TITLE:
Finite Elements Approaches in the Solution of Field Functions in Multidimensional Space: A Case of Boundary Value Problems
AUTHORS:
Chukwutoo Christopher Ihueze, Okafor Emeka Christian, Edelugo Sylvester Onyemaechi
KEYWORDS:
finite element, continuum, functional of function, extremum, boundary value
JOURNAL NAME:
Journal of Minerals and Materials Characterization and Engineering,
Vol.9 No.10,
October
20,
2010
ABSTRACT: An idealized two dimensional continuum region of GRP composite was used to develop an
efficient method for solving continuum problems formulated for space domains. The continuum
problem is solved by minimization of a functional formulated through a finite element procedure
employing triangular elements and assumption of linear approximation polynomial. The
assemblage of elements functional derivatives system of equations through FEM assembly
procedure made possible the definition of a unique and parametrically defined model from which
the solution of continuum configuration with an arbitrary number of scales is solved. The finite
element method(FEM )developed is recommended to be applied in the evaluation of the function
of functions in irregular shaped continuum whose boundary conditions are specified such as in
the evaluation of displacement in structures and solid mechanics problems, evaluation of
temperature distribution in heat conduction problems, evaluation of displacement potential in
acoustic fluids evaluation of pressure in potential flows, evaluation of velocity in general flows,
evaluation of electric potential in electrostatics, evaluation of magnetic potential in
magnetostatics and in the solution of time dependent field problems. A unified computational
model with standard error of 0.15 and correlation coefficient of 0.72 was developed to aid
analysis and easy prediction of regional function with which the continuum function was
successfully modeled and optimized through gradient search and Lagrange multipliers
approach. Above all the optimization schemes of gradient search and Lagrangian multiplier
confirmed local minimum of function as 0.006-0.00847 to confirm the predictions of FEM and
constraint conditions.