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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.

The Galerki Approach for Finite Elements of Field Functions: The Case of Buckling in GRP