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 , and it is shown on the right of Fig 1.

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)

##### Define** F **using DOF

F = sparse(loaddof,1,-1,ndof,1);

to

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

##### Define** F **using node corrdinates (recommandded)

Change Lines 11-14 to define the load

% 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 = 3*loadnid(:) - 2; % DOFx loaddofy = 3*loadnid(:) - 1; % DOFy % loaddofz = 3*loadnid(:); % DOFz

Change the following line

F = sparse(loaddof,1,-1,ndof,1);

to

F = sparse(ndof, 1); F(loaddofx,1) = 3; F(loaddofy,1) = -4;

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

F = (10,1) 3 (11,1) -4 (22,1) 3 (23,1) -4