# Programming-FEM-5th-Fortran

**Repository Path**: chen_tianhai/Programming-FEM-5th-Fortran

## Basic Information

- **Project Name**: Programming-FEM-5th-Fortran
- **Description**: Programming the Finite Element Method_I M Smith & D V Griffiths_Microsoft Visual Studio_Intel Visual Fortran
- **Primary Language**: Unknown
- **License**: MIT
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2021-09-14
- **Last Updated**: 2021-09-14

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# Programming the finite element method_5th edition  
## Overview  
As a engineering student, I has been appealed by the classic textbook - [Programming the finite element method](https://www.amazon.com/Programming-Finite-Element-Method-Smith/dp/1119973341) for more than five years. When I was a bachelor, my supervisor Prof. Shang guided me to understand the theory of finite element method using coding. It was really impressive. Recently, I realize that it may be meaningful to reconstruct the code using [Microsoft Visual Studio 2012](https://visualstudio.microsoft.com/zh-hans/vs/older-downloads/?rr=https%3A%2F%2Fwww.google.com%2F) and [Intel Visual Fortran Composer XE 2013](https://software.intel.com/en-us/forums/intel-software-development-products-download-registration-licensing), making it convenient for debuging and second development.  

I once used Microsoft Windowing Application to present the modelling results. However, the Graphical User Interface (GUI) is not satisfactory. In this repository, I do not pay attention to visualization. What I focus on are the input and output files,  algorithms, and the readibility of the code.    

## Prerequisites  
* [Programming the finite element method](https://www.amazon.com/Programming-Finite-Element-Method-Smith/dp/1119973341).
* [Microsoft Visual Studio 2012](https://visualstudio.microsoft.com/zh-hans/vs/older-downloads/?rr=https%3A%2F%2Fwww.google.com%2F).
* [Intel Visual Fortran Composer XE 2013](https://software.intel.com/en-us/forums/intel-software-development-products-download-registration-licensing).

## Documentation  
### Static Equilibrium Structures  
### Static Equilibrium Linear Elastic Solids  
### Material Nonlinearity  
### Steady State Flow  
<a href="https://www.codecogs.com/eqnedit.php?latex=k_x\frac{\partial^2&space;\phi}{\partial&space;x^2}&space;&plus;&space;k_y\frac{\partial^2&space;\phi}{\partial&space;y^2}&space;=&space;0" target="_blank"><img src="https://latex.codecogs.com/gif.latex?k_x\frac{\partial^2&space;\phi}{\partial&space;x^2}&space;&plus;&space;k_y\frac{\partial^2&space;\phi}{\partial&space;y^2}&space;=&space;0" title="k_x\frac{\partial^2 \phi}{\partial x^2} + k_y\frac{\partial^2 \phi}{\partial y^2} = 0" /></a>  
### Transient Problems  
<a href="https://www.codecogs.com/eqnedit.php?latex=c_x\frac{\partial^2&space;u_w}{\partial&space;x^2}&space;&plus;&space;c_y\frac{\partial^2&space;u_w}{\partial&space;y^2}&space;=&space;\frac{\partial&space;u_w}{\partial&space;t}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?c_x\frac{\partial^2&space;u_w}{\partial&space;x^2}&space;&plus;&space;c_y\frac{\partial^2&space;u_w}{\partial&space;y^2}&space;=&space;\frac{\partial&space;u_w}{\partial&space;t}" title="c_x\frac{\partial^2 u_w}{\partial x^2} + c_y\frac{\partial^2 u_w}{\partial y^2} = \frac{\partial u_w}{\partial t}" /></a>  
### Coupled Problems  
Conservation of incompressible mass :  
<a href="https://www.codecogs.com/eqnedit.php?latex=\frac{\partial&space;u}{\partial&space;x}&space;&plus;&space;\frac{\partial&space;v}{\partial&space;y}&space;=&space;0" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\frac{\partial&space;u}{\partial&space;x}&space;&plus;&space;\frac{\partial&space;v}{\partial&space;y}&space;=&space;0" title="\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0" /></a>  
Conservation of momentum :  
<a href="https://www.codecogs.com/eqnedit.php?latex=\rho&space;\left&space;(&space;\frac{\partial&space;u}{\partial&space;t}&space;&plus;&space;u\frac{\partial&space;u}{\partial&space;x}&space;&plus;&space;v\frac{\partial&space;u}{\partial&space;y}\right&space;)&space;=&space;\boldsymbol{F}_x&space;&plus;&space;\left&space;(&space;\frac{\partial&space;\sigma_x}{\partial&space;x}&space;&plus;&space;\frac{\partial&space;\tau_x_y}{\partial&space;y}\right&space;)" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\rho&space;\left&space;(&space;\frac{\partial&space;u}{\partial&space;t}&space;&plus;&space;u\frac{\partial&space;u}{\partial&space;x}&space;&plus;&space;v\frac{\partial&space;u}{\partial&space;y}\right&space;)&space;=&space;\boldsymbol{F}_x&space;&plus;&space;\left&space;(&space;\frac{\partial&space;\sigma_x}{\partial&space;x}&space;&plus;&space;\frac{\partial&space;\tau_x_y}{\partial&space;y}\right&space;)" title="\rho \left ( \frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y}\right ) = \boldsymbol{F}_x + \left ( \frac{\partial \sigma_x}{\partial x} + \frac{\partial \tau_x_y}{\partial y}\right )" /></a>  
<a href="https://www.codecogs.com/eqnedit.php?latex=\rho&space;\left&space;(&space;\frac{\partial&space;v}{\partial&space;t}&space;&plus;&space;u\frac{\partial&space;v}{\partial&space;x}&space;&plus;&space;v\frac{\partial&space;v}{\partial&space;y}\right&space;)&space;=&space;\boldsymbol{F}_y&space;&plus;&space;\left&space;(&space;\frac{\partial&space;\sigma_y}{\partial&space;y}&space;&plus;&space;\frac{\partial&space;\tau_x_y}{\partial&space;x}\right&space;)" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\rho&space;\left&space;(&space;\frac{\partial&space;v}{\partial&space;t}&space;&plus;&space;u\frac{\partial&space;v}{\partial&space;x}&space;&plus;&space;v\frac{\partial&space;v}{\partial&space;y}\right&space;)&space;=&space;\boldsymbol{F}_y&space;&plus;&space;\left&space;(&space;\frac{\partial&space;\sigma_y}{\partial&space;y}&space;&plus;&space;\frac{\partial&space;\tau_x_y}{\partial&space;x}\right&space;)" title="\rho \left ( \frac{\partial v}{\partial t} + u\frac{\partial v}{\partial x} + v\frac{\partial v}{\partial y}\right ) = \boldsymbol{F}_y + \left ( \frac{\partial \sigma_y}{\partial y} + \frac{\partial \tau_x_y}{\partial x}\right )" /></a>  
Stress equations :  
<a href="https://www.codecogs.com/eqnedit.php?latex=\sigma_x&space;=&space;-p&space;-&space;\frac{2\mu}{3}(\frac{\partial&space;u}{\partial&space;x}&space;&plus;&space;\frac{\partial&space;v}{\partial&space;y})&space;&plus;&space;2\mu\frac{\partial&space;u}{\partial&space;x}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\sigma_x&space;=&space;-p&space;-&space;\frac{2\mu}{3}(\frac{\partial&space;u}{\partial&space;x}&space;&plus;&space;\frac{\partial&space;v}{\partial&space;y})&space;&plus;&space;2\mu\frac{\partial&space;u}{\partial&space;x}" title="\sigma_x = -p - \frac{2\mu}{3}(\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}) + 2\mu\frac{\partial u}{\partial x}" /></a>  
<a href="https://www.codecogs.com/eqnedit.php?latex=\sigma_y&space;=&space;-p&space;-&space;\frac{2\mu}{3}(\frac{\partial&space;u}{\partial&space;x}&space;&plus;&space;\frac{\partial&space;v}{\partial&space;y})&space;&plus;&space;2\mu\frac{\partial&space;u}{\partial&space;y}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\sigma_y&space;=&space;-p&space;-&space;\frac{2\mu}{3}(\frac{\partial&space;u}{\partial&space;x}&space;&plus;&space;\frac{\partial&space;v}{\partial&space;y})&space;&plus;&space;2\mu\frac{\partial&space;u}{\partial&space;y}" title="\sigma_y = -p - \frac{2\mu}{3}(\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}) + 2\mu\frac{\partial u}{\partial y}" /></a>  
<a href="https://www.codecogs.com/eqnedit.php?latex=\tau_x_y&space;=&space;\mu(\frac{\partial&space;u}{\partial&space;y}&space;&plus;&space;\frac{\partial&space;v}{\partial&space;x})" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\tau_x_y&space;=&space;\mu(\frac{\partial&space;u}{\partial&space;y}&space;&plus;&space;\frac{\partial&space;v}{\partial&space;x})" title="\tau_x_y = \mu(\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x})" /></a>  
### Eigenvalue Problems  
### Forced Vibrations  

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