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Unformatted text preview: Thus, like
nite di erence methods, the nite element process has discretized the partial di erential equation but, unlike nite di erence methods, the approximate solution is known
throughout the domain as a pieceise polynomial function and not just at a set of points.
Logan 10] attributes the discovery of the nite element method to Hrennikof 8] and
McHenry 11] who decomposed a two-dimensional problem domain into an assembly of
one-dimensional bars and beams. In a paper that was not recognized for several years,
Courant 6] used a variational formulation to describe a partial di erential equation with
a piecewise linear polynomial approximation of the solution relative to a decomposition of
the problem domain into triangular elements to solve equilibrium and vibration problems.
This is essentially the modern nite element method and represents the rst application
where the elements were pieces of a continuum rather than structural members.
Turner et al. 13] wrote a seminal paper on the subject that is widely regarded
1 2 Introduction as the beginning of the nite element era. Th...
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This document was uploaded on 03/16/2014 for the course CSCI 6860 at Rensselaer Polytechnic Institute.
- Spring '14