Single Storey Model Flowchart:
Start Create rectangle in plan 40m by 40m
Move the surface Z-axis, 8m
Curved Surface
Extract Points
Move surface control points to form a free form curved surface
Generate random points on surface N = 54
Distance.(-6m,6m) Direction.(Z-axis)
Variable 01
Model Support 01
Define Supports
Voronois
Scale the voronoi and move down
Select points as support loca�ons N = 10
Set points as center points of voronoi
Scale factor.(0.1,0.9) Move Distance. (0.5m, 2m)
Variable 02 Variable 03
Model Support 02
Columns
Project the moved voronoi to XY plane
Lo� the voronois as suppor�ngs
Roof Panels Random reduce top voronois as glazing N = 43
Multi-storey Model Flowchart:
Create rectangle in plan 40m by 40m
Support Center
Column Base
Straight Square Column
Set grid 4x4 Extract intersected points
Use points as center of squares Square Side Length = 2 * R1
Extrude squares as columns Extrude Height = X1 Variable 01
0.30 < R1< 1.00
Variable 02
2.00 < X1 < 3.00 Direction.(Z-axis)
Arc Pi
4 - X1
1/4 R2 - R1 R1 X1
Floor Height (4m)
R2
4 - X1
X1 R1
Second Floor Column Base
Dimension of Top Square
Square Column Edge
Extract the top square ‘Cull pa�erns’, if the area is less than 15.
Because R2 -R1 = 4 - X1, So, R2 = R1 + (4 - X1)
Extract edges on the top of columns
If (2 * R2)² < 15 m² stop calculating; the column is one-storey high R4
R2 - R3
Pi
4 - X3
X2
R3
X3
1/4
R4 - R3
1/4
Arc Pi
Arc
R3
R2
4 - X2 X2
Second Floor Column
Dimension of Third Floor Column
Set R3 = 1/6 R2 So, X2 = R2 - R3 = 5/6 R2 = 5/6 [R1 + (4 - X1)]
Because R4 - R3 = 4 - X3 So, R4 = 1/6 [R1 + (4 - X1)] + (4 + X3)
If (2 * R3)² < 0.5 m² stop calculating; the column is two-storey high
1.50 < X3< 3.00
Column Massing Sweep 1 Rail to form arc massings and extrude squares Rail: squares; Sec�on: Arc Variable 03
Columns are in different height
Structures
Suppor�ng Pipes
Column Massing Massing & Floors
Sweep 1 Rail to form arc massings and extrude squares Rail: squares; Sec�on: Arc
Extract Iso Curve Extract Iso curves as support pipes 5 Curves on each surface U=5
Void Conditions
Region Difference
Move floors
If the area of top rectangle < 15 m2, Generate squares (5m x 5m)
Extract squares as voids Pink color indicates floors
Move the surface as floors above Distance = 4m, Direc�on= Z-axis
Final View - Columns
Final View - Massing & Floors
The ver�cal structure - mushroom columns & edge columns are highlighted.
The horizontal structure - floors & roof are highlighted.
Edge Columns Extract vectors of the trimmed surface Use vectors as start points of edge columns
Constraints
Evolutionary Process:
Gen 240.10
View Area Sum: 3467.81 m2 Max Displacement 7.92 cm
Gen 80
Max Displacement 11.33 cm Elastic energy: 157.45 KNm
Gen 240.20
View Area Sum: 3490.31 m2 Max Displacement 7.83 cm
Gen 120
Max Displacement 11.86 cm Elastic energy: 164.87 KNm
Gen 240.40
View Area Sum: 3495.94 m2 Max Displacement 8.12 cm
Gen 160
Max Displacement 10.21 cm Elastic energy: 145.81 KNm
Gen 240.60
View Area Sum: 3496.07 m2 Max Displacement 7.65 cm
Gen 200
Max Displacement 8.46 cm Elastic energy: 148.24 KNm
Gen 240.80
View Area Sum: 3496.23 m2 Max Displacement 7.98 cm
Gen 240
Max Displacement 7.92 cm Elastic energy: 144.12 KNm
Gen 240.100
View Area Sum: 3498.81 m2 Max Displacement 7.88 cm
3. Structure Dimension
Max Displacement 13.46 cm Elastic energy: 144.53 KNm
2. View Rose Optimization
1. Massing Optimization
Gen 40
Final Result_ Geometric View
Column Mathematical Relation:
R2 - R1 = Y1 Y1 = 4 - X1
R3
X3
R2 = (4 - X1) + R1
R3
Stop; Column is one-storey high; No floor above
Ground Floor (4m)
X2 Y1 X1 2(R1)
R3 = 1/6 R2 (Constraints) X2 = R2 - R3 X2 = 5/6 [(4 - X1) + R1]
R2 (1/4 Pi) Arc (Constraints)
Displacement (cm) Mushroom columns Edge Columns Floor Beams Roof Beams Mesh load const Gravity Ground Supports (base poitns of mushroom columns)
Y2 =4 - 5/6 [(4 - X1) + R1]
4 - x1 x1
Types of Load Numbers of Supports
If (2*R2)² < 15
R3
Fitness Structure Elements
1st Floor
Y2
Mathematical Relation:
1. Fixed supports center 2. Fixed floor height (4m) 3. Square section 4. 1/4 Pi Arc
R1 R1
If (2*R3)² < 5 Stop; Column is two-storey high; No floor above R4 - R3 = Y3 Y3 = 4 - X3 R4 = R3 + (4 - X3)
2nd Floor
2nd Floor (4m) 1st Floor (4m)
R4 Y3
Constraints:
0.30 < R1 < 1.00 2.00 < X1 < 3.00 1.50 < X3 < 3.00
Ground Floor
Variables & Domain :
R4 = 1/6 [(4 - X1) + R1] + (4 - X3)
Geometric Model: Three-storey high Column Two-storey high Column
Loading Conditions:
Structure Detail Isometric Section
Gen 240 Perspective View
Second Floor Displacement:
Mass Isometric:
Gen 40
Gen 80
Max Displacement 13.46 cm Elastic energy: 144.53 KNm
Gen 120
Max Displacement 11.33 cm Elastic energy: 157.45 KNm
Gen 160
Max Displacement 11.86 cm Elastic energy: 164.87 KNm
Max Displacement 10.21 cm Elastic energy: 145.81 KNm
Gen 200 Max Displacement 8.46 cm Elastic energy: 148.24 KNm
Gen 240 Max Displacement 7.92 cm Elastic energy: 144.12 KNm
16 14
8.04 cm
12
7.19 cm 6.35 cm 5.5 cm 4.66 cm 3.81 cm 2.96 cm 2.12 cm
Displacement (cm)
8.88 cm
13.46 11.33
11.86 10.21
10
8.46
8
7.92
6 4 2 0 0
40
80
120
160
200
240
Generation
Structure Optimisation convergence graph
Gen 240 Isometric View
View Rose Area:
Mass Isometric:
Gen 240.10
Gen 240.20
View Area Sum: 3467.81 m2 Max Displacement 7.92 cm
View Area Sum: 3490.31 m2 Max Displacement 7.83 cm
Gen 240.40
Gen 240.60
View Area Sum: 3495.94 m2 Max Displacement 8.12 cm
View Area Sum: 3496.07 m2 Max Displacement 7.65 cm
Gen 240.80 View Area Sum: 3496.23 m2 Max Displacement 7.98 cm
Gen 240.100 View Area Sum: 3498.81 m2 Max Displacement 7.88 cm
View Rose Optimization: 8.88 cm 8.04 cm 7.19 cm 6.35 cm 5.5 cm 4.66 cm 3.81 cm 2.96 cm
After optimizing the structure, I set up three points in the space, assuming that this is the main exhibition area. Then, observe which result has the largest observable region among the various results of the 240 generation. During the optimization this time, we can see that the massing is gradually stable.
2.12 cm
Gen 240.100 View Rose Isometric
Final Result View Rose
Material Dimension Optimization:
Final Structure Information:
Structure ID: Mushroom Column Cross Section : O Section Material: Reininforced Steel B500-EN Diameter (cm): 20 Wall Thickness (cm): 1
Structure ID: Edge Column Cross Section : [] Section Material: Steel S235 Height (cm): 15 Flange Width (cm): 10
Structure ID: Floor Beam Cross Section : I Section Material: Steel S235 Height (cm): 30 Flange Width (cm): 20
Structure ID: Roof Beam Cross Section : I Section Material: Steel S235 Height (cm): 30 Flange Width (cm): 20
5.04 cm 4.47 cm 3.89cm 3.32 cm 2.74 cm 2.17 cm 1.59 cm 1.02 cm 0.44 cm
Max Displacement: 4.63 cm Elastic energy: 146.56 KNm
Final Result Displacement Isometric
Final Result Massing Isometric