Topology Optimization - How to apply load at different nodes

I am working on a standard code for the topology optimization of a MBB beam as in the figure.The force has to be defined at the upper left corner. The design domain is descretized into finite elements, say 100 elements in the x-direction and 10 elements in the y-direction. Both node numbers and element numbers are numbered column wise from left to right.Now, I want to change the position of code the midpoint of right side end of the beam. How do I do that?

Answer 1

[Anderson Pereira]

Hi Sagar,

If you are refering to the 99-line code, available at https://www.topopt.mek.dtu.dk/Apps-and-software/A-99-line-topology-optimization-code-written-in-MATLAB, the corner nodes are labeled as

upper left corner = 1

bottom left corner = nely+1

upper right corner = (nelx)*(nely+1)+1

bottom left corner = (nelx+1)*(nely+1)

Finally, considering that nely is even, the middle node of the right edge is

midpoint = (nelx)*(nely+1)+1+nely/2

Best,

Anderson

[Sagar Gupta Satrasala]

Thank you for your answer and I am working with the top99 code.I am actually having trouble understanding how the nelx and nely work i.e; upper right corner = (nelx)*(nely+1)+1 in this way. Could you please elaborate and explain me how it works. I am new to matlab and I have difficulties in understanding the code.Also, could you explain me the lines (37-48) and (68 - 69) in the code,

38 function [xnew]=OC(nelx,nely,x,volfrac,dc)

39 l1 = 0; l2 = 100000; move = 0.2;

40 while (l2-l1 > 1e-4)

41 lmid = 0.5*(l2+l1);

42 xnew = max(0.001,max(x-move,min(1.,min(x+move,x.

*sqrt(-dc./lmid)))));

43 if sum(sum(xnew)) - volfrac*nelx*nely > 0;

44 l1 = lmid;

45 else

46 l2 = lmid;

47 end

48 end

68 K = sparse(2*(nelx+1)*(nely+1), 2*(nelx+1)*(nely+1));

69 F = sparse(2*(nely+1)*(nelx+1),1); U = sparse(2*(nely+1)*(nelx+1),1);

[Sagar Gupta Satrasala]

Hi Anderson,

I tried giving this (midpoint = (nelx)*(nely+1)+1+nely/2) for the load but my iterations are not stopping and the optimized beam is not correct. Can you please tell me where I went wrong.

Thank you

[Anderson Pereira]

Hi Sagar,

Lines 37–48 are related to the Optimality criteria based optimizer. Please take a look at the code article:

Sigmund, O. A 99 line topology optimization code written in Matlab. Struct Multidisc Optim 21, 120–127 (2001). https://doi.org/10.1007/s001580050176

Best,

Anderson

[Sagar Gupta Satrasala]

Hi,

I am trying to calculate stress at each element of the beam in the same code and included the code to calculate that inside the while loop(lines 46-48). But I am getting very high stress values. Can anyone please help me to find the reason for that,