FEALiTE2D

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A finite element analysis library for 2D frame, beams and truss elements using C#

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# FEALiTE2D
A fast and reliable finite element analysis library for 2D frame, beam and truss elements using C#.

| [![NuGet](https://img.shields.io/nuget/dt/FEALiTE2D.svg)](https://www.nuget.org/packages/FEALiTE2D/) | FEALiTE2D |
------------ | -------------
| [![NuGet](https://img.shields.io/nuget/dt/FEALiTE2D.Plotting.svg)](https://www.nuget.org/packages/FEALiTE2D.Plotting/) | FEALiTE2D.Plotting |

## Features
* [x] Analysis of frame, beam, truss/link members.
* [x] Various load types:
  * [x] Frame point load.
  * [x] Frame uniform load.
  * [x] Frame trapezoidal load.
  * [x] Nodal point load.
  * [x] Support displacement.
* [x] Loads can be set in global and element's local coordinate system.
* [x] Nodes can have local and global coordinate system.
* [x] Loads can be assigned in variant load cases of different natures.
* [x] Loads can be combined in a load combination with load magnification factors.
* [x] Rigid Supports of 3 degrees of freedom.
* [x] Elastic supports using translational and rotational springs.
* [x] Variety of predefined cross-sections.
* [x] Linear mesher for better analysis results.

## Sign convention for loads in global and local coordinate system.
![Loads - Global Local](https://user-images.githubusercontent.com/21183259/110838377-0d5ab900-82ab-11eb-838c-655865ae767b.png)

## Example
Here is a 2D framed strcture subjected to various loading conditions
![Example1-Loads](https://user-images.githubusercontent.com/21183259/110694187-fce60800-81f0-11eb-8c27-06d883906f06.png)

```C#

public void TestStructure()
{
     // units are kN, m
     FEALiTE2D.Structure.Structure structure = new FEALiTE2D.Structure.Structure();

Node2D n1 = new Node2D(0, 0, "n1");
     Node2D n2 = new Node2D(9, 0, "n2");
     Node2D n3 = new Node2D(0, 6, "n3");
     Node2D n4 = new Node2D(9, 6, "n4");
     Node2D n5 = new Node2D(0, 12, "n5");
     n1.Restrain(NodalDegreeOfFreedom.UX, NodalDegreeOfFreedom.UY, NodalDegreeOfFreedom.RZ); //fully restrained
     n2.Restrain(NodalDegreeOfFreedom.UX, NodalDegreeOfFreedom.UY, NodalDegreeOfFreedom.RZ); //fully restrained

structure.AddNode(n1, n2, n3, n4, n5);
     IMaterial material = new GenericIsotropicMaterial() { E = 30E6, U = 0.2, Label = "Steel", Alpha = 0.000012, Gama = 39885, MaterialType = MaterialType.Steel };
     IFrame2DSection section = new Generic2DSection(0.075, 0.075, 0.075, 0.000480, 0.000480, 0.000480 * 2, 0.1, 0.1, material);
    
     FrameElement2D e1 = new FrameElement2D(n1, n3, "e1") { CrossSection = section };
     FrameElement2D e2 = new FrameElement2D(n2, n4, "e2") { CrossSection = section };
     FrameElement2D e3 = new FrameElement2D(n3, n5, "e3") { CrossSection = section };
     FrameElement2D e4 = new FrameElement2D(n3, n4, "e4") { CrossSection = section };
     FrameElement2D e5 = new FrameElement2D(n4, n5, "e5") { CrossSection = section };
     structure.AddElement(new[] { e1, e2, e3, e4, e5 });

LoadCase loadCase = new LoadCase("live", LoadCaseType.Live);
     structure.LoadCasesToRun.Add(loadCase);
     n2.SupportDisplacementLoad.Add(new SupportDisplacementLoad(10E-3, -5E-3, -2.5 * Math.PI / 180, loadCase));
     e3.Loads.Add(new FramePointLoad(0, 0, 7.5, e3.Length / 2, LoadDirection.Global, loadCase));
     e4.Loads.Add(new FrameTrapezoidalLoad(0, 0, -15, -7, LoadDirection.Global, loadCase, 0.9, 2.7));
     e5.Loads.Add(new FrameUniformLoad(0, -12, LoadDirection.Local, loadCase));
     n3.NodalLoads.Add(new NodalLoad(80, 0, 0, LoadDirection.Global, loadCase));
     n5.NodalLoads.Add(new NodalLoad(40, 0, 0, LoadDirection.Global, loadCase));
     n1.NodalLoads.Add(new NodalLoad(40, 0, 0, LoadDirection.Global, loadCase));

structure.LinearMesher.NumberSegements = 35;
     structure.Solve();
}
```

## Ploting internal forces and displacments
Use ploting Library ```FEALiTE2D.Plotting```, create dxf plotter with correct options and save the file on your local machine.

```C#
 var op = new FEALiTE2D.Plotting.Dxf.PlottingOption 
 { 
     NFDScaleFactor = 0.01,
     SFDScaleFactor = 0.01,
     BMDScaleFactor = 0.01, 
     DisplacmentScaleFactor = 1,
     DiagramsHorizontalOffsets = 10 
 };
var plotter = new FEALiTE2D.Plotting.Dxf.Plotter(structure, op);
plotter.Plot("D:\\internal forces.dxf", loadCase);
```
![internal forces](https://user-images.githubusercontent.com/21183259/133887224-05bf37e7-9cd4-43e9-bde1-00a0f5eb48eb.png)

FEALiTE2D

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