Shape optimization by the homogenization method
44
Transcript of Shape optimization by the homogenization method
![Page 1: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/1.jpg)
![Page 2: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/2.jpg)
![Page 3: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/3.jpg)
![Page 4: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/4.jpg)
![Page 5: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/5.jpg)
![Page 6: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/6.jpg)
![Page 7: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/7.jpg)
![Page 8: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/8.jpg)
![Page 9: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/9.jpg)
![Page 10: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/10.jpg)
![Page 11: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/11.jpg)
![Page 12: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/12.jpg)
![Page 13: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/13.jpg)
![Page 14: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/14.jpg)
![Page 15: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/15.jpg)
![Page 16: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/16.jpg)
![Page 17: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/17.jpg)
![Page 18: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/18.jpg)
![Page 19: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/19.jpg)
![Page 20: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/20.jpg)
![Page 21: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/21.jpg)
![Page 22: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/22.jpg)
![Page 23: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/23.jpg)
![Page 24: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/24.jpg)
![Page 25: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/25.jpg)
![Page 26: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/26.jpg)
![Page 27: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/27.jpg)
![Page 28: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/28.jpg)
![Page 29: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/29.jpg)
![Page 30: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/30.jpg)
![Page 31: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/31.jpg)
![Page 32: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/32.jpg)
![Page 33: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/33.jpg)
![Page 34: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/34.jpg)
![Page 35: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/35.jpg)
![Page 36: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/36.jpg)
![Page 37: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/37.jpg)
Iterations
Perf
orm
ance
0 10 20 305 15 25
0.4
0.5
0.35
0.45
![Page 38: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/38.jpg)
Iterations
Perf
orm
ance
0 10050 150
0.35
0.36
0.37
0.355
0.365
0.375 With filtering Without filtering
![Page 39: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/39.jpg)
![Page 40: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/40.jpg)
0 10050 1501
1.1
1.2
1.3
1.4
1.5
Relaxation Convexification Penalizing from the start
beginning of the penalization
Iterations
Perf
orm
ance
![Page 41: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/41.jpg)
![Page 42: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/42.jpg)
![Page 43: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/43.jpg)
![Page 44: Shape optimization by the homogenization method](https://reader034.fdocuments.net/reader034/viewer/2022052419/586e0cbb1a28abdd018b63d4/html5/thumbnails/44.jpg)