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Unformatted text preview: 117 Introduction to the Finite Element Method 8.1 INTRODUCTION In thermomechanical members and structures, finiteelement analysis (FEA) is typi cally invoked to compute displacement and temperature fields from known applied loads and heat fluxes. FEA has emerged in recent years as an essential resource for mechanical and structural designers. Its use is often mandated by standards such as the ASME Pressure Vessel Code, by insurance requirements, and even by law. Its acceptance has benefited from rapid progress in related computer hardware and soft ware, especially computeraided design (CAD) systems. Today, a number of highly developed, userfriendly finiteelement codes are available commercially. The purpose of this chapter is to introduce finiteelement theory and practice. The next three chapters focus on linear elasticity and thermal response, both static and dynamic, of basic structural members. After that, nonlinear thermomechanical response is considered. In FEA practice, a design file developed using CAD is often “imported” into finite element codes, from which point little or no additional effort is required to develop the finiteelement model and perform sophisticated thermomechanical analysis and simulation. CAD integrated with an analysis tool, such as FEA, is an example of computeraided engineering (CAE). CAE is a powerful resource with the potential of identifying design problems much more efficiently and rapidly than by “trial and error.” A major FEM application is the determination of stresses and temperatures in a component or member in locations where failure is thought most likely. If the stresses or temperatures exceed allowable or safe values, the product can be rede signed and then reanalyzed. Analysis can be diagnostic, supporting interpretation of productfailure data. Analysis also can be used to assess performance, for example, by determining whether the designstiffness coefficient for a rubber spring is attained. 8.2 OVERVIEW OF THE FINITEELEMENT METHOD Consider a thermoelastic body with force and heat applied to its exterior boundary. The finiteelement method serves to determine the displacement vector u ( X , t ) and the temperature T( X , t ) as functions of the undeformed position X and time t . The process of creating a finiteelement model to support the design of a mechanical system can be viewed as having (at least) eight steps:...
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 Spring '11
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 Finite Element Method, Finite Element Analysis, analyst, CRC Press LLC, CRC CRC Press, CRC CRC Press LLC, ﬁniteelement model

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