Defining nodal coordinates for a 3D cubic lattice.

Hi,

I wish to create a 3D lattice formed by joining together many 8-node cubic elements (see figure). I wish to define the number of cubic elements I want in the x, y and z direction whilst also being able to obtain the coordinates for each node in an array C. Where C(:,1) refers to the x coordinates, C(:,2) refers to the y and C(:,3) to the z and where C(1,:) refers to the first node, C(2,:) the second etc.

My script thus far is attached. I am struggling with two key issues:

1. Creating a loop that adds additional elements with the correct node assignments.
2. Assuring that the code is robust such that the entire structure maintains its cubic/cuboidal shape despite varying user inputs.

Any help would very much be appreciated.

Sam

Note: The figure represents the desired output when the user defines 2 elements in the x, y and z axis.

Note: This figure denotes the preferred node arrangement for a 3x2x1 cubic lattice.

Answer 1

[Samuel Thompson]

For those who this may be useful, I modified a code provided from another MATLAB user, Marten for ease of use. https://uk.mathworks.com/matlabcentral/fileexchange/48373-stl-lattice-generator?s_tid=srchtitle

Find the code attached.

[MD SHARIER]

It doesn't seem to be working.Is there any updated version of it?

[DGM]

Looks like it works just fine to me.

%% CUBE COORDINATE MAPPING TRIALS
clc
clearvars

O = [0 0 0];% origin
Nx = 3;     % defines number of elements in x direction
Ny = 3;     % defines number of elements in y direction
Nz = 3;
Lx = 1;     % defines length of single element in x direction
Ly = 1;     % defines length of single element in y direction
Lz = 1;     % defines length of single element in z direction

%% COORDINATES FOR BODY-CENTERED CUBIC (BCC) ELEMENT
nodes = [O; O(1)+Lx, O(2), O(3); O(1)+Lx, O(2)+Ly, O(3); O(1), O(2)+Ly, O(3);...
    O(1), O(2), O(3)+Lz; O(1)+Lx, O(2), O(3)+Lz; O(1)+Lx, O(2)+Ly, O(3)+Lz;...
    O(1), O(2)+Ly, O(3)+Lz; O(1)+Lx/2, O(2)+Ly/2, O(3)+Lz/2];

no_nodes = length(nodes); 

%% LATTICE NODES
% cell replication - produce every node in lattice (including duplicates)
for nix=1:Nx-1  %Modified to include variable number of nodes for each cell type
    for i=1:no_nodes
        nodes(no_nodes+no_nodes*(nix-1)+i,:)=[nodes(i,1)+nix*Lx,nodes(i,2),nodes(i,3)];
    end
end
for niy=1:Ny-1
    for i=1:no_nodes*Nx
        nodes(no_nodes*Nx+no_nodes*Nx*(niy-1)+i,:)=[nodes(i,1),nodes(i,2)+niy*Ly,nodes(i,3)];
    end
end
for niz=1:Nz-1
    for i=1:no_nodes*Nx*Ny
        nodes(no_nodes*Nx*Ny+no_nodes*Nx*Ny*(niz-1)+i,:)=[nodes(i,1),nodes(i,2),nodes(i,3)+niz*Lz];
    end
end

%% Remove duplicate nodes
[C,~,~]=unique(nodes,'rows');

%% SCATTER NODES
figure
scatter3(C(:,1),C(:,2),C(:,3),'rx');
hold on
C1 = C(:,1); C2 = C(:,2); C3 = C(:,3);

for k=1:length(C)
    text(C1(k),C2(k),C3(k),num2str(k))
end

daspect([1 1 1])
xlabel('xaxis'); ylabel('yaxis'); zlabel('zaxis');

% xlim([-0.5*L,Nx])
% ylim([-0.5*L,Ny])
% zlim([-0.5*L,2])