Post on 23-Feb-2022
Topology optimization as structural form findingRick van Dijk - 4373618
p5Committee:Dr. ir. Pirouz Nourian – AE+T / Design informaticsDr. ir. Matthijs Langelaar – 3ME / Structural optimization and mechanics
Index
01
1. Research framework
2. What is Topology Optimization?
3. Toy problems
4. Results
5. Conclusions
01Topology Optimization
02
01Topology Optimization
02
Make a tower that:
• Does not fall
• Is 16 blocks high
• Has a rectangular shape
01Topology Optimization
02
Make a tower that:
• Does not fall
• Is 16 blocks high
• Has a rectangular shape
48 blocks!
01Topology Optimization
03
Make a tower that:
• Does not fall
• Is 16 blocks high
• Has a rectangular shape
32 blocks!
01Topology Optimization
04
Make a tower that:
• Does not fall
• Is 16 blocks high
• Has a rectangular shape
24 blocks!
01Background
05>Earthy result
01Background
06
01Background
06
01Background
06
01Background
07
01The main problem
08
“Topology optimization is an often-used method to generate complex shapes with a maximized stiffness and little volume. Implementations in (masonry) architecture look promising but requires the implementation
of density dependent forces”.
01Objective
09
Inputs of topology optimization:
- Structural- Heat distribution- Water flow
Topology optimization in buildings:
- Structural- Preset forces / Area loads- Self weight- Snow loads- Wind loads
01Objective
09
Inputs of topology optimization:
- Structural- Heat distribution- Water flow
Topology optimization in buildings:
- Structural- Preset forces / Area loads- Self weight- Snow loads- Wind loads
01Objective
10
Implement density dependent forces in topology optimization and apply this algorithm to buildings.
01Sub objectives
11
create a working topology optimization methodology and translate this in the form of an algorithm.
implement density dependent forces in the methodology and in the algorithm.
translate the methodology and the algorithm to 3D geometry.
01Research framework
12
01Methodology
13
01Methodology
14
create a working topology optimization methodology and translate this in the form of an algorithm.
implement density dependent forces in the methodology and inthe algorithm.
translate the methodology and the algorithm to 3D geometry.
01Methodology
15
“create a working topology optimization methodology and translate this in the form of an algorithm.”
TOY1• Get TopOp to work in Rhino• User-Inputs
ForcesSupportsNumber of elements
• Implement the existence of voids• User-based input of voids
01Methodology
16
“create a working topology optimization methodology and translate this in the form of an algorithm.”
TOY2• Implement area loads• A void indexing system
Multiple voidsComplex design spaces
• Forces inside the design space• User-input for these “rooms”
01Methodology
17
“implement density dependent forces in the methodology and in the algorithm.”
TOY3• Implement self weight in the algorithm• Define sizes of self weight
01Methodology
18
“implement density dependent forces in the methodology and in the algorithm.”
TOY4• Apply area loads dependent on the roof shape• Implement a roofing constraint
01Methodology
19
“translate the methodology and the algorithm to 3D geometry.
TOY5• Implement an indexing system• Handle inputs, including voids• Algorithm optimization
01Methodology
20
“translate the methodology and the algorithm to 3D geometry.
TOY6• Implement density dependent forces• Implement roof constraint• Explore possibilities in architecture
02What is topology optimization?
21
03Literature
22
(Bensoe & Sigmund, 2003)
03Literature
23
(Sigmund, 1999)
𝑐 𝑥 𝑈 𝐾𝑈
Minimize compliance
min 𝑥:Subject to:
::
𝑉 𝑥𝑉 𝑣𝑜𝑙𝑓𝑟𝑎𝑐
𝐾𝑈 𝐹0 𝑥 𝑥 1
03Literature
24
Define the problem
(Bensoe & Sigmund, 2003)
03Literature
25
Finite element analysis
(Bensoe & Sigmund, 2003)
03Literature
26
(Bathe, 2006)
𝑘𝐹 𝐹
𝑈 𝑈
𝐾𝑈 𝐹
𝑖 𝑗
𝐾 𝑘 𝑘𝑘 𝑘
𝑘 𝑘𝑘 𝑘
𝑈𝑈
𝐹𝐹
03Literature
27
Sensitivity analysis
(Bensoe & Sigmund, 2003)
03Literature
28
(Sigmund, 1999)
𝜕𝐶𝜕𝑥 𝑝 𝑥 𝑈 𝑘 𝑈
03Literature
29
Moving asymptotesSensitivity
(Bensoe & Sigmund, 2003)
𝑉 𝑥𝑉 𝑣𝑜𝑙𝑓𝑟𝑎𝑐
03Literature
30
(Bendsoe, 1995)
𝑥 =
𝑖𝑓 𝑥 𝐵 𝑚𝑎𝑥 𝑥 , 𝑥 𝑚 : 𝐦𝐚𝐱 𝒙𝒎𝒊𝒏, 𝒙𝒆 𝒎 𝑖𝑓 max 𝑥 , 𝑥 𝑚 𝑥 𝐵 min 1, 𝑥 𝑚 : 𝒙𝒆 𝑩𝒆
𝜼
𝑖𝑓 min 1, 𝑥 𝑚 𝑥 𝐵 ∶ 𝒎𝒊𝒏 𝟏, 𝒙𝒆 𝒎
0 𝑥 𝑥 1
Where:m(move) is a positive move-limit (= 0.2)η is the numerical damping coefficient (= 1/2)And 𝐵 is found from the optimality condition
03Literature
31
Update design variables
(Bensoe & Sigmund, 2003)
03Toy problems
32
TOY1“create a working topology optimization methodology and translate this in the form of an algorithm.”
03Toy problems
33
TOY1• Get TopOp to work in Rhino• User-Inputs
ForcesSupportsNumber of elements
• Implement the existence of voids
03Toy problems
34
TOY1• Get TopOp to work in Rhino• User-Inputs
ForcesSupportsNumber of elements
• Implement the existence of voids
03Toy problems
35
TOY1• Get TopOp to work in Rhino• User-Inputs
ForcesSupportsNumber of elements
• Implement the existence of voids
Voidlist
Where voids = 0.001
03Toy problems
36
TOY1• Verification
Result Ansys:
03Toy problems
37
TOY1• Verification
03Toy problems
38
TOY2Configure more complex buildings with multiple voids and forces
03Toy problems
39
TOY2• Implement area loads• A void indexing system
Multiple voidsComplex design spaces
• Forces inside the design space• User-input for these “rooms”
03Toy problems
40
TOY2• Implement area loads• A void indexing system
Multiple voidsComplex design spaces
• Forces inside the design space• User-input for these “rooms”
03Toy problems
41
TOY2• Implement area loads• A void indexing system
Multiple voidsComplex design spaces
• Forces inside the design space• User-input for these “rooms”
03Toy problems
42
TOY2• Implement area loads• A void indexing system
Multiple voidsComplex design spaces
• Forces inside the design space• User-input for these “rooms”
03Toy problems
43
TOY2• Force size
03Toy problems
44
TOY2• Force size
03Toy problems
45
TOY3implement self-weight in the methodology and in the algorithm
03Toy problems
46
TOY3• Implement self-weight in the algorithm• Define sizes of self-weight
03Toy problems
46
TOY3• Implement self-weight in the algorithm• Define sizes of self-weight
03Toy problems
46
TOY3• Implement self-weight in the algorithm• Define sizes of self-weight
03Toy problems
47
TOY3• Implement self-weight in the algorithm• Define sizes of self-weight
03Toy problems
48
TOY3• Implement self-weight in the algorithm• Define sizes of self-weight
03Toy problems
49
TOY3• Implement self-weight in the algorithm• Define sizes of self-weight
03Toy problems
50
TOY3• Implement self-weight in the algorithm• Define sizes of self-weight
03Toy problems
51
TOY3• Implement self-weight in the algorithm• Define sizes of self-weight
03Toy problems
52
TOY3Verification
03Toy problems
53
TOY3Verification
03Toy problems
54
TOY3Verification
03Toy problems
55
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
56
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
57
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
58
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
(Blackman & Miller, 2016)
03Toy problems
58
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
(Blackman & Miller, 2016)
03Toy problems
59
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
60
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
60
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
60
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
61
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
62
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
63
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
64
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
65
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
66
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
67
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
67
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
68
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
68
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
69
TOY4• Implement a roofing constraint• Add area loads dependent on roof shape
03Toy problems
70
TOY5• Implement an indexing system• Handle inputs, including voids• Algorithm optimization
03Toy problems
71
TOY5• Implement an indexing system• Handle inputs, including voids• Algorithm optimization
(Liu & Tovar, 2014)
03Toy problems
72
TOY5• Implement an indexing system• Handle inputs, including voids• Algorithm optimization
(QNCC, 2019)
03Toy problems
73
TOY5• Implement an indexing system• Handle inputs, including voids• Algorithm optimization
03Toy problems
74
TOY5• Implement an indexing system• Handle inputs, including voids• Algorithm optimization
03Toy problems
75
TOY5• Implement an indexing system• Handle inputs, including voids• Algorithm optimization
03Toy problems
76
TOY5• Implement an indexing system• Handle inputs, including voids• Algorithm optimization
03Toy problems
77
TOY5• Implement an indexing system• Handle inputs, including voids• Algorithm optimization
(Shewchuck, 1997)
03Toy problems
78
TOY5• Implement an indexing system• Handle inputs, including voids• Algorithm optimization
03Toy problems
79
TOY5• Result
03Toy problems
80
TOY5• Result
03Toy problems
81
TOY6• More complex geometry• Implement density dependent forces• Implement roof constraint
03Toy problems
82
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
83
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
84
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
85
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
86
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
87
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
04Results
88
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
89
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
90
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
91
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
92
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
93
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
94
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
95
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
96
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
97
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
98
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
99
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
03Toy problems
100
TOY6• Implement density dependent forces• Implement roof constraint• More complex geometry
04Conclusions
101
create a working topology optimization methodology and translate this in the form of an algorithm.
implement density dependent forces in the methodology and in the algorithm.
translate the methodology and the algorithm to 3D geometry.
04Conclusions
102
create a working topology optimization methodology and translate this in the form of an algorithm.
04Conclusions
103
implement self-weight in the methodology and in the algorithm.
04Conclusions
104
translate the methodology and the algorithm to 3D geometry.
04Conclusions
105
04Conclusions
106
04Conclusions
107
(Kakadiaris, 2007)
108
Thank you