FEM Beam Analysis (MATLAB + ANSYS)

Overview

Finite element analysis of a multi-section beam using Euler–Bernoulli beam elements.
The project includes a MATLAB implementation of the FEM formulation and validation using ANSYS simulation.

Objectives

• Develop a beam finite element model
• Compute nodal displacements and rotations
• Calculate reaction forces and bending moments
• Perform modal analysis to determine natural frequencies
• Validate results using ANSYS

Engineering Approach

• Derivation of the beam element stiffness matrix
• Assembly of the global stiffness matrix
• Application of boundary conditions
• Solution of the displacement system
• Eigenvalue analysis for natural frequencies

Tools

• MATLAB
• ANSYS
• Finite Element Method (FEM)

Results

• Deflection distribution along the beam
• Rotation and bending moment diagrams
• Natural frequencies of the structure

Repository Contents

• MATLAB code for FEM beam analysis
• ANSYS simulation results
• Plots of structural response
• Project documentation

MATLAB Code

The finite element formulation was implemented in MATLAB using Euler-Bernoulli beam elements.

The code includes:

• global stiffness and mass matrix assembly
• static solution for nodal displacements
• reaction force calculation
• deflection, rotation, and bending moment plotting
• midpoint deflection evaluation
• natural frequency extraction by solving the generalized eigenvalue problem

Main script:

• code/fem_beam_analysis.m