How do i find geometry properties of triangles?

Asked by Nasser Ramsis

Nasser Ramsis (view profile)

on 21 Dec 2016
Latest activity Commented on by KSSV

KSSV (view profile)

on 28 Dec 2016
Accepted Answer by KSSV

KSSV (view profile)

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

KSSV (view profile)

on 22 Dec 2016

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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KSSV

KSSV (view profile)

on 26 Dec 2016
that is a version problem...the same error is discussed there in the link, you can correct it.
Nasser Ramsis

Nasser Ramsis (view profile)

on 27 Dec 2016
yeah that was me who posted. unfortunately I'm not good enough at matlab to do so.
KSSV

KSSV (view profile)

on 28 Dec 2016
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.