# orthotropic-lamina-properties

## Description

It's simply a function that calculates basic elastic properties (Young's Modulus, Poisson's ratio, shear modulus) for unidirectional, two-dimensional, transversely isotropic lamina (refer to the "background" for more info!)

## Dependencies

Please note that mathjs is needed to make this thing going. Main reason for it is that some matrix manipulation is done.

## Install

To install package, hit:

```
npm install --save orthotropic-lamina-properties
```

## Usage

Function called `transformProperties`

is one and only export of this package.

```
import transformProperties from 'orthotropic-lamina-properties';
```

## API

### Input

Function `transformProperties`

takes 5 arguments, all numbers, all obligatory, in following order:

- E1 - Young's modulus of lamina along fiber direction [GPa]
- E2 - Young's modulus of lamina normal to fiber direction [GPa]
- G - Shear Modulus [GPa]
- e12 - Poisson's ratio
- angle - rotation angle [degrees]

### Output

Function `transformProperties`

return object, including information on elastic properties of lamina at given angle. Output object structure:
*C - Transformed stiffnes matrix, 3x3 array
*S - Transformed compliance matrix, 3x3 array
*E1 - Young Modulus at given angle
*G - Shear Modulus at given angle
*e12 - Poisson's ratio at given angle

### Example

This

```
import transformProperties from 'orthotropic-lamina-properties';
console.log(transformProperties(82,4,2.8,0.25,90));
```

Logs output:

```
C : [
[4.01223241590214, 1.003058103975535, -2.456783792784904e-16],
[1.003058103975535, 82.25076452599389, -4.043206985808815e-16],
[-2.456783792784904e-16, -4.043206985808815e-16, 2.8]
],
S : [
[0.25, -0.003048780487804878, 2.1495324915347708e-17],
[-0.003048780487804878, 0.012195121951219513, 1.49347170627726e-18],
[2.1495324915347708e-17, 1.49347170627726e-18, 0.35714285714285715]
],
E1 : 4,
G : 2.8,
e12 : 0.012195121951219513
```

## Background

To understand need for and purpose of such package, basic knowledge on unidirectional, orthotropic (transversely isotropic) laminated materials is needed. Basically, this function does matrix transformations that normally would be made on paper. Moreover, this package was developed for another project All mathematical operations and matrix transformations are widely known in literature on this field. Please refer to these publications for further problem investigation:

- Cristescu, Nicolaie Dan, Eduard-Marius Craciun, and Eugen Soós. Mechanics of Elastic Composites. CRC Press, 2003.
- Gibson, Ronald F. Principles of Composite Material Mechanics, Fourth Edition. CRC Press, 2016.
- Hwu, Chyanbin. Anisotropic Elastic Plates. Springer Science & Business Media, 2010.