FEM-Bridge-Simulator

A complete finite element analysis pipeline for bridge structural simulation

Overview

FEM-Bridge-Simulator is an end-to-end finite element analysis (FEA) framework designed for simulating and visualizing structural behavior of bridges under various load conditions. The toolkit implements a complete FEM pipeline from mesh generation to real-time visualization, offering researchers and engineers a comprehensive tool for bridge structural analysis.

Motivation

Understanding structural integrity is crucial in civil engineering, especially for complex structures like cable-stayed bridges. This project addresses the need for:

• Accessible FEA Tools: Providing an open-source alternative for educational and research purposes
• Complete Pipeline: Integrating preprocessing, solving, and postprocessing in a unified framework
• Visual Insights: Enabling real-time visualization of stress distributions and deformations
• Performance Analysis: Comparing different numerical methods and optimization strategies

Key Features

• Mesh Generation: Interactive geometric modeling with Gmsh integration
• Multiple Solvers: Full and banded matrix solvers with various renumbering strategies
• Real-time Visualization: OpenGL-based rendering of displacement fields and stress distributions
• Stress Analysis: Von Mises stress, principal stresses (σxx, σyy, σxy)
• Animation Support: Time-based deformation and load movement visualization
• Performance Optimization: Reverse Cuthill-McKee (RCM) renumbering for bandwidth reduction

Architecture

The toolkit is organized into three specialized modules:

FEM-Bridge-Simulator/
├── pre-processor/   # Mesh generation & problem definition
├── processor/       # FEM solver & computation engine
└── post-processor/  # Visualization & results analysis

1. PreProcessor

Generates computational meshes and defines boundary conditions:

• Interactive geometry creation using Gmsh
• Support for triangular and quadrilateral elements
• Plane stress, plane strain, and axisymmetric formulations
• Flexible boundary condition specification

2. Processor

Core FEM computation engine:

• Linear elasticity solver for structural analysis
• Multiple matrix solver implementations (full/banded)
• Node renumbering strategies (X/Y coordinate, RCM)
• Efficient sparse matrix operations

3. PostProcessor

Advanced visualization and analysis:

• Interactive 3D rendering with OpenGL
• Real-time stress field visualization
• Deformation animation capabilities
• Data export for external plotting (Python scripts included)

Preliminary Work

The homeworks/ directory contains foundational implementations developed prior to the main project. These modules explore individual FEM concepts and serve as building blocks for the complete bridge simulator:

Module	Description
GeoMesh	Mesh generation and geometric modeling basics
Integrate	Numerical integration schemes for FEM
BandSolver	Banded matrix solver implementation
Poisson	2D Poisson equation solver
LinearElasticity	Core elasticity formulation
LinearElasticityForces	Extended elasticity with force handling

Quick Start

Prerequisites

# Required libraries
- CMake (>= 3.10)
- OpenGL
- GLFW
- Gmsh SDK

Build & Run

# 1. PreProcessor - Generate mesh
cd pre-processor
mkdir build && cd build
cmake .. && make
./myFem

# 2. Processor - Solve FEM problem
cd ../../processor
mkdir build && cd build
cmake .. && make
./myFem

# 3. PostProcessor - Visualize results
cd ../../post-processor
mkdir build && cd build
cmake .. && make
./myFem

Example Results

The toolkit can simulate various structural scenarios:

• Cable-stayed Bridge: Full bridge with pylons and stay cables
• Simplified Bridge: Basic deck structure for validation
• Beam Analysis: Classical beam bending with analytical comparison
• Dynamic Loading: Moving loads and time-dependent deformations

Technical Details

Solver Capabilities

• Element Types: 3-node triangles, 4-node quadrilaterals
• Material Models: Linear elastic (isotropic)
• Problem Types: Plane stress, plane strain, axisymmetric
• Matrix Solvers: Gaussian elimination (full/banded)

Optimization Features

• Node Renumbering: Reduces matrix bandwidth for efficient solving
• Sparse Storage: Banded matrix format for memory efficiency
• Parallel Visualization: Non-blocking rendering pipeline

Performance

The RCM renumbering algorithm typically reduces matrix bandwidth by 60-80%, significantly improving computational efficiency for large meshes.

Documentation

Each module contains detailed README with:

• Build instructions
• Usage examples
• API documentation
• Configuration options

See module-specific READMEs in respective directories.

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Author

	Mathis DELSART
	Adrien ANTONUTTI

License

This project is developed for academic purposes as part of university coursework.

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Built for LEPL1110 - Eléments finis @ UCLouvain (Université catholique de Louvain).

Built for structural engineering enthusiasts