How to export 3D spheres (3D plot) generated in Matlab to ANSYS or Abaqus. ?

 I want to export 3D spheres generated in Matlab to ANSYS or Abaqus. 3D spheres are randomly generated and I want to mesh the 3D spheres and analyse those. Can anyone help me to export the 3D sphere plot to any meshing software like Gmsh or Ansys or Abaqus?

[Anton Semechko]

The spheres in your image, are they represented by level-sets of an implicit function?

[Sadeep Thilakarathna]

Hi..These spheres are randomly generated such that they do not overlap.ellipsoid function in Matlab is used.

Answer 1

[Anton Semechko]

The builtin 'ellipsoid' and 'sphere' functions produce bad quality meshes (in terms of element shapes and connectivity of the vertices). You can get much better quality meshes using functions from here.

Here are is an example:

% Unit sphere based on subdivision of an icosahedron; triangular mesh
TRa=SubdivideSphericalMesh(IcosahedronMesh,4);

% Unit sphere based on subdivision of a cube; quadrilateral mesh
TRb=SubdivideSphericalMesh(QuadCubeMesh,4);

% Visualize
figure('color','w')
subplot(1,3,1)
h=trimesh(TRa); 
set(h,'EdgeColor','k','FaceColor',[0.9 0.9 0.9],'EdgeAlpha',0.5);
axis equal off vis3d
view([30 30])
zoom(1.5)
avp=GetAxesViewProps(gca);

ha=subplot(1,3,2);
h=patch(TRb); 
set(h,'EdgeColor','k','FaceColor',[0.9 0.9 0.9],'EdgeAlpha',0.5);
axis equal off vis3d
MatchAxesView(avp,ha)

% Plot sphere generated with built-in 'sphere' function for comparison
ha=subplot(1,3,3);
[X,Y,Z]=sphere(20);
h=surf(X,Y,Z);
set(h,'EdgeColor','k','FaceColor',[0.9 0.9 0.9],'EdgeAlpha',0.5);
axis equal off vis3d
MatchAxesView(avp,ha)

Functions 'GetAxesViewProps' and 'MatchAxesView' used in this example can be downloaded from here.

1) When exporting the meshes, do you want the program to recognize the individual spheres or would it be OK if the their face-vertex connectivity lists were merged (so you would have a single mesh containing multiple disconnected spheres)?

2) What type of meshes will you be generating after exporting the spheres; hexahedral or tetrahedral?

[Sadeep Thilakarathna]

Thank You very much for the Answer. What I want to do is to model a concrete cube with embedded aggregates. I want to analyze it in FEM software like ANSYS, Abaqus or LS Dyna with suitable material models. If I can export the geometry to those software, I think meshing can be done in the software or meshed geometry can be imported in to the software. Please let me know if you know a method to do this.

1. It is okay if it is a single mesh containing multiple disconnected spheres. 2. Tetrahedral or hexahedral. Either is fine.

Thank you again.

[Anton Semechko]

Below is an example of how you can export multiple spheres to a .msh file (Gmsh standard). Assuming you already got the functions for generating spheres from here, for this example to work, you will also need to get functions 'gmsh_mesh2d_write.m' and 'mesh_base_one.m' from here. Let me know if you run into any problems.

function sphere_mesh_export_demo

% Suppose you have N spheres. Let C and R be N-by-3 and N-by-1 arrays
% containing centroid coordinates and radii of the spheres, respectively.
% As an example, I will use N=10, R=linspace(0.1,0.3,N), and distribute 
% spheres along the x-axis without them touching one another.
N=10;
R=1:N;
C=zeros(N,3); % initialize centroid coordinates
ds=min(R)/10; % separation between closest points on two adjacent spheres
for n=2:N
    C(n,1)=C(n-1,1) + R(n-1) + R(n) + ds;
end

% Step 1: Get mesh of a unit sphere 
n_sub=4;                                              % number of icosahedron subdivisions 
TRo=SubdivideSphericalMesh(IcosahedronMesh,n_sub);    % mesh will have Nv=10*4^n_sub+2 vertices and Nf=2*Nv-4 faces
[Fo,Vo]=GetMeshData(TRo);                             % Fo is a Nf-by-3 array of faces and Vo is a Nv-by-3 array of vertex coordinates  

% Step 2: Generate a composite mesh with spheres distributed accroding to C and R
Nv=size(Vo,1);
[F,V]=deal(cell(N,1));
for n=1:N    
    V{n}=bsxfun(@plus,R(n)*Vo,C(n,:));                % scale and translate TRo to get a sphere with radius R(n) and centroid C(n,:)
    F{n}=Fo+(n-1)*Nv;                                 % face-vertex connectivity of the n-th sphere 
end
V=cell2mat(V);                                        % compposite list of vertices 
F=cell2mat(F);                                        % composite list of faces

% Visualize result
figure('color','w')
h=patch('Faces',F,'Vertices',V);
set(h,'EdgeColor','none','FaceColor',0.75*[1 1 1],'FaceAlpha',0.5);
axis equal off
camlight('headlight')
lighting phong
material('dull')
%keyboard

% Step 3: Export mesh represented by F and V to a .msh file (Gmsh standard)
FileName='SphereMeshDemo.msh';
gmsh_mesh2d_write(FileName,...
                  3,...
                  size(V,1),...
                  V',...
                  3,...
                  size(F,1),...
                  F');

[Sadeep Thilakarathna]

Thank you very much for the code. I tried to run this in Matlab. code runs fine and the 'SphereMeshDemo' .msh file is generated using the above code. However, when I try to open this in Gmsh, an error popos up and the geometry is not shown. I have attached the error. Could you please suggest a possible solution for this. Thanks

[Anton Semechko]

OK. Let's export mesh to a .stl file. To do this, change code under step 3 to:

FileName='SphereMeshDemo.stl';
stlwrite(FileName,F,V)

You can get 'stlwrite' function here.

Ignore that 'stlwrite' will say 'Wrote 3 faces'. It exports the mesh correctly (see snapshot below). If you want to correct this export status bug, change line (inside 'stlwrite') that reads:

fprintf('Wrote %d faces\n',size(faces, 2));

to

fprintf('Wrote %d faces\n',size(faces, 1));

[Sadeep Thilakarathna]

Hi, Thank you very much for the code again. I have imported the stl file in to Abaqus as shown in the figure. Your method works. However it is in 2D and I want solid spheres. So, I think it is suitable to develop spheres in Abaqus or Ansys using the coordinates and radius data saved in an excels file using Matlab. Thanks.

[Anton Semechko]

I was under the assumption that you were going to be using surface meshes as input to generate volumetric tet meshes in the program of your choice. If you want, you can also generate tet meshes directly in Matlab using 'iso2mesh' toolbox. 's2m' is name of the function you want to be using. Description of this function can be found here .

[Sadeep Thilakarathna]

Yes...I wanted to generate volumetric meshes in Abaqus. However, when the a surface mesh is imported in to software, it cannot be remeshed. There is a plugin to convert the mesh in to the geometric model again in Abaqus. However, when it is converted to the geometry it will become a surface and volumetric meshes cannot be applied to the model. Thank you very much for the solutions you gave me. I will try to use the iso2mesh as well.

[Biltu Mahato]

How did you assign material properties to .stl file? Abaqus doesn't let me assign material properties in Abaqus for .stl file imported from Matlab.