【正文】 AS軟件在 CAE中的應(yīng)用 (文獻(xiàn)翻譯 ) 13 五種可能的單元畸變形式及其粗略限制如下： (1) 長寬比畸形（單元的伸長度）（圖 ） (2) 單元角度畸形（圖 ），單元兩邊夾角接近于 0176。（歪斜或斜錐度） (3) 單元曲率畸形（圖 ），當(dāng)把節(jié)點(diǎn)和幾何點(diǎn)匹配時單元的直邊扭曲成曲邊 (4) 凹入形單元的體積畸形，如第六章所討論的，在計算單元剛度矩陣時，為了將物理坐標(biāo)系中不規(guī)則形狀的單元轉(zhuǎn)化成無量綱自然坐標(biāo)系中規(guī)則形狀的單元，使用了映射方法。在自然坐標(biāo)系中對陰影區(qū)域的單元體積積分將得到負(fù)值。 (5) 在具有中間節(jié)點(diǎn)的高階單元中中間節(jié)點(diǎn)的畸變，中 間節(jié)點(diǎn)應(yīng)該盡可能的靠近單元邊的中點(diǎn)，中間節(jié)點(diǎn)偏離單元邊中點(diǎn)的極限長度是單元邊長的 1/4，如圖 所示。 在很多有限元軟件包中前處理器為生成網(wǎng)格提供分析單元扭曲率的工具，使用者所需要做的是在生成網(wǎng)格后及在分析之前調(diào)用這些工具，這些工具為分析者的測試報告所產(chǎn)生的扭曲率。 and solids can be created by connecting, rotating or translating the existing surfaces. Points, lines and curves, surfaces and solids can be translated, rotated or reflected to form new ones. Graphic interfaces are often used to help in the creation and manipulation of the geometrical objects. There are numerous Computer Aided Design (CAD) software packages used for engineering design which can produce files containing the geometry of the designed engineering system. These files can usually be read in by modelling software packages, which can significantly save time when creating the geometry of the models. However, in many cases, plex objects read directly from a CAD file may need to be modified and simplified before performing meshing or discretization. It may be worth mentioning that there are CAD packages which incorporate modelling and simulation packages, and these are useful for the rapid prototyping of new products. Knowledge, experience and engineering judgment are very important in modelling the geometry of a system. In many cases, finely detailed geometrical features play only an aesthetic role, and have negligible effects on the performance of the engineering system. These features can be deleted, ignored or simplified, though this may not be true in some cases, where a fine geometrical change can give rise to a significant difference in the simulation results. IDEAS軟件在 CAE中的應(yīng)用 (文獻(xiàn)翻譯 ) 21 An example of having sufficient knowledge and engineering judgment is in the simplification required by the mathematical modelling. For example, a plate has three dimensions geometrically. The plate in the plate theory of mechanics is represented mathematically only in two dimensions (the reason for this will be elaborated in Chapter 2). Therefore, the geometry of a ‘mechanics’ plate is a twodimensional flat surface. Plate elements will be used in meshing these surfaces. A similar situation can be found in shells. A physical beam has also three dimensions. The beam in the beam theory of mechanics is represented mathematically only in one dimension, therefore the geometry of a ‘mechanics’ beam is a onedimensional straight line. Beam elements have to be used to mesh the lines in models. This is also true for truss structures. Meshing Meshing is performed to discretize the geometry created into small pieces called elements or cells. Why do we discretize? The rational behind this can be explained in a very straightforward and logical manner. We can expect the solution for an engineering problem to be very plex, and varies in a way that is very unpredictable using functions across the whole domain of the problem. If the problem domain can be divided (meshed) into small elements or cells using a set of grids or nodes, the solution within an element can be approximated very easily using simple functions such as polynomials. The solutions for all of the elements thus form the solution for the whole problem domain. How does it work? Proper theories are needed for discretizing the governing differential equations based on the discretized domains. The theories used are different from problem to problem, and will be covered in detail later in this book for various types of problems. But before that, we need to generate a mesh for the problem domain. Mesh generation is a very important task of the preprocess. It can be a very time consuming task to the analyst, and usually an experienced analyst will produce a more credible mesh for a plex problem. The domain has to be meshed properly into elements of specific shapes such as triangles and quadrilaterals. Information, such as element connectivity, must be created during the meshing for use later in the formation of the FEM equations. It is ideal to have an entirely automated mesh generator, but unfortunately this is currently not available in the market. A semiautomatic preprocessor is available for most mercial application software packages. There are also packages designed mainly for meshing. Such packages can generate files of a mesh, which can be read by other modelling and simulation packages. Triangulation is the most flexible and wellestablished way in which to create meshes IDEAS軟件在 CAE中的應(yīng)用 (文獻(xiàn)翻譯 ) 22 with triangular elements. It can be made almost fully automated for twodimensional (2D) planes, and even threedimensional (3D) spaces. Therefore, it is monly available in most of the preprocessors. The additional advantage of using triangles is the flexibility of modelling plex geometry and its boundaries. The disadvantage is that the accuracy of the simulation results based on triangular elements is often lower than that obtained using quadrilateral elements. Quadrilateral element meshes, however, are more difficulty to generate in an automated manner. Some examples of meshes are given in Figures –. Property of Material or Medium Many engineering systems consist of more than one material. Property of materials can be defined either for a group of elements or each individual element, if needed. For different phenomena to be simulated, different sets of material properties are required. For example, Young’s modulus and shear modulus are required for the stress analysis of solids and structures, whereas the thermal conductivity coefficient will be required for a thermal analysis. Inputting of a material’s properties into a preprocessor is usually straightforwar