本程序是基于弹性力学与有限元课程的要求,实现有限元程序的计算部分。本项目使用 MATLAB 编程,以期达到运行效率与开发效率兼顾的目的。项目成员如下:
- 张泽凡
- 黄鹤飞
- 王政荣
- 王艺杰
- 张家豪
- 梅杰
FEM/
├── doc
│ ├── FEM原理说明.docx
│ ├── nabook.pdf
│ ├── painless-conjugate-gradient.pdf
│ └── 集成.docx
├── img
│ ├── WBS.jpg
│ ├── 数据流程图-0.1.jpg
│ ├── 数据流程图-0.1.vsdx
│ └── 甘特图.png
├── input
│ ├── sam1.0
│ │ ├── boundaryCondition.dat
│ │ ├── elementCoordinates.dat
│ │ ├── elementTopology.dat
│ │ ├── forceCondition.dat
│ │ ├── materials.dat
│ │ └── old.7z
│ └── Sample
│ ├── Readme.pdf
│ ├── Sample.fem
│ ├── Sample.mat
│ ├── Sample.pqu
│ └── Sample.uvw
├── LICENSE
├── main.m
├── output
│ ├── element_displacement_big.dat
│ ├── element_displacement.dat
│ ├── element_stress_big.dat
│ └── element_stress.dat
├── README.md
└── src
├── calElementStiffnessMatrix.m
├── calMatrixB.m
├── calMatrixD.m
├── calWholeStiffnessMatrix.m
├── calWholeStiffnessMatrixSparse.m
├── elementDisplacement.m
├── elementStrain.m
├── elementStress.m
├── openKspeace.m
├── processConstraint.m
├── processConstraintSparse.m
├── processForce.m
├── processForceSparse.m
├── solveEquation2.m
├── solveEquation.m
└── utils
├── calAera.m
└── conjugateGradient.m
统一采用 UTF-8 编码
结点个数
n
单元个数
m
全部结点坐标
all_element_X / n * 1
all_element_Y / n * 1
单元拓扑表
unit_topology_table / m * 3
所在行数即为单元的编号
约束
bound / 约束个数 * 3
代表: 点号 x/y(1/2) 位移大小
结点坐标
coord / n * 2
外力条件
P / n * 2
n为结点个数,每一行为"x y",行数对应结点号,x为x方向上力
单元材料
materials / m * 2
材料,输入为m行,m为单元个数,每一行为"e u"
单个单元的坐标使用两个列向量,依次为 i j m
double element_X / 三行,一列 3 * 1
double element_Y / 三行,一列 3 * 1
单元刚度阵k
element_k / 6 * 6
B矩阵
double matrixB / 3 * 6的矩阵
整体刚度阵K的储存
K 为一维数组 长度未知 下三角矩阵的值
K_info 储存主对角元在K中的位置 1 * n
整体的位移
whole_displacement / 2n * 1
calMatrixB.m / 计算 B 矩阵
calMatrixD.m / 计算 D 矩阵
openKspeace.m / 计算一维半带宽方法下的整体的劲
/ 度矩阵K中所包含的元素个数
calArea.m / 返回三角形单元的面积
calElementStiffnessMatrix.m / 返回单元的劲度矩阵
calWholeStiffnessMatrix.m / 计算一维半带宽方法下的整体的劲度矩阵K
calWholeStiffnessMatrixSparse.m / 计算稀疏矩阵方法下的整体的劲度矩阵K
elementStrain.m / 计算单元应变
elementStress.m / 计算单元应力
elementDisplacement.m / 通过整体结点位移计算各个单元的节点位移
processConstraint.m / 对 K 进行处理,使其满足约束
processConstraintSparse.m / 函数对K进行处理,使其满足约束
/ 用于稀疏矩阵方法
processForce.m / 对P进行处理,使其满足约束
processForceSparse.m / 函数对P进行处理,使其满足约束
/ 用于稀疏矩阵方法
solveEquation.m / 直接法解整体结点平衡方程
solveEquation2.m / 迭代法求解方程
开头小写、驼峰命名法
unitArea.m
unitStiffnessMatrix.m
开头小写、驼峰命名法
变量 下划线链接,小写
element_displacement
whole_displacement
常量 全部大写
E
直接法用时:
Elapsed time is 716.791396 seconds.
迭代法用时:
Elapsed time is 42.631346 seconds.
716.791396 / 42.631346
ans =
16.8137
Copyright 2016
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program; If not, see
http://www.gnu.org/licenses