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How to apply arbitrary loads in Top3d

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 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)
Define F using DOF
Change Line 22

  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)
Note that the coordinate for Node 4 is (1, 0, 0) and Node 8 is (1, 0, 1)

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
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