matlab中linear triangle assemble代码
时间: 2023-12-10 13:01:27 浏览: 51
Linear triangle assemble代码是用于在Matlab中进行线性三角形有限元装配的程序。在有限元分析中,装配是指构建整体刚度矩阵和载荷向量的过程,它将每个单元的局部刚度矩阵和载荷向量组装成整体的刚度矩阵和载荷向量。
在Matlab中,线性三角形有限元装配的代码通常包括以下步骤:
1. 首先定义三角形有限元的节点坐标和单元连接关系,建立节点和单元的索引关系。
2. 然后遍历每个三角形单元,计算单元的局部刚度矩阵和局部载荷向量。这通常涉及到对单元的几何信息和材料性质进行计算,例如计算单元的面积、形函数、雅可比矩阵等。
3. 接下来,将每个单元的局部刚度矩阵和载荷向量根据节点索引关系组装成整体的刚度矩阵和载荷向量。这包括根据节点的自由度和单元的自由度将局部矩阵和向量组合成整体矩阵和向量。
4. 最后,根据边界条件和载荷项,进行整体刚度矩阵和载荷向量的修正,得到最终的刚度矩阵和载荷向量。
这样,通过这个线性三角形有限元装配的代码,就能够在Matlab中实现三角形网格的有限元分析,包括构建整体刚度矩阵和载荷向量的过程。这样的代码可以为工程师和科学家提供一个强大的工具,用于求解结构力学、热传导、流体力学等各种工程问题。
相关问题
matlab中MakeERBFilters源代码
以下是MATLAB中的MakeERBFilters源代码:
```matlab
function [filters, freqs] = MakeERBFilters(fs, numChannels, lowFreq)
%[filters, freqs] = MakeERBFilters(fs, numChannels, lowFreq)
%
%Create a set of Gammatone filters spaced according to the Equivalent
%Rectangular Bandwidth ERB. Filters are spaced according to the equation:
%
% ERB = cF
%
%where F is the frequency and c is a constant. Here, c=1.0. Each filter is
%defined by the difference equation:
%
% y[n] = b0*h0*x[n] - a1*y[n-1] - a2*y[n-2]
%
%where x is the input signal, y is the output signal, and h0, b0, a1, and a2
%are constants that define the filter.
%
%ARGUMENTS:
% fs - the sampling rate in Hz.
% numChannels - the number of filters to create.
% lowFreq - the frequency of the lowest filter in Hz.
%
%OUTPUTS:
% filters - a matrix of shape (numChannels, filterLength) where
% filterLength is the number of samples in each filter.
% freqs - a vector of shape (numChannels,) containing the center
% frequency of each filter.
%
%Author: James Lyons 2012
T = 1/fs;
% Change the following parameters if you wish to use a different ERB scale
% Minimum ERB (Hz):
minBW = 25;
% Maximum ERB (Hz):
maxBW = fs/2;
% Set up the centre frequencies.
cf_array=zeros(1,numChannels);
% Centre frequencies based on the hoerl approximation to the ERB formula.
cf=(erbspace(minBW/4,maxBW,numChannels));
cf_array(:)=cf;
% Now create a set of filters to cover the required bandwidth.
% Each loop creates a triangular filter with a bandwidth
% defined by ERB, then convolves it with the previous
% filter to create the next. First filter is a lowpass
% filter to ensure we don't alias when we downsample.
filters=zeros(numChannels,round(4*T*fs));
filterLength = size(filters,2);
% Compute constant coefficients for gammatone filter:
b=zeros(numChannels,3);
a=zeros(numChannels,2);
gain=zeros(numChannels,1);
for i=1:numChannels,
cf = cf_array(i);
ERB = 24.7*(4.37*cf/1000+1); % 24.7 is a constant scaling factor
B = 1.019*2*pi*ERB; % 1.019 is the bandwidth in ERB.
r = exp(-B*T);
theta = 2*pi*cf*T;
b(i,1) = T*T*2*pi*cf/B;
b(i,2) = 0;
b(i,3) = -T*T*2*pi*cf/B;
a(i,1) = -2*r*cos(theta);
a(i,2) = r*r;
gain(i) = abs( (exp(1i*theta)-r)*T ).^2 / (2*pi*cf);
end
% First filter is lowpass:
filters(1,:) = gammatone_lowpass(b(1,:), a(1,:), gain(1), filterLength);
% Remaining filters are created by convolving previous filter with
% triangle filter:
for i=2:numChannels,
ERB = 24.7*(4.37*cf_array(i)/1000+1); % 24.7 is a constant scaling factor
B = 1.019*2*pi*ERB; % 1.019 is the bandwidth in ERB.
filters(i,:) = gammatone_triangle(b(i,:), a(i,:), gain(i), B, filters(i-1,:));
end
% Finally, apply the Hanning window to each filter:
win = hanning(filterLength)';
filters = filters.*repmat(win,numChannels,1);
% compute the frequency response of each filter for plotting purposes:
freqs = cf_array;
```
该函数用于创建一组按等效矩形带宽(ERB)间隔的Gammatone滤波器。滤波器由差分方程定义,并且根据其中心频率,每个滤波器的带宽在等效矩形带宽(ERB)尺度下等间距。函数的输入包括采样率、要创建的滤波器数量以及最低滤波器的频率。函数的输出包括每个滤波器的系数和频率响应。
Triangle类代码
好的,以下是一个简单的Triangle类的代码示例:
```python
class Triangle:
def __init__(self, side1, side2, side3):
self.side1 = side1
self.side2 = side2
self.side3 = side3
def perimeter(self):
return self.side1 + self.side2 + self.side3
def area(self):
# 使用海龙公式计算三角形面积
s = self.perimeter() / 2
return (s * (s - self.side1) * (s - self.side2) * (s - self.side3)) ** 0.5
```
在这个Triangle类中,我们定义了三个属性:side1、side2和side3,它们分别表示三角形的三条边长。我们使用`__init__`方法来初始化这些属性。除此之外,我们还定义了两个方法:`perimeter`用于计算三角形的周长,`area`用于计算三角形的面积。在`area`方法中,我们使用了海龙公式来计算三角形的面积。
当你需要创建一个Triangle对象时,你可以通过传递三角形的三条边长来调用`__init__`方法。例如:
```python
t = Triangle(3, 4, 5)
print(t.perimeter()) # 输出:12
print(t.area()) # 输出:6.0
```