JMMCE  Vol.9 No.5 , May 2010
Finite Elements in the Solution of Continuum Field Problems
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.

Cite this paper
C. Ihueze, "Finite Elements in the Solution of Continuum Field Problems," Journal of Minerals and Materials Characterization and Engineering, Vol. 9 No. 5, 2010, pp. 427-454. doi: 10.4236/jmmce.2010.95030.
References
[1]   Sundaram,V., Balasubramanian, R., Lakshminarayanan,K.A.,(2003) Engineering Mathematics ,Vol.3,VIKAS Publishing House LTD, New Delhi, p173.

[2]   Holman, J. P, (1981) Heat and mass Transfer, McGraw-Hill Inc.Book Company, p72.

[3]   Cook,R.D., Malkus, D.S. and Plesha,M.E.(1989) Concepts and Applications of Finite Element Analysis, 3 rd ed, John Wiley & Sons, New York in Astley, R.J., (1992), Finite Elements in Solids and Structures, Chapman and Hall Publishers, UK, p77.

[4]   Bathe, K.J., and Wilson, E.L. (1976) Numerical Methods in Finite Element Analysis, Prentice Hall, Englewood Cliffs.

[5]   Hughes,T.J.R. (1987) The Finite Element Method : Linear Static and Dynamic Finite Element Analysis, Prentice hall, Englewood Cliffs, .

[6]   Enetanya A. N. and Ihueze C. C., (2009) Finite Difference Approach for Optimum Compressive Strengths of GRP Composites, NSE TECHNICAL TRANSACTIONS,July.September, 2009,Vol.44 No3,p 40-55

[7]   Astley, R.J., (1992), Finite Elements in Solids and Structures, Chapman and Hall Publishers,UK, p77.

[8]   Zienkiewicz,O.C., and Cheung, Y.K,(1967) The Finite Element in Structural and Continuum Mechanics, McGraw-Hill publishing Coy Ltd, London, p148

[9]   Amazigo, J.C and Rubenfield, L.A (1980) Advanced Calculus and its application to the Engineering and Physical Sciences, John Wiley and sons Publishing, New York, p130.

[10]   Berg P. N (1962 ) Calculus of variations, in Handbook of Engineering Mechanics, chapter 16, ed. W. Flugge, Graw-Hill.

[11]   Ihueze, C. C,Umenwaliri,S.Nand Dara,J.E (2009) Finite Element Approach to Solution of Multidimensional Field Functions, African Research Review: An International Multi- Disciplinary Journal, Vol.3(5),October,2009, Ethiopia,p437-457.

 
 
Top