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
results.
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