Engineering Mechanics

This repository provides a set of Python classes and tools to model and solve engineering mechanics problems, including statics, and dyanmics problems. This repository is aimed at supporting mechanical engineering calculations and simulations.

Overview

This repository includes:

• BoundVector: A class to represent vectors in 3D space with automatic alphabetical naming for ease in handling multiple vectors in calculations.
• Load: A class containing a 6D bound vector to represent force and moment loading on a structure.
• Reaction: A class to represent reaction loads with additional applied constraints.
• Statics Study: Enables simplified workflow when working with multiple loadcases and configurations.
• Statics Calculations: Utilities for constructing equilibrium matrices, solving for reactions, and ensuring stability within mechanical systems.
• Constraint Modeling: Flexible constraint matrices that allow for complex and realistic modeling of supports, including coupled constraints.

Statics and Constraints

The statics tools provide utilities to:

• Set up equilibrium matrices for multi-reaction systems.
• Analyze whether a system is overconstrained or underconstrained.
• Handle advanced constraint matrices with non-diagonal elements, suitable for inclined or coupled constraints.

Installation

Clone this repository and install dependencies:

git clone https://github.com/davidson-engineering/engineering-mechanics.git
cd engineering-mechanics
pip install .

Examples

Static Equilibrium Check

For a fully constrained system with multiple reactions, you can construct an equilibrium matrix and check for overconstraints:

import numpy as np
from statics import StaticsStudy, Load, Reaction

# Define forces and reactions here, then use create a StaticsStudy to solve
loads = [
    Load(
        magnitude=np.array([0, 0, -100, 0, -10, 0]),
        location=np.array([1, 0, 0]),
        name="Load_A",
    )
]
reactions = [
    Reaction(
        location=np.array([0, 0, 0]), constraint=np.eye(6), name="Fixed support"
    ),
]

study = StaticsStudy(
    name="Example Study",
    description="Example study with one load and one reaction",
    reactions=reactions,
    loads=loads,
)
result = study.run()

One can also print a summary table using prettytable:

result.print_summary()

Input loads Summary:
+------+-------+-------+-------+------+------+---------+------+--------+------+
| Load | Loc X | Loc Y | Loc Z |  Fx  |  Fy  |    Fz   |  Mx  |   My   |  Mz  |
+------+-------+-------+-------+------+------+---------+------+--------+------+
| F_a  |  1.00 |  0.00 |  0.00 | 0.00 | 0.00 | -100.00 | 0.00 | -10.00 | 0.00 |
+------+-------+-------+-------+------+------+---------+------+--------+------+

Constraints Summary:
+---------------+-------------------+
| Reaction      | Constraint Matrix |
+---------------+-------------------+
| Fixed support |   [1 0 0 0 0 0]   |
|               |   [0 1 0 0 0 0]   |
|               |   [0 0 1 0 0 0]   |
|               |   [0 0 0 1 0 0]   |
|               |   [0 0 0 0 1 0]   |
|               |   [0 0 0 0 0 1]   |
+---------------+-------------------+

Reactions Summary:
+---------------+-------+-------+-------+------+------+--------+------+--------+-------+
| Reaction      | Loc X | Loc Y | Loc Z |  Fx  |  Fy  |   Fz   |  Mx  |   My   |   Mz  |
+---------------+-------+-------+-------+------+------+--------+------+--------+-------+
| Fixed support |  0.00 |  0.00 |  0.00 | 0.00 | 0.00 | 100.00 | 0.00 | -90.00 | 10.00 |
+---------------+-------+-------+-------+------+------+--------+------+--------+-------+

License

This project is licensed under the MIT License.