ABSTRACT This paper used the equation of the deflected axis of a beam to present procedures for solving
one-dimensional functions that can be expressed in the form of Poisson equation. The equation
of the deflected axis of a beam was solved for deflection for GRP composite component by Finite
Element Method (FEM) using integrated FEM-Galerki approach to derive the finite elements
equations. The critical stress of GRP structure at the onset of structural instability was computed
as 14.162 MPa using Euler relation while the maximum bending moment, a subject in the
equation of the deflected axis of a beam of structure was also estimated with classical relation.
The equation of the deflected axis of the beam is then solved as a one dimensional Poisson
equation following FEM-Galerki approach for deriving element equation. The maximum
optimum deflection a measure of maximum instability occurring around the mid span of element
of structure was estimated. Also the finite element predicted results were compared with
analytical results and the finite element results captured the general trend of the analytical
Cite this paper
C. Ihueze, "The Galerki Approach for Finite Elements of Field Functions: The Case of Buckling in GRP," Journal of Minerals and Materials Characterization and Engineering, Vol. 9 No. 4, 2010, pp. 389-409. doi: 10.4236/jmmce.2010.94028.
 Hawkes, B. and Abinett, R., (1985). The Engineering Design Process, Pitman Publishing.p101.
Ihueze, C.C., (2005).Optimum Buckling Response Model of GRP Composites, Ph.D Thesis, University of Nigeria. p111.
Chapra, S.C and Canale, R.P., (1998). Numerical Methods for Engineers, McGraw-Hill Publishers, 3rd edition, Boston, N.Y. p853.
Astley, R.J., (1992). Finite Elements in Solids and Structures, Chapman and Hall
Publishers, UK. p154.
Enetanya, A.N. and Ihueze, C. C., (2008). Computational Approaches for Strengths of GRP Composites. Journal of Engineering and Applied Sciences, vol.4 No.1 and 2. P62.
Black, P.H. and Adams, O.E., (1981).Machine Design. McGraw-Hill International Book Company, Tokyo. p41.
Benham, P.P. and Warnock, F.V., (1981). Mechanics of Solids and Structures.
Pitman Books, Toronto. p257.
Beer, F. P. and Johnston, B., (1977). Vector Mechanics for Engineers (Statics), 3rd edition. McGraw-Hill Book Company, New York. p354.
Koshal, D., (1998). Manufacturing Engineers Reference Book, Butterworth Heinemann Publisher. p102.
Rosen, B.W., (1965). Mechanics of Composite Strengthening: Fibre Composite
Materials, American Society of Metals, Chapter 3.
Kyriakides, S., Perry, E.J., and Liechti, K.M., (1994). Instability and failure of fibre
composites in compressive, ASME Journal of Applied Mechanics, Vol. 47, No. 6, S 262– 266.
Zienkiewicz, O.C., (1977). The Finite Element Method: Basic Formulation and Linear Problems, 3rd ed., vol.1, McGraw-Hill, London. p228-301.