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PART 4 Analysis Tools

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Finite-Element Analysis Chapter Outline 19–1 The Finite-Element Method 935 19–2 Element Geometries 937 19–3 The Finite-Element Solution Process 939 19–4 Mesh Generation 942 19–5 Load Application 944 19–6 Boundary Conditions 945 19–7 Modeling Techniques 946 19–8 Thermal Stresses 949 19–9 Critical Buckling Load 949 19–10 Vibration Analysis 951 19–11 Summary 952 19 933
934 Mechanical Engineering Design Mechanical components in the form of simple bars, beams, etc., can be analyzed quite easily by basic methods of mechanics that provide closed-form solutions. Actual com- ponents, however, are rarely so simple, and the designer is forced to less effective approximations of closed-form solutions, experimentation, or numerical methods. There are a great many numerical techniques used in engineering applications for which the digital computer is very useful. In mechanical design, where computer-aided design (CAD) software is heavily employed, the analysis method that integrates well with CAD is fnite-element analysis (FEA). The mathematical theory and applications of the method are vast. There is also a number of commercial FEA software packages that are available, such as ANSYS, NASTRAN, Algor, etc. The purpose of this chapter is only to expose the reader to some of the fundamen- tal aspects of FEA, and therefore the coverage is extremely introductory in nature. For further detail, the reader is urged to consult the many references cited at the end of this chapter. Figure 19–1 shows a ±nite-element model of a crankshaft that was developed to study the effects of dynamic elastohydrodynamic lubrication on bearing and struc- tural performance. 1 There are a multitude of FEA applications such as static and dynamic, linear and nonlinear, stress and de²ection analysis; free and forced vibrations; heat transfer (which can be combined with stress and de²ection analysis to provide thermally induced stresses and de²ections); elastic instability (buckling); acoustics; electrostatics and 1 S. Boedo, “Elastohydrodynamic Lubrication of Conformal Bearing Systems,” Proceedings oF 2002 ANSYS Users ConFerence, Pittsburgh, PA, April 22 24, 2002. ( a ) X Z Y ( b ) X Z Y Figure 19–1 Model of a crankshaft using ANSYS Fnite-element software. ( a ) Meshed model ( b ); stress contours. Courtesy of S. Boedo (see footnote 1).

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Finite-Element Analysis 935 magnetics (which can be combined with heat transfer); Fuid dynamics; piping analysis; and multiphysics. ±or purposes of this chapter, we will limit ourselves to basic mechan- ics analyses. An actual mechanical component is a continuous elastic structure (continuum). ±EA divides (discretizes) the structure into small but ²nite, well-de²ned, elastic sub- structures (elements). By using polynomial functions, together with matrix operations, the continuous elastic behavior of each element is developed in terms of the element’s material and geometric properties. Loads can be applied within the element (gravity, dynamic, thermal, etc.), on the surface of the element, or at the nodes of the element. The
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Ch19 - bud21932_ch19_932-956 5:14 PM Page 932 CONFIRMING...

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