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Home  >  Volume 36 (no2)

PIECEWISE CONTINUOUS TRIAL FUNCTIONS IN THE FINITE ELEMENT SOLUTION OF ONE DIMENSIONAL FIELD PROBLEM USING RAYLEIGH-RITZ METHOD by Emenogu N.Gand OruhB.I (pages101-110)
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Abstract
One the flaws of the traditional variational methods is that the trial functions are arbitrarily chosen and the weighted integrals are applied globally over the entire region of interest. Consequently, for complex regions, the boundary conditions, as well as the physics of the problem, are not satisfied. 
In this paper, we present the finite element method, it is an element-wise application of the Rayleigh-Ritz method. its essence is the minimization of an appropriate functional, which is developed on adoption of the Euler –Lagrange’s equation. The discretization of the region of interest is done using linear elements permitting a close approximation at discrete nodes. The element functional minimization results in a series of algebraic equations which on assembly using the direct stiffness method yields the system equation. The required nodal degree of freedom is obtained by imposing the boundary conditions
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