Table 2 Sensitivity values evaluated through the adjoint formulation and the finite difference method

From: Topology optimization of shape memory polymer structures with programmable morphology

Element no. Adjoint sensitivities Finite difference sensitivities Normalized error (× 10− 6)
1 − 0.2416477 − 0.2416476 0.482
2 − 0.0000000 − 0.0000001
3 0.2416477 0.2416475 1.07
4 − 0.2543351 − 0.2543351 0.00
5 0.0000000 0.0000000 0.00
6 0.2543351 0.2543350 0.599
7 − 0.2375154 − 0.2375154 0.00
8 0.0000000 0.0000000 0.00
9 0.2375154 0.2375153 0.516
10 − 0.2225283 − 0.2225282 0.376
11 0.0000000 0.0000000 0.00
12 0.2225283 0.2225281 0.661
13 − 0.2038087 − 0.2038086 0.359
14 0.0000000 0.0000000 0.00
15 0.2038086 0.2038085 0.619
16 − 0.1844918 − 0.1844917 0.539
17 − 0.0000001 − 0.0000001 0.00
18 0.1844916 0.1844915 0.563
19 − 0.1650572 − 0.1650571 0.244
20 − 0.0000010 − 0.0000010 0.00
21 0.1650567 0.1650565 0.793
22 − 0.1456293 − 0.1456293 0.00
23 − 0.0000042 − 0.0000041
24 0.1456292 0.1456291 0.818
25 − 0.1262059 − 0.1262059 0.00
26 − 0.0000104 − 0.0000104 0.00
27 0.1262118 0.1262119 0.958
28 − 0.1067716 − 0.1067717 0.454
29 − 0.0000017 − 0.0000017 0.00
30 0.1068102 0.1068101 0.441
31 − 0.0873091 − 0.0873091 0.00
32 0.0001378 0.0001379 82.9
33 0.0874321 0.0874320 1.46
34 − 0.0678103 − 0.0678104 0.276
35 0.0008085 0.0008084 55.2
36 0.0680543 0.0680542 0.724
37 − 0.0488513 − 0.0488514 1.12
38 0.0027865 0.0027864 1.30
39 0.0480513 0.0480513 0.00
40 − 0.0302951 − 0.0302951 0.00
41 0.0042528 0.0042528 0.00
42 0.0250887 0.0250886 2.65
43 − 0.0388250 − 0.0388251 0.415
44 − 0.0123738 − 0.0123738 0.00
45 0.0027180 0.0027181 18.5