【正文】 en in Chapter 3. VISUALIZATION The result generated after solving the system equation is usually a vast volume of digital data. The results have to be visualized in such a way that it is easy to interpolate, analyse and present. The visualization is performed through a socalled postprocessor, usually packaged together with the software. Most of these processors allow the user to display 3D objects in many convenient and colourful ways onscreen. The object can be displayed in the form of wireframes, group of elements, and groups of nodes. The user can rotate, translate and zoom into and out from the objects. Field variables can be plotted on the object in the form of contours, fringes, wireframes and deformations. Usually, there are also tools available for the user to produce isosurfaces, or vector fields of variable(s). Tools to enhance the visual effects are also available, such as shading, lighting and shrinking. Animations and movies can also be produced to simulate the dynamic aspects of a problem. Outputs in the form of tables, text files and x–y plots are also routinely available. Throughout this book, worked examples with various postprocessed results are given. Ad。 IDEAS軟件在 CAE中的應(yīng)用 (文獻(xiàn)翻譯 ) 14 IDEAS軟件在 CAE中的應(yīng)用 (文獻(xiàn)翻譯 ) 15 IDEAS軟件在 CAE中的應(yīng)用 (文獻(xiàn)翻譯 ) 16 英文原文 COMPUTATIONAL MODELLING INTRODUCTION The Finite Element Method (FEM) has developed into a key, indispensable technology in the modelling and simulation of advanced engineering systems in various fields like housing, transportation, munications, and so on. In building such advanced engineering systems, engineers and designers go through a sophisticated process of modelling, simulation, visualization, analysis, designing, prototyping, testing, and lastly, fabrication. Note that much work is involved before the fabrication of the final product or system. This is to ensure the workability of the finished product, as well as for cost effectiveness. The process is illustrated as a flowchart in Figure . This process is often iterative in nature, meaning that some of the procedures are repeated based on the results obtained at a current stage, so as to achieve an optimal performance at the lowest cost for the system to be built. Therefore, techniques related to modelling and simulation in a rapid and effective way play an increasingly important role, resulting in the application of the FEM being multiplied numerous times because of this. This book deals with topics related mainly to modelling and simulation, which are underlined in Figure . Under these topics, we shall address the putational aspects, which are also underlined in Figure . The focus will be on the techniques of physical, mathematical and putational modelling, and various aspects of putational simulation. IDEAS軟件在 CAE中的應(yīng)用 (文獻(xiàn)翻譯 ) 17 A good understanding of these techniques plays an important role in building an advanced engineering system in a rapid and cost effective way. So what is the FEM? The FEM was first used to solve problems of stress analysis, and has since been applied to many other problems like thermal analysis, fluid flow analysis, piezoelectric analysis, and many others. Basically, the analyst seeks to determine the distribution of some field variable like the displacement in stress analysis, the temperature or heat flux in thermal analysis, the electrical charge in electrical analysis, and so on. The FEM is a numerical method seeking an approximated solution of the distribution of field variables in the problem domain that is difficult to obtain analytically. It is done by dividing the problem domain into several elements, as shown in Figures and . Known physical laws are then applied to each small element, each of which usually has a very simple geometry. Figure shows the finite element approximation for a onedimensional case schematically. A continuous function of an unknown field variable is approximated using piecewise linear functions in each subdomain, called an element formed by nodes. The unknowns are then the discrete values of the field variable at the nodes. Next, proper principles are followed to establish equations for the elements, after which the elements are ‘tied’ to one another. This process leads to a set of linear algebraic simultaneous equations for the entire system that can be solved easily to yield the required field variable. This book aims to bring across the various concepts, methods and principles used in the formulation of FE equations in a simple to understand manner. Worked examples and case studies using the well known mercial software package ABAQUS will be discussed, and effective techniques and procedures will be highlighted. IDEAS軟件在 CAE中的應(yīng)用 (文獻(xiàn)翻譯 ) 18 PHYSICAL PROBLEMS IN ENGINEERING There are numerous physical engineering problems in a particular system. As mentioned earlier, although the FEM was initially used for stress analysis, many other physical problems can be solved using the FEM. Mathematical models of the FEM have been formulated for the many physical phenomena in engineering systems. Common physical problems solved using the standard FEM include: ? Mechanics for solids and structures. ? Heat transfer. ? Acoustics. ? Fluid mechanics. ? Others. This book first focuses on the formulation of finite element equations for the mechanics of solids and structures, since that is what the FEM was initially designed for. FEM formulations for heat transfer problems are then described. The conceptual understanding of the methodology of the FEM is the most important, as the application of the FEM to all other physical problems utilizes similar concepts. Computer modelling using the FEM consists of the major steps discussed in the n