In this tutorial, you will learn how to apply arbitrary loads in Top3d.

Consider a unit cube with 8 nodes (Fig 1 on the left), each node has 3 degrees of freedom. Then the force vector F has the dimension of $latex 24 \times 1$, and it is shown on the right of Fig 1.2017-03-16_08-53-50

Fig 1. Unit Cube

Now applying force at Node 4 and Node 8 with scale 10 on the -y direction. The Force vector F will be all zeros expect at DOF 11 and DOF 23 where are -10

Fig 2. Unit cube with -y load applied

Now considering a load at Node 4 and Node 8 with scale 5 on the direction shown on Fig 3 upper left. The load can be decomposed into x-direction and y-direction as shown on Fig 3 lower left, and the force vector F becomes

Fig 3. Unit cube with arbitrary load applied

To apply the load as shown on Fig 3 in Top3d, you have the following two options:
  • define the load vector F using DOF, or
  • define the load vector F using node coordinates (recommandded)
[expand title="Define F using DOF" expanded="true" tag="h5"] Change Line 22

[matlab firstline="22"]
F = sparse(loaddof,1,-1,ndof,1);
[/matlab]

to

[matlab firstline="22"]
F = sparse(24, 1);
F(10, 1) = 3; % Node 4 x-dir
F(11, 1) = -4; % Node 4 y-dir
F(22, 1) = -3; % Node 8 x-dir
F(23, 1) = -4; % Node 8 x-dir
[/matlab]

[/expand]

[expand title="Define F using node corrdinates (recommandded)" expanded="true" tag="h5"]
Note that the coordinate for Node 4 is $latex (1, 0, 0)$ and Node 8 is $latex (1, 0, 1)$

Change Lines 11-14 to define the load

[matlab firstline="11"]
% USER-DEFINED LOAD DOFs
il = [1 1]; % Nodal x coordinate
jl = [0 0]; % Nodal y coordinate
kl = [0 1]; % Nodal z coordinate
loadnid = kl*(nelx+1)(nely+1)+il(nely+1)+(nely+1-jl); % Node IDs (this mapping function is the same for all problems)
loaddofx = 3loadnid(:) - 2; % DOFx
loaddofy = 3
loadnid(:) - 1; % DOFy
% loaddofz = 3*loadnid(:); % DOFz
[/matlab]

Change the following line

[matlab]
F = sparse(loaddof,1,-1,ndof,1);
[/matlab]

to

[matlab]
F = sparse(ndof, 1);
F(loaddofx,1) = 3;
F(loaddofy,1) = -4;
[/matlab]

[/expand]

In either way, your final load vector will look like this:

[matlab light="true"]
F =
(10,1) 3
(11,1) -4
(22,1) 3
(23,1) -4
[/matlab]