Sensitivity of optimal double-layer grid designs to geometrical imperfections and geometric nonlinearity conditions in the analysis phase

Abstract

This study focuses on exploring the effects of geometrical imperfections and different analysis methods on the optimum design of Double-Layer Grids (DLGs), as used in the construction industry. A total of 12 notable meta-heuristics are assessed and contrasted, and as a result, the Slime Mold Algorithm is identified as the most effective approach for size optimization of DLGs. To evaluate the influence of geometric imperfections and nonlinearity on the optimal design of real-size DLGs, the optimization process is carried out by considering and disregarding geometric nonlinearity while incorporating three distinct forms of geometrical imperfections, namely local imperfections, global imperfections, and combinations of both. In light of the uncertain nature of geometrical imperfections, probabilistic distributions are used to define these imperfections randomly in direction and magnitude. The results demonstrate that it is necessary to account for these imperfections to obtain an optimal solution. It’s worth noting that structural imperfections can increase the maximum stress ratio by up to 70%. The analysis also reveals that the initial curvature of members has a more significant impact on the optimal design of structures than the nodal installation error, indicating the need for greater attention to local imperfection issues in space structure construction.

Graphical abstract

Keywords

double-layer grid / sizing optimization / metaheuristic algorithms / geometrical imperfections / analysis approach

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Appendix

Table A1 Material property

Title	Value
Region	USA
Type	Steel
Standard	ASTM A36
Grade	36
Weight per unit volume	76972.86 N/m3
E	2 × 1011 N/m2
G	7.69 × 1010 N/m2
Fy	2.482 × 108 N/m2
Fu	3.999 × 108 N/m2
U (Poisson)	0.3

Table A2 Section property: AISC pipe shape V15.0

No.	Section name	Area (cm2)	Moment of inertia (cm4)	Radius of gyration (cm)
1	PIPE1/2STD	1.6129	0.71134	0.663702
2	PIPE1/2XS	2.064512	0.835793	0.63627
3	PIPE10STD	76.83856	6690.088	9.331706
4	PIPE10XS	103.8708	8822.025	9.215628
5	PIPE10XXS	197.6125	15309.41	8.801608
6	PIPE1-1/2STD	5.16128	12.90317	1.581404
7	PIPE1-1/2XS	6.903212	16.23303	1.537208
8	PIPE1-1/4STD	4.322572	7.908397	1.370838
9	PIPE1-1/4XS	5.677408	9.989554	1.330198
10	PIPE12STD	94.06433	11627.01	11.11809
11	PIPE12XS	124.1288	15048.43	11.00988
12	PIPE12XXS	238.1286	26707.91	10.59002
13	PIPE14STD	103.5482	15515.44	12.24026
14	PIPE14XS	136.8384	20135.61	12.13155
15	PIPE16STD	118.774	23395.54	14.03579
16	PIPE16XS	157.0965	30465.64	13.92657
17	PIPE18STD	133.9352	33574.48	15.83131
18	PIPE18XS	177.3545	43836.25	15.72184
19	PIPE1STD	3.161284	3.635365	1.06807
20	PIPE1XS	4.129024	4.578546	1.032764
21	PIPE20STD	149.161	46346.12	17.62709
22	PIPE20XS	197.6125	60639.09	17.51736
23	PIPE2-1/2STD	10.96772	63.68341	2.406396
24	PIPE2-1/2XS	14.5161	79.91643	2.347214
25	PIPE2-1/2XXS	25.99995	119.4584	2.144268
26	PIPE24STD	179.548	80844.63	21.21865
27	PIPE24XS	238.1286	106112	21.10842
28	PIPE26STD	194.7738	103159.6	23.01443
29	PIPE26XS	258.4511	135566.6	22.90394
30	PIPE2STD	6.903212	27.88751	1.999234
31	PIPE2XS	9.548368	36.21213	1.94691
32	PIPE2XXS	17.16126	54.52632	1.784858
33	PIPE3/4STD	2.129028	1.541721	0.847598
34	PIPE3/4XS	2.774188	1.864301	0.816356
35	PIPE3-1/2STD	17.29029	199.3749	3.395218
36	PIPE3-1/2XS	23.74189	261.3933	3.318764
37	PIPE3STD	14.38707	125.7019	2.955544
38	PIPE3XS	19.48383	161.914	2.886202
39	PIPE3XXS	35.29025	249.3226	2.65938
40	PIPE4STD	20.45157	300.9353	3.83413
41	PIPE4XS	28.45156	399.9984	3.750818
42	PIPE4XXS	52.25796	636.0016	3.48869
43	PIPE5STD	27.74188	631.0068	4.769612
44	PIPE5XS	39.41928	860.3504	4.67106
45	PIPE5XXS	73.16114	1399.786	4.374388
46	PIPE6STD	35.99993	1171.275	5.70357
47	PIPE6XS	54.19344	1685.321	5.575046
48	PIPE6XXS	100.903	2760.863	5.231384
49	PIPE8STD	54.19344	3017.262	7.462012
50	PIPE8XS	82.32242	4400.399	7.310374
51	PIPE8XXS	137.4191	6742.117	7.003796

Competing interests

The authors declare that they have no competing interests.

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