Application of Finite Element Method in Structural Analysis of a Cantilever Beam with Varying Material Properties

Abstract

The structural analysis of beam is a fundamental problem in engineering, particularly in the design and evaluation of load-bearing members. This thesis investigates the application of the Finite Element Method(FEM) to analyze the behavior of beams under various boundary and loading conditions, with a specific focus on cantilever beams subjected to uniformly distributed loads and varying material properties. A series of beam configuration including simply supported, clamped-clamped, cantilever, and beams with point of moment loads were modeled using Hermite shape functions to approximate displacement within each finite element. The numerical simulations were implemented to compute deflection, shear force, and bending moment diagrams, providing insight into the structural response of beams. The result obtained from FEM were consistent with classical beam theory, validating the effectiveness of the method for accurate structural prediction. The study also highlighted the material parameters into formulations, the work demonstrates how FEM can be adapted to more realistic structural conditions. This thesis not only confirms the readability of FEM for static beam problems but also establishes a strong foundation for future investigation into more complex and non-linear structural system.