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1、名师精编优秀教案Teaching Plan -10: Finite element analysis Learning Outcomes On the completion of this unit you will be able to correctly grasp the following knowledge as follows: ?The concept of finite element analysis. ?The theory of finite element analysis. ?The steps of finite element software: preproce
2、ssor, post processor. Assessment Competency will be assessed by grasping the knowledge throughout this section. Resources Theory (Period: 2 classes in classroom) CAD/CAM Principles and Applications?Chapter 8: Finite element analysis Key Point Finite element analysis, preprocessor, post processor 名师精
3、编优秀教案Finite element analysis Conventional analytical methods for solving stresses and strains become very complex and almost impossible when the part geometry is intricate. Finite element modeling becomes a very convenient means to carry out the analysis. The finite element analysis is the right too
4、l that be applied to a range of engineering problems. The finite element modeling process allows for discretizing the intricate geometries into small fundamental volumes called finite elements. It is possible to write the governing equations and material properties for these elements. These equation
5、s are assembled by taking proper care of the constraints and loading, which results in a set of equations. These equations when be solved will give the results that describe the behavior of the original complex geometry which being analysed. Application of FEM is not limited to mechanical system alo
6、ne but to a a range of engineering problem: Stress analysis Dynamic analysis Deformation studies Fluid analysis Heat flow analysis Seepage analysis Magnetic flux studies Acoustic analysis 名师精编优秀教案So many commercial software systems are available for this application. Generally a very powerful comput
7、er is needed to solve a complex problem. With the help of FEA, it is possible to try a number of alternative designs before actually going for prototype manufacturing. Finite element modeling In order to understand the concept of FEM, the example of a simple one dimensional problem is given, and the
8、 same concepts can be extended to two or three dimensional problem similarly. A taper beam is considered with an unidirectional force acting in the direction of X axis. There are some concepts should be used during the solving process: displacement u, stress , strain , load F, elasticity E. =E The t
9、otal force T acting on the geometry consists of three components: the body force f, the traction force T and the point force P. the body force acts on every point of the body, e.g. the body weight. The traction force acts on the surface such as friction. Because the uniform cross-section of the beam
10、 make it difficult to discretize, it should be converted into a stepped shaft of different diameters and each of them is uniform in size. Each of these sections is called as finite elements and is numbered with different number. The nodes are used as the points of application of the point forces. Si
11、nce it is a one dimensional problem, each of the nodes only can have a displacement in one direction and has only one degree of freedom. Q represents the displacement and F represents the force. Q=QQ1,Q2,Q3,Q4, F=F1,F2,F3,F4. for = F/A =E ?=? l/l then F=A?E?l/l = (A ?E /l)?l stiffness K= E?A/l= E ?(
12、A /l) 名师精编优秀教案matrix K =E?A/l (A: cross-sectional area of each element, l: length of each element) F= (A ?E /l)?l matrix F=K?Q ( ) (Q: displacement of each element, F: force of each element) With the necessary boundary conditions and loading condition, the equation ( ) will be found the solution com
13、posite problem. It is possible to formulate similar methods for two and three dimensional as well as other type of problems such as heat transfer and fluid flow. FEM software The total process of solving a particular problem using the finite element analysis method consists of the steps as follows:
14、Convert the geometry into discretized elements and calculate various properties for each element such as geometry, material properties, constraints and loading. Assemble the global equations from the formulation specified in the previous stage and then solve them to obtain the results. Interpret the
15、 results in specific form depending upon the type of problem solved. Carrying out all above processes manually is a quite tedious task. Commercial comprehensive finite element analysis software can convert it into an easy job. 名师精编优秀教案Three stage approaches are executed in turn. Preprocessor The pre
16、processor of a FEM software allows for the following functions: Create the geometry Generate the finite element mesh Calculate the nodes and elemental properties Allow for the boundary conditions (support conditions and loading conditions) Allow for the properties to be specified. The modeling application provided in the FEM software is usually cumbersome compared to the ones in CAD systems. It is necessary to direct linkage in which the geometric model from CAD system can be used as the preproc
