FEniCS-GMSH Automation for Factor of Safety (FOS) Calculation

This project automates the process of calculating the Factor of Safety (FOS) for a 3D geometry defined in a STEP file. It uses GMSH for mesh generation and FEniCS for finite element analysis (FEA). The workflow is encapsulated in a single Python function, making it easy to use and integrate into larger workflows.

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Table of Contents

1. Overview
2. Dependencies
3. Inputs
4. Outputs

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Overview

The project consists of two Python functions, create_two_plate_assembly, which builds a STEP file of two overlapping plates with holes and can be customized to different plate and hole dimensions. This STEP file along with material properties as input to calculate_fos function which returns the Factor of Safety (FOS) along with stress and displacement plots. The functions performs the following steps:

1. Parametric 3D Model Generation: Uses build123d to generate a 3D model from parametric data.
2. Mesh Generation: Uses GMSH to generate a 3D mesh from the STEP file.
3. Mesh Conversion: Converts the GMSH mesh into XDMF format for use in FEniCS.
4. Finite Element Analysis: Solves the mechanical problem using FEniCS to compute stresses and diplacements.
5. FOS Calculation: Computes the von Mises stress and calculates the Factor of Safety (FOS) based on the yield stress.

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Dependencies

The code relies on the following Python libraries:

• build123d: For 3D Model generation.
• FEniCS: For finite element analysis.
• GMSH: For mesh generation.
• meshio: For converting GMSH mesh files to XDMF format.

Make sure you have the following installed:

• Python 3.x
• FEniCS (install via FEniCS documentation)
• GMSH (install via GMSH documentation)
• meshio (install via pip install meshio)
• build123d (install via pip install build123d)

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Inputs

Parameter	Type	Description	Example Value
step_file	string	Path to STEP file containing 3D geometry	"geometry.step"
E	float	Young's modulus in Pascals (Pa)	210e9 (for steel)
nu	float	Poisson's ratio (unitless)	0.3
yield_strength	float	Material yield strength in Pascals (Pa)	200e6
zero_disp_tags	list of integers	Surface tags where displacement = 0 (fixed boundaries)	[1, 2, 3]
traction_tags	list of integers	Surface tags where traction forces are applied	[4, 5]
traction_values	list of tuples	Traction vectors (x,y,z) in Pa for corresponding tags	[(1e6,0,0), (-1e6,0,0)]

Outputs

Output	Type	Description
Return value	float	Computed Factor of Safety (FOS)