Pipe elbow creation using MATLAB code

Hi

I am done with my MATLAB code which creates as many straight pipes I want. However, I want to connect them using pipe elbow looks like below. Any idea how to create this elbow in MATLAB?

[John D'Errico]

What does CREATING it mean? As after all, you already have a picture of what you want, and MATLAB is not a tool I would probably use to drive a CNC mill. A 90 degree elbow like that might be a difficult project to make anyway, even if I did have a million dollars of tooling on hand. Anyway, a pipe elbow like that would probably be formed using a hot extrusion process, and then bent into shape. And that means if I did want to create that object, a pipe bender would be the tool of choice. Just throw some heavy duty hydraulics at the problem.

Ok, that is all irrelevant, since I assume you want to make something in MATLAB, purely for graphics purposes. And for that, you already have all the curve radii, so all you needs are some circle segments, unless you also want pretty shading and lighting.

So what are you looking for here?

[Md Mia]

Thanks. Here is the way I tried to model the elbow using MATLAB. My target is to attach two pipes with this 90 degree elbow. At first I modleed a bent curve (basically the center line of the elbow - blue line in the fig below). Now knowing the x,y,z coordiantes of the points on the curve, I created 3d circles along those points and it looks like below. However, when I was trying to connect it with first straight pipe, it's not working. Is there any mistake I am doing during elbow modeling.

%% elbow inputs

pipe_size = 25.4; % in mm

d_outside = 33.4; % in mm

A = 38; % in mm (center-to-end distance) % Ref. 1 (page 16, Table 3)

% long radius elbow is used where radius of curvature is greater than pipe diamter (>= 1.5*pipe diamater)

% For 90° Long Radius elbows, center to end dimension given in dimension tables of ASME B16.9 is same as radius of elbow (Ref. 2)

x1 = 2100; % left_pipe_end_x

y1 = 0.00; % left_pipe_end_yo

x2 = 2138; % right_pipe_end_x

y2 = -38; % right_pipe_end_y

R = 38; % radius of curvature in mm

%% now let's calculate center point (x0,y0)

syms x0 y0

eq1 = R^2-((x0-x1)^2 + (y0-y1)^2);

eq2 = R^2-((x0-x2)^2 + (y0-y2)^2);

sol=solve([eq1,eq2,x0<=x1,y0<=y2],[x0,y0]);

x_c = double(sol.x0)

y_c = double(sol.y0)

%(x0,y0) = (2138,0)

%% other points

x = linspace(x1,x2,50);

x = x';

for i = 1:length(x)

x1 = x(i);

eqa1 = @(y) R^2 - ((x_c-x1)^2 + (y_c-y)^2);

format long g

y_l = [0 -38];

y(i) = fzero(eqa1,y_l);

end

y = y';

final_mat = [x,y];

plot(final_mat(:,1), final_mat(:,2), 'b-', 'LineWidth', 2)

hold on

load output;

for i = 1:length(final_mat(:,1))

[x_value{i},y_value{i},z_value{i}] = plotCircle3D ([x(i),y(i),0], [1,0,0], d_outside/2, n_ele_circum);

end

function [x_value,y_value,z_value] = plotCircle3D(center, normal, radius, n_ele_circum)

d_theta = 2*pi/n_ele_circum; % increment size

theta = 0:d_theta:(2*pi-d_theta); % in radian

v=null(normal);

points=repmat(center',1,size(theta,2))+radius*(v(:,1)*cos(theta)+v(:,2)*sin(theta));

plot3(points(1,:),points(2,:),points(3,:),'r-');

x_value = points(1,:);

y_value = points(2,:);

z_value = points(3,:);

end

Answer 1

[John D'Errico]

What is not working? Why do you think it is not working?

I would conjecture that one problem you have is you cannot model a 90 degree elbow as you tried to do. Your circles are drawn always parallel to each other. And that MUST be incorrect.

A second problem is you are drawing only circles. They will have no connection to each other along the length of the elbow. And that two will be a problem. So do this better by drawing a true surface, as what I would call a 2-manifold. Setting it up to follow a curve in space is a good idea.

The nice thing is, this makes it also trivial to generate a series of pipes, because the cylinder code I wrote does not care if the centerline path is a linear segment or a circular arc. For example

[pipe1x,pipe1y,pipe1z] = generalCylinder([-1 1 0;0 1 0],0.25,50);
[pipe2x,pipe2y,pipe2z] = generalCylinder([1 0 0;1 -1 0],0.25,50);
phi = linspace(0,pi/2)';
elbowarcxyz = 1*[cos(phi),sin(phi),zeros(numel(phi),1)];
[elbowx,elbowy,elbowz] = generalCylinder(elbowarcxyz,0.25,50);

H1 = surf(pipe1x,pipe1y,pipe1z);
hold on
H2 = surf(pipe2x,pipe2y,pipe2z);
H3 = surf(elbowx,elbowy,elbowz);
H1.FaceColor = 'b';
H2.FaceColor = 'g';
H3.FaceColor = 'r';
box on
hold off
axis equal

I attached generalCylinder to this answer.

Now all you need do is create a centerline path through space, and then use the cylinder code to build the cylinder as a surface that follows that path.

[Md Mia]

Thank you so much for sharing the function and code. Some points to metntion here:

Comment: "A second problem is you are drawing only circles. They will have no connection to each other along the length of the elbow. And that two will be a problem. So do this better by drawing a true surface, as what I would call a 2-manifold. Setting it up to follow a curve in space is a good idea."

Answer: Basically these circles have points which are recorded in matlab. Later I defined four noded shell element connecting these nodes.

Comment: "Your circles are drawn always parallel to each other. And that MUST be incorrect".

ANswer: In 3d plot, its better understnadable. It was shown in 2d. Later the nodes on the circles are connected using four noded shell element.

Finally, the way you showed to create elbow with pipes seems excellent to me. Just a quick question, if I used this code and say developed pipes and elbow, will I be able to still use shell element as it's must in our project. If so, how I can do that. I am using LSDyna as fem software. Thanks.

[John D'Errico]

A surface as surf creates is already directly composed of 4-node shell elements. For example:

[X,Y] = meshgrid(1:5);
Z = (X-Y).*(X+Y);
surf(X,Y,Z)

So here 16 quad shell elements are seen.

[Md Mia]

Thank you so much for the clarification.

[Md Mia]

Hi

I need a help from you again. I was using your sent code to form elbow with pipes. Could you please tell me what should be elbowarcxyz in my case where A(2100,0,0) and B(2138,-38,0). My code is as below:

[pipe1x,pipe1y,pipe1z] = generalCylinder([0 0 0;2100 0 0],33.4/2,26);

[pipe2x,pipe2y,pipe2z] = generalCylinder([2138 -38 0;2138 -2138 0],33.4/2,26);

phi = linspace(0,pi/2)';

elbowarcxyz = ???????*[cos(phi),sin(phi),zeros(numel(phi),1)]; % (STUCK IN THIS LINE)

[elbowx,elbowy,elbowz] = generalCylinder(elbowarcxyz,33.4/2,26);

H1 = surf(pipe1x,pipe1y,pipe1z);

hold on

H2 = surf(pipe2x,pipe2y,pipe2z);

H3 = surf(elbowx,elbowy,elbowz);

H1.FaceColor = 'b';

H2.FaceColor = 'g';

H3.FaceColor = 'r';

box on

hold off

axis equal

[Md Mia]

I figured it out and solved it. I found that I made mistake in defining the elbow center. However, thanks for your (@John D'Errico) generalcylinder function. I highly appreciate it.