TITLE:
Finite Elements in the Solution of Continuum Field Problems
AUTHORS:
Chukwutoo Christopher Ihueze
KEYWORDS:
Calculus of variation, functional, finite element, continuum, field problems, boundaryconditions.
JOURNAL NAME:
Journal of Minerals and Materials Characterization and Engineering,
Vol.9 No.5,
May
20,
2010
ABSTRACT: A finite element functional solution procedure was presented employing variational calculus.
The Functionals of field continuum were developed on adoption of Euler minimum integral
theorem and finite element procedures on Laplace model. The elements functionals minimization
resulted to series of partial differential equations describing the variation of the function of
interest at various discrete nodal points. The assembly of the partial differential equations gave
a unifying algebraic system of equation was solved for the unique solutions of the function. To
simulate the finite element model, boundary conditions of temperature field was assumed. The
solution and post processing of FEM of this study showed that once the stiffness matrix of a
continuum is established and the boundary conditions specified the continuum is solved
uniquely. Regression method was used to establish the error associated with FEM results and to
establish a simple prediction model for environmental temperatures. The procedure of this study
presented the basis for insulation design for solid, hollow or shell pipes in fluid transport design
in oil and gas transport system. The finite element method evaluated the temperature distribution
of the region to serve as a guide in quantifying quantity of heat to the environment from the
transit fluid. The error of FEM prediction was estimated at 0.006 and the coefficient of
determination for goodness of regression fit is estimated as 0.99999. This study also presents an
approximate procedure for processing polar systems as rectangular systems by using the
circumference of the circular section as one dimensional independent variable and the difference
between the inner and outer radius (thickness) as the second independent variable.