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        "author": "Joseph Contreras",
        "author_email": "26684136+JosephJContreras@users.noreply.github.com",
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            "License :: OSI Approved :: MIT License",
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        "description": "# FEmethods\n\n[![PyPI version](https://badge.fury.io/py/femethods.svg)](https://badge.fury.io/py/femethods)\n[![Build Status](https://travis-ci.org/josephjcontreras/FEMethods.svg?branch=master)](https://travis-ci.org/josephjcontreras/FEMethods)\n[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://github.com/josephjcontreras/FEMethods/blob/master/License.txt)\n[![Coverage Status](https://coveralls.io/repos/github/josephjcontreras/FEMethods/badge.svg?branch=master)](https://coveralls.io/github/josephjcontreras/FEMethods?branch=master)\n[![Documentation Status](https://readthedocs.org/projects/femethods/badge/?version=latest)](https://femethods.readthedocs.io/en/latest/?badge=latest)\n\n\n## Introduction\n_FEmethods_ is a python module that uses Finite Element Methods to determine the\nreactions, and plot the shear, moment, and deflection along the length of a beam.\n\nUsing Finite elements has the advantage over using exact solutions because it \ncan be used as a general analysis, and can analyze beams that are statically \nindeterminate. The downside of this numerical approach is it will be less \naccurate than the exact approach.\n\nThe official documentation is on [Read the Docs](https://femethods.readthedocs.io/en/latest/). \n\n## Installation\n\n__FEMethods__ is hosted on PyPi, so installation is simple.\n\n`pip install femethods`\n\n\n## General Layout\n\n`FEMethods` is made up of several sub-classes to make it easy to define loads\nand reaction types.\n\n### femethods.loads\nThere are currently only two different load types that are implemented.\n\n * `PointLoad`, a normal force acting with a constant magnitude on a single point\n * `MomentLoad`, a rotational moment acting with a constant magnitude acting at a single point\n\nAll loads are defined by a `location` along the element, and a `magnitude`. \nThe `location` must be positive, and must lie on the length of the beam,\nor it will raise a `ValueError`\n\n_Future goals are to add a library of standard distributed loads \n(constant, ramp, etc) as well as functionality that will allow a distributed \nload function to be the input._\n\n#### femethods.loads.PointLoad\nThe `PointLoad` class describes a standard point load. A normal load acting at\na single point with a constant value. It is defined with a location and a \nmagnitude.\n\n```python\n>>> PointLoad(-10, 5)\nPointLoad(magnitude=-10, location=5)\n```\n\nThe `location` must be a positive value, and less than or equal to the length\nof the beam, otherwise it raise a `ValueError`.\n\n#### femethods.loads.MomentLoad\nA `MomentLoad` class describes a standard moment load. A moment acting at a \nsingle point with a constant value. It is defined with a location and a value.\n\n```python\n>>> MomentLoad(2, 5)\nMomentLoad(magnitude=2, location=5)\n```\n\nThe `location` must be a positive value, and less than or equal to the length\nof the beam, otherwise it raise a `ValueError`.\n\n### femethods.reactions\n\nThere are two different reactions that can be used to support an element.\n\n  * `FixedReaction` does not allow vertical or rotational displacement\n  * `PinnedReaction` does not allow vertical displacement but does allow rotational displacement\n\nAll reactions have two properties, a `force` and a `moment`. They represent\nthe numerical value for the resistive force or moment acting on the element \nto support the load(s). These properties are set to `None` when the reaction \nis instantiated (ie, they are unknown). They are calculated and set when \nanalyzing a element. Note that the `moment` property of a `PinnedReaction` \nwill always be `None` because it does not resist a moment.\n\nThe `value` property is a read-only combination of the `force` and `moment` \nproperties, and is in the form `value = (force, moment)`\n\nAll reactions have an `invalidate` method that will set the `force` and\n`moment` back to `None`. This is useful when changing parameters and the\n calculated reactions are no longer valid.\n\n#### femethods.reactions.FixedReaction\nThe `FixedReaction` is a reaction class that prevents both vertical and angular\n(rotational displacement). It has boundary conditions of `bc = (0, 0)`\n\n```python\n>>> FixedReaction(3)\nFixedReaction(location=3)\n\n>>> print(FixedReaction(3))\nFixedReaction\n  Location: 3\n     Force: None\n    Moment: None\n```\n\nThe `location` must be a positive value, and less than or equal to the length\nof the beam, otherwise it raise a `ValueError`.\n\n#### femethods.reactions.PinnedReaction\nThe `PinnedReaction` is a reaction class that prevents vertical displacement, \nbut allows angular (rotational) displacement. It has boundary conditions of `bc = (0, None)`\n\n```python\n>>> PinnedReaction(7)\nPinnedReaction(location=7)\n>>> print(PinnedReaction(7))\nPinnedReaction\n  Location: 7\n     Force: None\n    Moment: None\n```\n\nThe `location` must be a positive value, and less than or equal to the length\nof the beam, otherwise it raise a `ValueError`.\n\n### femethods.elements.Beam\nDefines a beam as a finite element. This class will handle the bulk of the \nanalysis, populating properties (such as meshing and values for the reactions).\n\nTo create a `Beam` object, write the following:\n\n```python\nb = Beam(length, loads, reactions, E=1, Ixx=1)\n```\n\nWhere the loads and reactions are a list of `loads` and `reactions` respectively.\n\n**Note**\nLoads and reactions must be a list, even when there is only one.\n\n The `E` and `Ixx` parameters are Young's modulus and the polar moment of \n inertia about the bending axis. They both default to `1`.\n\n## Examples\n\nThis section contains several different examples of how to use the beam \nelement, and their results.\n\nFor all examples, the following have been imported:\n\n```python\nfrom femethods.elements import Beam\nfrom femethods.reactions import FixedReaction, PinnedReaction\nfrom femethods.loads import PointLoad, MomentLoad\n```\n\n### Example 1: Cantilevered Beam with Fixed Support and End Loading\n\n```python\nbeam_len = 10\n# Note that both the reaction and load are both lists. They must always be\n# given to Beam as a list,\nr = [FixedReaction(0)]                            # define reactions as list\np = [PointLoad(magnitude=-2, location=beam_len)]  # define loads as list\n\nb = Beam(beam_len, loads=p, reactions=r, E=29e6, Ixx=125)\n\n# an explicit solve is required to calculate the reaction values\nb.solve()\nprint(b)\n```\n\nThe output of the program is\n```\nPARAMETERS\nLength (length): 10\nYoung's Modulus (E): 29000000.0\nArea moment of inertia (Ixx): 125\nLOADING\nType: point load\n    Location: 10\n   Magnitude: -2\n\nREACTIONS\nType: fixed\n    Location: 0\n       Force: 2.0\n      Moment: 20.0\n```\n\n### Example 2: Cantilevered Beam with 3 Pinned Supports and End Loading\n\n```python\nbeam_len = 10\n\n# Note that both the reaction and load are both lists. They must always be\n# given to Beam as a list,\nr = [PinnedReaction(0), PinnedReaction(2), PinnedReaction(6)]  # define reactions\np = [PointLoad(magnitude=-2, location=beam_len)]               # define loads\n\nb = Beam(beam_len, loads=p, reactions=r, E=29e6, Ixx=125)\n\n# an explicit solve is required to calculate the reaction values\nb.solve()\nprint(b)\n```\n\nThe output of the program is\n```\nPARAMETERS\nLength (length): 10\nYoung's Modulus (E): 29000000.0\nArea moment of inertia (Ixx): 125\nLOADING\nType: point load\n    Location: 10\n   Magnitude: -2\n\nREACTIONS\nType: pinned\n    Location: 0\n       Force: 1.3333333333333346\n      Moment: 0.0\nType: pinned\n    Location: 2\n       Force: -4.000000000000004\n      Moment: 0.0\nType: pinned\n    Location: 6\n       Force: 4.666666666666671\n      Moment: 0.0\n```\n\n## TODO\n * Add a more thorough documentation for all the features, limitations and FE fundamentals for each section\n * Add additional element types, such as the bar element\n\n## Acknowledgements\n[Derivation of stiffness matrix for a beam](https://www.12000.org/my_notes/stiffness_matrix/stiffness_matrix_report.htm#x1-50002.1.1) by Nasser M. Abbasi\n[An idiot\u00e2\u20ac\u2122s guide to Python documentation with Sphinx and ReadTheDocs](https://samnicholls.net/2016/06/15/how-to-sphinx-readthedocs) by [Sam Nicholls](https://samnicholls.net/about/) for\n a very helpful guide on how to get sphinx set up\n\n\n",
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