How do i find geometry properties of triangles?

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Nasser Ramsis
Nasser Ramsis 2016-12-21
评论： KSSV 2016-12-28
I want to write a code to find the polar moment of inertia of an airfoil. Being a complex shape, a friend suggested a numerical estimate. I wrote a code to create the airfoil geometry and split it up into triangles using delaunay. I now need to find the moment of inertia about x and y for each triangle and use the parallel axis theorem to relate those to the centroid.
I have the delaunay triangulation complete but how can i find the Ix and Iy of each triangle? I don't even know where to start.
here's the code i have:
chord = 0.25; %chord of airfoil
nacanum = 12; % NACA XX## number for the airfoil
t = nacanum/100; %max thickness of airfoil
x=0:0.005:chord; %points along x axis from 0 to chord length
distratio = x/chord; %ratio of points along x to the chord
% function generating top half of airfoil
yt = 5*t*(0.2969*sqrt(distratio)-0.126*distratio-0.3516*distratio.^2+0.2843*distratio.^3-0.1015*distratio.^4);
ytneg=yt*-1; %generatingg bottom half of airfoil
yfull= [yt ytneg]; % full points for y axis of airfoil
y=yfull';
x2=flipud(x);
xfull=[x x2];%full points for x axis of airfoil
x=xfull';
TR=delaunayTriangulation(x,y); %triangulation of the airfoil
triplot(TR,x,y) %plotting the triangulation

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KSSV
KSSV 2016-12-22
You can access x,y coordinates of each triangle like below:
nodes = TR.ConnectivityList ; % nodal connectivity matrix
coor = TR.Points ; % coordinates
ntri = size(nodes,1) ; % number of triangles
% loop for each triangle
for i = 1:ntri
xi = coor(nodes(i,:),1) ; % x coordinates of i'th rriangle
yi = coor(nodes(i,:),2) ; % y coordinates of i'th triangle
% do what you want
end
But let me tell you, your mesh of air foil is very bad. I suggest you to go through the following meshing package: https://in.mathworks.com/matlabcentral/fileexchange/25555-mesh2d-automatic-mesh-generation
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Nasser Ramsis
Nasser Ramsis 2016-12-27
yeah that was me who posted. unfortunately I'm not good enough at matlab to do so.
KSSV
KSSV 2016-12-28
Check with this link: http://people.sc.fsu.edu/~jburkardt/m_src/mesh2d/mesh2d.html
tsearch problem, can be sorted by minor editing the code. I have done it very long ago, if I get time I will check it. Mean while go through the above link.

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