A numerical study on the thermal expansion coefficients of fiber
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A numerical study on the thermal expansion coefficients of fiber

A numerical study on the thermal expansion coefficients of fiber A numerical study on the thermal expansion coefficients of fiber

fbe.deu.edu.tr
from fbe.deu.edu.tr More from this publisher
06.11.2014 Views

47 radius of the interphase requires making complicated experiments on the produced samples.

CHAPTER FOUR FINITE ELEMENT METHOD 4.1 Historical Perspective The finite element method has become a powerful tool for the ong>numericalong> solution of a wide range of engineering problems such as steady, transient, linear or nonlinear problems in stress analysis, heat transfer, fluid flow, and electromagnetism. With the advantages in computer technology and computer-aided design systems, complex problems can be modeled with relative ease. Several alternative configurations can be tested on a computer before the first prototype is built. In this method of analysis, a complex region defining a continuum is reduced into simple geometric shapes called finite elements. The material properties and the governing relationships are considered over these elements and expresses in terms of unknown values at element corners. An assembly process, considering the loading and the constraints, results in a set of equations. Solution of these equations gives us the approximate behavior of the continuum. The origin of the modern finite element method may be traced back to early 1900s, when some investigators approximated and modeled elastic continua using discrete equivalent elastic bars. But basic ideas of the finite element method originated from advances in aircraft structural analysis. In 1941, Hrenikoff presented a solution of elasticity problem using the “frame network method”. Courant’s paper, which used a piecewise polynomial interpolation over triangular subregions to model torsion problems, appeared in 1943. Turner et al. derived stiffness matrices for truss, beam and other elements and presented their findings in 1956. The term finite element was first coined and used by Clough in 1960 (Chandrupatla, & Belegundu, 2002)(Moaveni, 1999). In the early 1960s, engineers used the method for approximate solution of problems in stress analysis, fluid flow, heat transfer and other areas. A book by 48

47<br />

radius <strong>of</strong> <strong>the</strong> interphase requires making complicated experiments <strong>on</strong> <strong>the</strong> produced<br />

samples.

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