julio-design/ARDO

Augmented Reality Design Optimization for orthotropic and isotropic materials

FortranMIT

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 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 and Intel Visual Fortran Composer XE 2013, 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

Documentation

Static Equilibrium Structures

Static Equilibrium Linear Elastic Solids

Material Nonlinearity

Steady State Flow

$k_x\frac{\partial^2 \phi}{\partial x^2} + k_y\frac{\partial^2 \phi}{\partial y^2} = 0$

Transient Problems

$c_x\frac{\partial^2 u_w}{\partial x^2} + c_y\frac{\partial^2 u_w}{\partial y^2} = \frac{\partial u_w}{\partial t}$

Coupled Problems

Conservation of incompressible mass :
$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0$
Conservation of momentum :
$\rho \left ( \frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y}\right ) = \boldsymbol{F}_x + \left ( \frac{\partial \sigma_x}{\partial x} + \frac{\partial \tau_x_y}{\partial y}\right )$
$\rho \left ( \frac{\partial v}{\partial t} + u\frac{\partial v}{\partial x} + v\frac{\partial v}{\partial y}\right ) = \boldsymbol{F}_y + \left ( \frac{\partial \sigma_y}{\partial y} + \frac{\partial \tau_x_y}{\partial x}\right )$
Stress equations :
$\sigma_x = -p - \frac{2\mu}{3}(\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}) + 2\mu\frac{\partial u}{\partial x}$
$\sigma_y = -p - \frac{2\mu}{3}(\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}) + 2\mu\frac{\partial u}{\partial y}$
$\tau_x_y = \mu(\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x})$

Eigenvalue Problems

Forced Vibrations

Support and Cooperation

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