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Sensors and Materials, Vol. 35, No. 10 (2023) 4681–4696
MYU Tokyo
S & M 3422

Analysis and Design of Single-layer Lattice
Aluminum Domes Using ANSYS Workbench
Wei-Ling Hsu,1 Hong-Wei Yu,2 Chao-Ming Hsu,2*Te-Hsun Lin,3 Sufen Wei,4 and Cheng-Fu Yang5,6**
1School of Civil Engineering, Jiaying University, Meizhou, Guangdong, 514015, China

2Department of Mechanical Engineering, National Kaohsiung University of Science and Technology,

Kaohsiung 807, Taiwan

3School of Economics and Management of Jiaying University, Meizhou, Guangdong, 514015, China
4School of Ocean Information Engineering, Jimei University, Xiamen 361021, China

5Department of Chemical and Materials Engineering, National University of Kaohsiung, Kaohsiung 811, Taiwan
6Department of Aeronautical Engineering, Chaoyang University of Technology, Taichung 413, Taiwan(Received July 15, 2023; accepted September 25, 2023)

Keywords: single-layer lattice aluminum dome, stress and deformation, ANSYS Workbench, uneven live
load

The single-layer reticular aluminum dome has gained popularity in the fabrication industryof domes for trough roofs owing to its numerous advantages, including its lightweight nature,
durability, affordability, ease of assembly and disassembly, as well as convenient maintenance.
The objective of this study was to simulate and analyze domes designed on the basis of the test
standards specified in the American Petroleum Institute’s API Standard 650: Appendix G, whichpertains to single-layer reticulated aluminum domes, and to ensure compliance with its
requirements. Two types of vault were designed with varying dimensions and methods ofconnecting groove walls. To assess the structural integrity of the domes, finite element analysis
was performed. Both vault designs were subjected to six different load combinations todetermine if the material would fail owing to insufficient yield strength. The primary focus of
this research is on the vault structure’s design and finite element analysis. Following thecompilation of design points, a three-dimensional model of the vault was created. The stress anddeformation of the vault were simulated using the finite element analysis software ANSYSWorkbench, considering various conditions. The stress and deformation analyses indicated thatboth vault designs successfully met the criteria outlined in the code.

1.

Introduction

The single-layer mesh aluminum vault is a fixed groove roof that possesses a uniquegeometric structure. This structure allows for the effective and even distribution of tension
throughout the entire vault. Consequently, the peripheral support beams connected to the tankwall are capable of sustaining the entire structure without the need for additional support*Corresponding author: e-mail: yhleepp@gmail.com**Corresponding author: e-mail: cfyang@nuk.edu.twhttps://doi.org/10.18494/SAM4595

ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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columns or reinforcements. The straightforward design of the single-layer mesh aluminum vault
offers several competitive advantages. It is lightweight, durable, cost-effective, and easy toassemble and disassemble, and requires minimal maintenance. These qualities enable the use of
fewer building materials and simpler manufacturing processes, resulting in significantly reduced
construction costs. Hence, the single-layer mesh aluminum vault holds considerable researchvalue, and its structure design and analysis constitute the primary focus of this research.
Presently, the advancement of computer technology allows for the solution of complex nonlinear
problems. Numerical analysis, which employs simulations to predict the stress and deformationof structures, has become a widely used method in this regard.
Kato et al. presented their findings on the impact of determining the section proportions of
single-layer reticulated dome members.(1) Their approach, based on linear buckling stress,
utilized a geometric stiffness matrix for precise linear buckling analysis.(1) Building upon thiswork, Chandiwala conducted an examination of steel domes using the computer analysis
software STAAD.Pro.(2) This software provided valuable insights and analysis capabilities forstudying the structural properties of the domes. Fan et al. proposed the Hamilton variational
principle as a solution to address the current collision problem. They introduced the central
difference method, an effective approach within the finite element method, to tackle collision
problems and successfully solve nonlinear dynamic problems.(3) This method proved to beparticularly suitable and efficient in handling complex dynamic scenarios. Fan et al. examinedthe dynamic collapse mechanism of single-layer reticulated shells subjected to harmonic loads,
sudden loads, and earthquake loads.(4) Their study delved into the behavior of these structures
under various loading conditions.
Nie et al. presented their findings on the impact of reducing the cross-sectional area ofstructural members. They discovered that decreasing the cross-sectional area led to reductions inplastic development and structural ductility, indicating poor performance.(5) The effects ofdifferent static preloads on counter-intuitive collapse were investigated by Ma et al.(6) Theirresearch highlighted that single-story reticulated domes with significant initial collapse underdynamic loads were affected by these preloads.(6) Jihong and Nian proposed a novel numericalanalysis method to explore complex mechanical behaviors, such as the large deformation ofsubstantial or extremely large components, material nonlinearity, and fracture. Their study
aimed to facilitate further investigations into these intricate phenomena.(7) Together, theseadvancements in structural analysis and solution methodologies have significantly contributed
to the field, enabling improved understanding and practical applications in the design andanalysis of reticulated dome members, steel domes, and other structural systems.
Previously, two common methods were utilized to assess the efficacy of a designed bulletresistant door. The first method involved the application of sensors positioned at various
locations to detect any cracking that occurred upon impact. For example, Nie and Liu utilized
three-dimensional acceleration sensors, strategically placed at eight measuring points, to analyze
the dynamic acceleration response.(8) Similarly, Zhao et al. utilized displacement sensors to
examine the mechanical properties of a single-layer aluminum-alloy combined lattice shellstructure.(9) These studies, cited as Refs. 5–9, suggest that employing simulation methods todesign domes and assess their stability under different loads is a highly efficient and valid

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approach. Simulation methods offer the advantage of eliminating the need for a significant
financial investment in constructing physical domes. However, it is important to note that mostresearch studies have focused on utilizing only a single variable as the simulation parameter forthe designed domes. In real-world scenarios, domes are subject to multiple simultaneous loads,
and only a limited number of studies have specifically investigated the effects of different loads
on the stability of the designed domes. Therefore, there is a need for further research to explore
the impact of various loads acting simultaneously on domes and their stability. Suchinvestigations would provide valuable insights into the behavior and performance of domes
under real-world conditions, leading to more robust and reliable designs.
The primary objective and innovative aspect of this study revolve around analyzing theeffects of various loads on stress and deformation patterns within a designed dome structure.
The rapid advancement of computer technology has made it possible to tackle more complex
nonlinear problems through simulation methods. Numerical analysis, which involves simulating
the stress state of a structure and predicting its resulting stress and deformation, has become
widely employed in engineering practice. Among different dome types, single-layer reticulated
aluminum domes offer numerous competitive advantages such as low weight, structuralrobustness, high durability, cost-effectiveness, ease of assembly and disassembly, and simplified
maintenance. Therefore, in this study, we focus on simulating the behavior of single-layer
reticulated aluminum domes using two different connection methods: welding and sliding bases.
To conduct simulations, we utilized the FEM analysis software ANSYS Workbench.
This software enables the accurate modeling and analysis of the dome structure undervarious loading conditions. By comparing the results obtained from the two different connection
methods, we aim to gain insights into the structural performance, stress distribution, anddeformation characteristics of single-layer reticulated aluminum domes. This information isvaluable for the design and optimization of such dome structures. Uematsu et al. conducted aseminal study on wind loads and the dynamic properties induced by wind in a long-span dome.
(10) Their research focused on a rigidly connected single-layer lattice structure.(10) Building uponthis work, Wang and Shen employed a Lagrangian formulation to carry out three-dimensional
nonlinear analyses of beam elements.(11) Their analyses included the consideration of large
rotations and displacements at joints, particularly under the effects of strong wind loads andearthquake forces.
In this study, we investigated the stability and resilience of single-layer reticulated aluminum
domes by subjecting them to various load combinations. Six different load combinations wereconsidered: static load, static load combined with uneven live load, static load combined withaverage live load, static load combined with wind load, static load combined with uneven live
load and wind load, and static load combined with average live load and wind load. By analyzing
the resulting data, which included the maximum and minimum principal stresses as well as total
deformations, we aimed to assess the ability of the designed domes to withstand internal stress(static load) and external stresses (uneven live load, average live load, and wind load). Our
primary focus was to prevent structure failure caused by two factors: (a) the stresses induced byexternal forces exceeding the yield stress of the material and (b) permanent deformations
resulting from external forces.

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Our findings demonstrate that, across the six different load scenarios applied to the twodomes, the maximum stresses experienced were significantly lower than the maximum stressthreshold of the chosen material, namely, the 6061-T6 aluminum alloy. Furthermore, thedeformations observed during simulations did not result in permanent deformations. The main
purpose of this study is to design single-layer lattice aluminum domes with different loads
systematically and scientifically, and computer-aided engineering is used to simulate the actual
structural behavior of the designed domes. After obtaining simulation analysis results, it will bepossible to assess whether the designs of the single-layer lattice aluminum domes can meet
specified safety standards under various specific conditions.

2.

Simulation Process and Parameters

To ensure the structural integrity and functionality of the single-layer reticulated aluminum
domes across various climates and potential environmental factors worldwide, a standard design
guideline, namely, API Standard 650: Appendix G, has been established. This guideline sets
forth the necessary design loads to fabricate domes with high security and resilience. In
adherence to API Standard 650: Appendix G, we conducted simulation designs and structural
analyses for the single-layer reticulated aluminum domes. These rigorous processes aimed toensure the safety and security of the domes, enabling them to withstand diverse natural or manmade factors. A critical requirement specified in the standard is the maximum radius ofcurvature (R) for single-layer mesh aluminum domes. It states that R should not exceed 1.2 times
the diameter (D) of the barrel tank, while the minimum R value should not be less than 0.7 D.
The R/D ratio directly impacts the shape and load-bearing capacity of the dome, underscoring its
importance in the design process.
The designed domes had a span of 36.19 m, a ratio of the radius of curvature to the diameterof the barrel tanks set at one, and a height of 6.26 m, as shown in Fig. 1(a). In addition to these
design parameters, the connection methods between the domes and the barrel tanks were ofsignificant interest. To address this, two distinct connection methods were devised andillustrated in Figs. 1(b) and 1(c): welding base (referred to as dome 1) and sliding base (dome 2).
By employing these connection methods, the aim was to compare the effects of loading on thedomes’ three normal stresses and maximum deformations under six different load combinations.
This comparison was necessary owing to the utilization of multiple load combinations, allowing
for an assessment of how the different connection methods affected the aforementioned stressand deformation characteristics of the domes.
Given the extensive application of Kaiweit-type reticulated domes in the installation andconstruction of storage tanks, we opted to utilize such domes as the designed structure for our
simulations. However, we took into consideration that the outermost end of the reticulated shellis supported by the ring beam, resulting in a nonuniform stress distribution on the outermost
ring of the Kaiweit-type structure. This uneven distribution of supports would be detrimental to
the lower tank body. To address this issue, we introduced several circles of square grids, which
served to distribute the bearing stress more uniformly on the ring beam. This modification
aimed to improve the uneven stress distribution caused by the original design. In summary,Sensors and Materials, Vol. 35, No. 10 (2023)

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Fig. 1. (Color online) Schematic diagrams of (a) top view of the designed dome and connection method,(b) welding, and (c) sliding structures.

taking into account the structural characteristics of large-scale storage tanks, we designed
mixed-type reticulated domes with a hybrid structure combining the Kaiweit-type structure andthe joint-square structure. In the design of the storage tank’s reticulated domes, special
consideration was given to the section of rods. Unlike traditional building reticulated domes, theskins of the storage tank’s domes were directly in contact with the rods.
Since the rods were subjected to bending moments, using round tubes for the rods was notsuitable. Instead, I-beam members were preferred owing to their ability to withstand bending
loads effectively. Furthermore, to facilitate the connections between the I-beam members, platetype nodes were chosen over socket-type nodes. This decision was made to ensure robust andsecure connections throughout the structure. As a result, the cross sections of the I-structural
beams within the single-layer reticulated aluminum domes were adjusted to accommodate theseplate-type connections, enabling efficient load transfer and enhanced structural integrity. These
dimensions were carefully selected to meet the specific requirements of each beam type,ensuring optimal performance and load-bearing capacity within the reticulated dome structure.
The single-layer reticulated aluminum domes in the design employed two different
connection methods, resulting in distinct boundary conditions. First, a fixed support was
implemented at the end of the support beams in the outermost ring, effectively constraining all
degrees of freedom. This arrangement simulated the connection approach wherein the domes are
welded to the tank walls. Subsequently, the sliding supports at the endpoint of the outermost

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support beams were converted to the cylindrical coordinate method, limiting all degrees of
freedom except for radial translation. This condition replicated the installation scenario where adome is mounted on a sliding tank. In terms of loads, the domes were subjected to multiple
forces. Apart from the static load that accounted for their own weight, live load and wind load
were also considered. The live load was further divided into uneven live load and average live
load, accounting for variations in applied loads across the dome’s surface. These loads werecrucial for analyzing the structural response and stability of the domes under operational
conditions.
In this study, we utilized the 6061-T6 aluminum alloy as the material for the I-beams in the
single-layer reticulated aluminum domes. This particular alloy is renowned for its exceptional
strength and lightweight properties, making it highly suitable for constructing domes thatnecessitate both strength and reduced weight. Note that the study focused solely on the material’scharacteristics at room temperature, as the impact of varying ambient temperature was notaddressed. Table 1 presents the specific values of the material property parameters at room
temperature. To assess the compliance of the single-layer reticulated aluminum domes withsafety specifications, we subjected them to six load combinations, as outlined in Table 2. Thesesimulations aimed to ascertain whether the domes can withstand the specified load scenarios
while maintaining their structural integrity and safety standards.

3.

Simulation Results and Discussion

The allowable load Wa encompasses both static and live loads (measured in kPa). It is definedas the maximum load that the single-layer reticulated aluminum domes can safely sustain
without compromising their structural integrity and safety standards. The static load accounts
for the weight of the domes themselves, while the live load represents additional external forces
imposed on the domes during their operation. By considering both static and live loads, theallowable load ensures that the domes can withstand the combined effects of these loads andremain secure and stable. The static load refers to the weight of an object, encompassing the
cumulative weight of all its components, such as beams, sheets, battens, gussets, and fasteners.
In the case of the designed single-layer reticulated aluminum domes, the total static load,
including the weight of the domes and their accessories, amounts to approximately 270,000 N.
This value reflects the combined weight of all structural elements and supplementarycomponents in the domes. On the other hand, the live load, also known as the dynamic load,
primarily comprises external forces imposed on the single-layer reticulated aluminum domes. It

Table 1
Relative properties of 6061-T6 aluminum alloy.
Material property
Value
Unit weight27173.7 N/m3
Young’s modulus
71000 MPa
Yield stress
280.0 MPa
Ultimate tensile stress
310.0 MPa
Poisson’s ratio
0.33

Table 2Different load combinations for the designed domes.
Condition 1
Static load
Condition 2
Static load + uneven live load
Condition 3
Static load + average live load
Condition 4
Static load + wind load
Condition 5
Static load + uneven live load + wind load
Condition 6
Static load + average live load + wind load

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represents loads that result from external factors, such as foreign objects placed on the domes.
The live load can be further categorized into two types, namely, uneven live load and average
live load, considering variations in load distribution across the surface of the domes. These loadclassifications are essential in assessing the structural response and stability of the domes under
different operational scenarios.
The analysis process involved several steps. First, the designed dome model was imported
into the ANSYS Workbench, which is a finite element analysis software program. Subsequently,
material parameters for the various I-structural beams were defined, and the dome model wasthen meshed, creating a discretized representation for analysis. Once the meshing was complete,boundary conditions were applied to simulate real-world scenarios. According to API Standard
650: Appendix G, specific load requirements were considered. The average live load, mandated
to be at least 1 kPa, was uniformly distributed across the entire surface of the domes.
Additionally, the uneven live load, stipulated to be at least 0.5 kPa, was applied to half of thedome’s area. In terms of wind load, API Standard 650 specified that the minimum wind loadcorresponds to a static wind pressure of 1.48 kPa, resulting from winds with a speed of
190 km/h. To calculate the actual wind pressure at the site, a factor of (155/190)² was applied,
resulting in a wind pressure of 0.982 kPa. The wind load was then determined by multiplying
this wind pressure by specific pressure coefficients. For the windward direction, 1/4 of the load
was obtained by multiplying −0.9 by 0.982, resulting in −0.884 kPa. The middle ward direction
accounted for 1/2 of the load and was calculated as −0.7 multiplied by 0.982, yielding −0.688
kPa. Lastly, the leeward direction represented 1/4 of the load and was determined by multiplying−0.5 by 0.982, giving −0.491 kPa. These values reflect the respective wind pressures acting on
different sides of the domes during the analysis.
According to the elasticity theory, it is possible to rotate an infinitesimal volume of material
within a solid in such a way that only principal stresses remain while all shear stresses become
zero. These principal stresses are referred to as the remaining three principal stresses.(12) Amongthem, the maximum principal stress (σ1), middle principal stress (σ 2), and minimum principal
stress (σ 3) are the primary stresses under discussion. Note that the relationship between thesethree principal stresses is such that σ1 > σ 2 > σ 3. These three parameters are then combined withthe allowable stress design method to determine whether the material of the domes undergoes
deformation or damage. The simulated and analyzed results should encompass the maximum
and minimum principal stresses, as well as the overall deformation of the single-layer reticulated
aluminum domes being designed. The critical parameter for evaluating whether the dome
material has undergone deformation in the design process is the allowable stress (σa). The σa forthe designed domes can be determined by multiplying the yield stress (σ y) of the dome material
by a safety factor (SF) of 1.65.
σa = σ y / SF

(1)

For instance, if the yield stress (σ y) of the dome material is 280 MPa, thenσa = 280 MPa / 1.65 = 169.7 MPa.

(2)

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Therefore, if the maximum values of the principal stresses σ1 and σ 3 (or the maximum valueof the principal stress, σmax) of the designed domes exceed 169.7 MPa, the domes, whensubjected to different loads, will surpass the yield stress limit of the material used. Consequently,
they will not comply with the safety specifications.
Taking into account the static load caused by its own weight, the initial stress experienced bya dome becomes significant. Thus, it is crucial to consider this load during the analysis of initialstress. In the case of analyzing the domes under static load conditions, only the static load wasapplied. The analysis results for dome 1 are presented in Fig. 2, where Figs. 2(a) to 2(c) illustrate
σ1 as 5.20 MPa, σ 3 as −6.39 MPa, and the maximum deformation as 3.82 mm, respectively.
Similarly, the analysis results for dome 2 are shown in Figs. 3(a) to 3(c), revealing σ1 as
14.97 MPa, σ 3 as −17.52 MPa, and the maximum deformation as 5.88 mm, respectively.
Importantly, these results are compliant with safety regulations. When subjected to static loadconditions, the values of σ1, σ 3, and maximum deformation for both designed domes 1 and 2 are
relatively small, and the values for dome 2 are larger than those for dome 1.

Fig. 2. (Color online) (a) Maximum principal stress, (b) minimum principal stress, and (c) maximum deformationof dome 1 with static load.

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Fig. 3. (Color online) (a) Maximum principal stress, (b) minimum principal stress, and (c) maximum deformationof dome 2 with static load.

In this simulation scenario, we analyzed the effects of both the static and uneven live loads on
dome structures. The analysis focused on dome 1, and the results showed that the stress σ1 was
53.01 MPa, σ 3 was −70.58 MPa, and the maximum deformation was 12.02 mm, as shown in Figs.
4(a)–4(c), respectively. For dome 2, the analysis results were as follows: σ1 = 55.87 MPa,σ 3 = −63.37 MPa, and the maximum deformation was 21.97 mm (note shown here). These values
were obtained when both static and uneven live loads were applied simultaneously. Comparing
the analysis results of domes 1 and 2, it was evident that the presence of the uneven live load had
an impact. In both cases, the stresses σ1, σ 3, and the maximum deformation were higher when
only the static load was applied. This outcome can be attributed to the effect of the uneven live
load on the structures. Importantly, the simulation results demonstrated that the stresses σ1 andσ 3, and the maximum deformation of both designed domes 1 and 2 were still within the limits
specified by safety regulations. Thus, these structures complied with the necessary safety
standards. Overall, the results indicate that even when both static and uneven live loads are4690

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Fig. 4. (Color online) (a) Maximum principal stress, (b) minimum principal stress, and (c) maximum deformationof dome 1 with static load combined with uneven live load.

simultaneously applied to different domes, there are no significant differences in the stresses σ1and σ 3, and the maximum deformation between the two scenarios.
The simultaneous application of the static and average live loads was performed on thedesigned domes, and the subsequent analysis focused on dome 1 (analysis results not shown).
The analysis of dome 1 revealed that σ1 was 34.38 MPa, σ 3 was −43.14 MPa, and the maximum
deformation was 15.69 mm. Figure 5 illustrates the analysis results of dome 2; σ1, σ 3, and the
maximum deformation were 95.92 MPa, −112.3 MPa, and 40.48 mm, respectively. These results
were found to comply with safety regulations. When both the static load and average live loads
were considered, the σ1, σ 3, and maximum deformation values of the designed domes 1 and 2
were significantly greater than when only the static load and the static load combined with theuneven live load were applied. Hence, the average live load is recognized as a crucial factor
affecting the safety of the designed dome structures.

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Fig. 5. (Color online) (a) Maximum principal stress, (b) minimum principal stress, and (c) maximum deformationof dome 2 with static load combined with average live load.

Upon applying the different loads to the designed domes, the domes exhibited minimal
vibration before settling into deformation in the same direction. As the live load is uniformly
distributed and eventually incorporated into the calculation of gravity loads, it can act as aconcentrated point load on specific areas. Consequently, when both the static and average live
loads are simultaneously applied, the σ1 and σ 3, and maximum deformation values will be larger
than when only the static load and the static load combined with the uneven live load wereapplied. However, it is important to note that the σ1 and σ 3, and maximum deformation values ofdome 2 were considerably greater than those of dome 1. This indicates that the structure of dome
1 is more stable and safer than that of dome 2.
The fluctuating wind loads or wind pressures generated by flowing winds are significant
factors that impact the stability of long-span domes. In this simulation scenario, both the staticand wind loads were applied simultaneously, and the analysis results focused on dome 1, asshown in Fig. 6. The analysis revealed that σ1 was 49.14 MPa, σ 3 was −31.88 MPa, and the4692

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Fig. 6. (Color online) (a) Maximum principal stress, (b) minimum principal stress, and (c) maximum deformationof dome 1 with static load combined with wind load.

maximum deformation was 10.41 mm. For dome 2 (analysis results not shown), the values wereas follows: σ1 = 68.22 MPa, σ 3 = −60.09 MPa, and the maximum deformation was 21.71 mm.
These simulation results for the stresses σ1 and σ 3, and the maximum deformation of both domes
1 and 2 were found to comply with safety regulations. Note that the stresses σ1 and σ 3, and the
maximum deformation of dome 2 were significantly larger than those of dome 1, further
emphasizing that the structure of dome 1 is more stable and safer than that of dome 2.
When the static load combined with the uneven live load and the wind load were applied tothe designed dome simultaneously, the analysis results of dome 1 revealed that σ1 was 65.15
MPa, σ 3 was −59.71 MPa, and the maximum deformation was 13.31 mm, as shown in Fig. 7. For
dome 2 (analysis not shown), the analysis results showed that σ1 was 57.15 MPa, σ 3 was −49.90
MPa, and the maximum deformation was 20.26 mm. Interestingly, when the static, the uneven
live, and wind loads were applied simultaneously to both domes 1 and 2, there were no
significant differences in σ1 and σ 3, and maximum deformation compared with the case whenSensors and Materials, Vol. 35, No. 10 (2023)

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Fig. 7. (Color online) (a) Maximum principal stress, (b) minimum principal stress, and (c) maximum deformationof dome 1 with static load combined with uneven live load and wind load.

only the static and uneven live loads were applied simultaneously.
Under the simulated conditions, the static load combined with the average live load and thewind load were applied simultaneously to the domes. The analysis results of dome 1 (analysis
results not shown) indicate that σ1 was 34.29 MPa, σ 3 was −54.34 MPa, and the maximum
deformation was 10.85 mm. For dome 2, as shown in Fig. 8, the values were as follows: σ1 =63.01 MPa, σ 3 = −71.58 MPa, and the maximum deformation was 21.78 mm. When the static,
average live, and wind loads were applied simultaneously, dome 1 exhibited negligible changes
in the values of σ1, σ 3, and maximum deformation compared with the case where only the staticand average live loads were applied. However, in the case of dome 2, the σ1, σ 3, and maximum
deformation were significantly reduced when the static, average live, and wind loads wereconsidered together, as opposed to when only the static and average live loads were applied.
One possible explanation for this phenomenon is that the direction of the forces generated by4694

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Fig. 8. (Color online) (a) Maximum principal stress, (b) minimum principal stress, and (c) maximum deformationof dome 1 with static load combined with average live load and wind load.

the wind differs from that of the forces generated by the static and average live loads (especiallythe average live load). As a result, the stresses induced by the average live and wind loads
partially offset each other, leading to a reduction in the response of the designed domes to theaverage live load. Consequently, σ1, σ 3, and the maximum deformation become smaller in thepresence of all three loads. These results once again confirm that the static, uneven live, andwind loads are not the primary factors affecting the safety of the designed domes. Instead, theaverage live load remains the most crucial factor in determining the structural safety of thedomes.
On the basis of our simulation results, none of the single-layer mesh aluminum domes
designed in this study demonstrated any permanent deformation. This outcome serves ascompelling evidence that the designed mesh aluminum domes successfully meet the required
safety specifications. Moreover, these designed domes effectively distribute the loads, thereby

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minimizing the concentration of forces at individual nodes. This means that the various loads
are uniformly distributed to all nodes and tubes in accordance with their respective load
distribution regions. Consequently, the domes ensure an even distribution of stress throughout
the structure. To comprehensively analyze the structural performance, we have consolidated all
the relevant data in Tables 3 and 4. These tables provide a comprehensive overview of the
maximum normal stresses and deformations under different load conditions. By examining theirvalues, we gain valuable insights into the structural behavior of the mesh aluminum domes andcan evaluate their performance with greater precision.
The analysis reveals that, in the majority of load conditions, dome 1 exhibits a smaller
maximum normal stress than dome 2. Additionally, all maximum deformations observed indome 1 are significantly smaller than those observed in dome 2. These findings, as presented inTables 4 and 5, highlight the structural performance differences between the two domes.
Furthermore, the combined static and average live loads lead to dome 2 experiencing the highest
levels of stress and deformation. Therefore, it is crucial to give special consideration to thisparticular load condition during the dome’s design phase. However, it is important to note thateven when subjected to the six different loads, both domes exhibit maximum stresses that areconsiderably lower than the maximum stress tolerance of the material used (6061-T6 aluminumalloy). Consequently, even with a maximum deformation of 40.48 mm caused by the static load
combined with the average live load, the domes will not undergo permanent deformation. Theseobservations provide reassurance regarding the structural integrity of the designed domes andvalidate their compliance with safety standards.

4.

Conclusions

Table 3
Analysis results of the maximum normal stress of the designed domes for various load combinations.
Maximum normal stress σ max (MPa)
Load combinations
Dome 1
Dome 2
Static load
6.39
17.52
Static load + uneven live load
70.58
63.37
Static load + average live load
43.14
122.3
Static load + wind load
49.14
68.22
Static load + uneven live load + wind load
65.15
57.15
Static load + average live load + wind load
53.34
71.58

Table 4
Analysis results of the maximum deformation of the designed domes for various load combinations.
Maximum deformation (mm)Load combinations
Dome 1
Dome 2
Static load
3.82
5.88
Static load + uneven live load
12.02
21.97
Static load + average live load
15.69
40.48
Static load + wind load
10.41
21.71
Static load + uneven live load + wind load
13.31
20.26
Static load + average live load + wind load
10.85
21.78

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In this study, simulation results indicated that dome 1 experienced a maximum stress of 70.58
MPa under static load combined with uneven live load, and a maximum deformation of 15.69mm under static load combined with average live load. For dome 2, both the maximum stress(122.3 MPa) and maximum deformation (40.48 mm) occurred under static load combined withaverage live load. Throughout the six load conditions, most of the maximum normal stresses
were lower in dome 1 than in dome 2. However, when static load was combined with uneven live
load or combined with uneven live load and wind load, the maximum normal stresses in dome 1
surpassed those in dome 2. Nevertheless, under all six load conditions, dome 1 exhibited smaller
maximum deformations than dome 2. When the static, average live, and wind loads were applied
simultaneously, dome 1 displayed negligible changes in σ1, σ 3, and maximum deformationcompared with the case where only the static and average live loads were considered. Conversely,
dome 2 experienced significant reductions in σ1, σ 3, and maximum deformation when the static,
average live, and wind loads were applied, as opposed to when only the static and average live
loads were applied. This phenomenon can possibly be explained by the different forces generated
by the wind compared with the forces generated by the static and average live loads, particularly
the average live load.

Acknowledgments
This work was supported by the Foreign Cooperation Project of Fujian Provincial Departmentof Science and Technology (Grant No. 2020I0022), MOST 109-2221-E-390-023, MOST 1102622-E-390-002, and MOST 110-2221-E-390-020.

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