about the shape attributes of the compon
39、ent. DRS also allows the user to attach boundary conditions to the b-rep entities (vertex, edge, face) in the geometric model, therefore the system has an integrated representation of the geometry and the boundary conditions. At the very least this information can be used to intelligently limit the
40、options given to the user. For example, if the geometry is not axi-symmetric, the option for axi-symmetric 2- D elements may not be shown to the user. Going a step further a knowledge-base can be developed which makes use of the geometric and boundary conditions representation and the available doma
41、in specific information. This knowledge-base can be used to provide expert advice to a novice user.Architecture of the Proposed FEA AgentA schematic of the proposed architecture is shown in Figure 2. The Central Representation Module will be implemented in CLIPS. It will maintain all the aspects of
42、a FE model listed in Section 4.2. The Geometry Kernel will be provided by the non-manifold geometric modeler called NOODLES. The graphics display programs will be written using TK/TCL interface builder. I-DEAS will be used for Mesh Generation, Analysis and Post-Processing. The Knowledge-based Module
43、 will be written using CLIPS rules and facts.The Interface Module will be able to read and write IGES and STEP files, write I-DEAS program files and use EITs software for agent communication.Figure 2 Schematic Diagram of the Proposed FEA Agent (Arrows indicate information flow.)Concluding RemarksThe
44、 implementation of the proposed agent will be CLIPS/C/TK/TCL based.Some of the features described in the earlier section have been previously implemented in Lisp. These are as follows: Data structures for attaching boundary conditions to b-rep entities Simple shape recognition and b-rep updating Cal
45、culation of inertial properties such as volumes, centroids, moments of inertia, etc. from the solid b-reps Creation of I-DEAS program files for modal analysis of beam models有限元分析软件的发展介绍最近有一种将有限元分析用在设计早期的趋势。设计人员可以使用有限元分析软件来设计和验证结构的完整性或者优化参数设计技术。本文讨论了对结构分析媒介的要求，并且提供了一个在给定的设计环境下的有限单元分析的优化体系结构。下一节将简要介绍有
46、限单元是怎样被用在典型工业的生产上的。第3节介绍了现有的有限元工具的调查。第4节讨论了一些涉及到有限元分析的发展问题。第4节发现的详细问题是有限元分析的起因，笔者在第5节对其提出了一个结构体系并在在第6节做出了总结。有限元分析的发展有限元是伴随确认重要部位和对物理学问题的构想进行的。1 重要的区域可能是一个配件、元件或者是元件的一部分。一个静止配件的配合和重要部件的环境条件是捕获的两种途径。-一种代表配合的方法是用理想化的负载和位移做为重要部位的系统规定参数。例如，把一个元件用焊接的方法固定在一个更大的部件上将导致这个点上所有的自由度受到约束。另一种常用的方法是使用弹簧或者间隙元素。-分析师们
47、通常绘制一个重要部分的自由体受力图来阐述它与静止元件的配合并以此获得更多的有关结构性能的数据。然后从有限元程序的实体造型中检索所需的部件和组件。近年来，一些商业系统开始提供两种软件：实体建模和有限元分析。在这种情况下，数据交换可能会出现两个不相同的模块。以前用于几何分析的设计有时过于复杂。分析师们将其简化后减少了设计的成本。这种简化的几何设计被称为整体理想化。整体理想化可能涉及几何特征的一些修改。分析师可能会选择利用对称度和分析模型的一部分。-如果是轴对称的，他们会将三维问题减少为二维问题来分析。如果分析师打算做一个几何限制，首先他们可以选择从草稿软件包里导入一个几何软件包，然后再从软件分析包
48、里进行修改。理想化的特征元素是由整体理想化对象的有限元延伸产生的。原来的三维几何结构可转化为一维的集合，二维和三维实体取决于对各种不同几何部件的描述比如：梁，壳板材，固体元素。理想化特征元素的确定是基于两个因素：形状对象和边界条件。下一步的建模过程，是选择元素的类型和他们的物理属性。根据这些，用户就可以用有限元分析离散化那些理想化的几何形状。这一步通常称为Mesh Generation。网格时代-传统上，负载和边界的条件，被用于节点和元素的界限。-在所推荐的系统里他们被用于几何图形上。最后，他们选择了分析的种类和解决办法并为有限元模型做好了分析的准备。未经处理的原始答案必须用有限元做进一步的处理。类似于派生数量的计算（例如应力和应变），计算机运算的错误估计，创建图形显示的外形形变，应力、外形、平面图等等。所有这些任务都统称为后处理。基于后处理结果，用户可以修改的任何理想化阶段（包括原设计本身的模型），并进入下一个阶段。分析过程的一个概述如图1所示。图1.有限元分析步骤有限元工具的发展由于分析过程有显著地提高，所以不管是科研领域或商业领域有限元分析软件的诞生都是近乎于爆炸式的创新。有限元分析工具的发展遵循着与自动化设计工具发展类似的路径。早期的软件也支持有限元分析，其主要目的是为了在详细分析阶段的进行自动化任务，即
