1. School of Civil and Transportation Engineering, Guangdong University of Technology, Guangzhou 510006, China 2. School of Advanced Manufacturing, Guangdong University of Technology, Jieyang 515231, China 3. College of Civil Engineering, Tongji University, Shanghai 200092, China 4. Tongji Lvjian Co., Ltd, Shanghai 200092, China
This study proposes a shape optimization method for K6 aluminum alloy spherical reticulated shells with gusset joints, considering geometric, material, and joint stiffness nonlinearities. The optimization procedure adopts a genetic algorithm in which the elastoplastic non-linear buckling load is selected as the objective function to be maximized. By confinement of the adjustment range of the controlling points, optimization results have enabled a path toward achieving a larger elastoplastic non-linear buckling load without changing the macroscopic shape of the structure. A numerical example is provided to demonstrate the effectiveness of the proposed method. In addition, the variation in structural performance during optimization is illustrated. Through parametric analysis, practical design tables containing the parameters of the optimized shape are obtained for aluminum alloy spherical shells with common geometric parameters. To explore the effect of material nonlinearity, the optimal shapes obtained based on considering and not considering material non-linear objective functions, the elastoplastic and elastic non-linear buckling loads, are compared.
The model that considers geometric nonlinearity and material elasticity.
MN
The model that considers both geometric and material nonlinearities.
INI
The design variables of the initial shape of the reticulated shell.
LZ
The optimal design variables obtained by the ML model.
NZ
The optimal design variables obtained by the MN model.
ML-INI
The ML model with design variables INI.
ML-LZ
The ML model with design variables LZ.
ML-NZ
The ML model with design variables NZ.
MN-INI
The MN model with design variables INI.
MN-LZ
The MN model with design variables LZ.
MN-NZ
The MN model with design variables NZ.
Tab.4
Fig.14
model type
f/L
γ
Pc (kN·m?2)
INI
NZ
LZ
MN
1/4
0
54.827
89.669
84.778
1/4
52.051
83.758
74.370
1/2
41.646
70.033
62.551
1
28.331
48.629
43.362
1/5
0
44.202
80.501
75.069
1/4
42.760
71.128
55.643
1/2
34.501
43.629
40.918
1
23.091
39.947
31.951
1/6
0
37.748
63.330
68.969
1/4
35.555
59.595
43.640
1/2
28.483
35.532
37.893
1
19.306
27.346
26.984
ML
1/4
0
55.001
95.152
95.328
1/4
52.211
74.661
93.599
1/2
44.365
74.090
79.593
1
32.222
53.489
51.194
1/5
0
44.386
76.344
75.328
1/4
42.800
55.212
59.549
1/2
36.098
49.454
41.359
1
21.702
26.260
26.306
1/6
0
38.097
76.957
65.172
1/4
35.953
42.065
59.589
1/2
30.556
41.251
34.601
1
21.351
27.543
27.518
Tab.5
Fig.15
Fig.16
Fig.17
Fig.18
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