Introduction#

Welcome to the documentation of the library! This is the place where you can find all the information you need to use the library effectively. The documentation is divided into several parts, each of them serving a different purpose. The documentation is written in a way that it is easy to navigate and find the information you are looking for. If you are new to the library, we suggest you start with the User Guide.

The structure of the documentation#

The documentation is devoted to three main parts:

  • Getting Started Guide - This very guide you are reading. It helps you to get started with the library by laying down the steps of a miniature course, through wich you hopefully get a hang of things.

  • User Guide - Introduces the concepts of the library and illustrates the usage of the classes and algorithms by small examples. The user guide also has a lot of references to other parts of the documentation, including the API Reference. This is the best place to start if you are new to the library. All of the chapters can be downloaded as Jupyter Notebooks from the source repository of the library using the link at the top of the pages.

  • API Reference - The documentation of the classes and algorithms of the library. The API Reference is rich in examples and explanations, and this should be the primary source of information as to how to use the library. If you are a seasoned developer, you might consider jumping into the API Reference directly.

  • Gallery - This is a collection of examples that involve some kind of visualization. The code is ususally provided as one big block of execution, with ocassional internal notes. These examples doesn’t have much explanation. If all this is new to you, we suggest to go through the User Guide first.

What is sigmaepsilon.solid.fourier?#

The `sigmaepsilon.solid.fourier`_ library offers semi-analytic solutions to some beam and plate bending problems, where the boundary conditions are a-priori satisfied by careful selection of the approximating functions. Although the calculations only cover a handful of boundary conditions, when they are applicable, they are significantly faster than let say a finite element solution. For this reason, it is very useful for a couple of things:

  • experimentation

  • verification

  • concept validation

  • education

  • publication

Highlights#

  • Semi-analytic solutions of beam and plate problems.

  • Easy to use, high level interface to define various kinds of loads.

  • Support for arbitrary loads using Monte-Carlo based coefficient determination.

  • Industry-grade performance based on highly parallel, performant code.

  • Tight integration with popular Python libraries like NumPy, SciPy, xarray, etc.

  • A gallery of examples for plotting with Matplotlib for all types of problems.

  • A collection of downloadable Jupyter Notebooks ready for execution covering all available functionality.

  • Getting Started, User Guide and API Reference in the documentation.

  • The library is intensively tested on CircleCI and has a high coverage level (read more about testing below).

Prerequisities#

In order to use the library effectively, you should be familiar with

  • Python - any level for usage, advanced for contribution

  • `NumPy`_, `SciPy`_ - intermediate level familiarity is required

It is not crucial, but it`s better to have a basic understanding of

  • `Numba`_ - Numba is critical for the performance of the library as it does most of the heavy lifting, alongside NumPy and SciPy of course. In most cases it uses JIT-compilation to speed stuff up and it helps to understand how this all works. This is crucial if you consider to contribute to any of the libraries in the sigmaepsilon namespace.

It is recommended to be familiar with

  • `xarray`_ and `Pandas`_ - This is an optional dependency, but highly suggested to use either xarray or Pandas to handle results. Otherwise, you will have to deal with multidimensional arrays and remembering the meaning of each axis will be a pain.

  • `Matplotlib`_ - Most of the examples and the user guide is full of plots, most of them using matplotlib. The plots are high quality, publication ready illustrations. It might be useful to learn how to use it if you have no prior experience. Also, by using the poltting facility, you can give some feedback if you feel something is missing, becoming a contributor yourself.

What about performance?#

Yes, it is. The library is designed to be fast, as it relies on the vector math capabilities of `NumPy`_ and `SciPy`_, while other computationally sensitive calculations are JIT-compiled using `Numba`_. Thanks to `Numba`_, the implemented algorithms are able to bypass the limitations of Python’s GIL and are parallelized on multiple cores, utilizing the full potential of what the hardware has to offer.

Installation#

To install the library, follow the instructions in the Installation Guide.

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