## Deforming sheet into conical structure

I am trying to deform a flat sheet into a conical structure using MATLAB. (Pls see the image below)

L = length of sheet; R= bigger radius; r = smaller radius

Here’s my approach:

First i create an upward ramp (as shown in the image above), with a displacement in z-direction given by:

u_1 = r/L * (pi-1) * x

2. Then curve the edges of rectangular sheet into the conical form, given by displacements:

3. Hence the net displacement of any point becomes u_1 + u_2.

I have written this as a matlab code:

for i=1:length(A)

A(i,2) = A(i,2) + (sqrt(2*A(i,3)*r – A(i,3)*A(i,3))-A(i,2))*(A(i,1)/L);

A(i,3) = A(i,3) + ((r/L)*(pi-1)*(A(i,1)) + (R-sqrt(R*R – A(i,2)*A(i,2))*(1-(A(i,1)/L))) + ((R-r)+ (2/pi)*A(i,2))*(A(i,1)/L));

A here is the matrix with initial coordinates of the flat sheet. Then using a for loop, i apply the u_1 + u_2 displacement, changing the y and z coordinates of the sheet.

However, after running the code, i get one side to be very nicely fitting the curvature of the cone, whereas on the other side, all the points coincide at one single point rather than forming a circular face. Please see the images below.

Original flat sheet

Curved conical sheet with the issue

Can someone please help me with this?I am trying to deform a flat sheet into a conical structure using MATLAB. (Pls see the image below)

L = length of sheet; R= bigger radius; r = smaller radius

Here’s my approach:

First i create an upward ramp (as shown in the image above), with a displacement in z-direction given by:

u_1 = r/L * (pi-1) * x

2. Then curve the edges of rectangular sheet into the conical form, given by displacements:

3. Hence the net displacement of any point becomes u_1 + u_2.

I have written this as a matlab code:

for i=1:length(A)

A(i,2) = A(i,2) + (sqrt(2*A(i,3)*r – A(i,3)*A(i,3))-A(i,2))*(A(i,1)/L);

A(i,3) = A(i,3) + ((r/L)*(pi-1)*(A(i,1)) + (R-sqrt(R*R – A(i,2)*A(i,2))*(1-(A(i,1)/L))) + ((R-r)+ (2/pi)*A(i,2))*(A(i,1)/L));

A here is the matrix with initial coordinates of the flat sheet. Then using a for loop, i apply the u_1 + u_2 displacement, changing the y and z coordinates of the sheet.

However, after running the code, i get one side to be very nicely fitting the curvature of the cone, whereas on the other side, all the points coincide at one single point rather than forming a circular face. Please see the images below.

Original flat sheet

Curved conical sheet with the issue

Can someone please help me with this? I am trying to deform a flat sheet into a conical structure using MATLAB. (Pls see the image below)

L = length of sheet; R= bigger radius; r = smaller radius

Here’s my approach:

First i create an upward ramp (as shown in the image above), with a displacement in z-direction given by:

u_1 = r/L * (pi-1) * x

2. Then curve the edges of rectangular sheet into the conical form, given by displacements:

3. Hence the net displacement of any point becomes u_1 + u_2.

I have written this as a matlab code:

for i=1:length(A)

A(i,2) = A(i,2) + (sqrt(2*A(i,3)*r – A(i,3)*A(i,3))-A(i,2))*(A(i,1)/L);

A(i,3) = A(i,3) + ((r/L)*(pi-1)*(A(i,1)) + (R-sqrt(R*R – A(i,2)*A(i,2))*(1-(A(i,1)/L))) + ((R-r)+ (2/pi)*A(i,2))*(A(i,1)/L));

A here is the matrix with initial coordinates of the flat sheet. Then using a for loop, i apply the u_1 + u_2 displacement, changing the y and z coordinates of the sheet.

However, after running the code, i get one side to be very nicely fitting the curvature of the cone, whereas on the other side, all the points coincide at one single point rather than forming a circular face. Please see the images below.

Original flat sheet

Curved conical sheet with the issue

Can someone please help me with this? deformation MATLAB Answers — New Questions