1. Introduction
As global climate change increasingly affects building design and structural performance, coastal buildings face numerous challenges, particularly regarding wind loads [
1], corrosive environments [
2], and structural durability [
3]. Wind loads not only threaten the stability and safety of buildings but also contribute to wind-induced fatigue, impacting long-term performance [
4]. Therefore, selecting appropriate building materials [
5] and design solutions [
6] is crucial for structures located in coastal areas. This is especially true for dynamic structures like movable sculptures, where wind-induced fatigue significantly affects their shape changes and structural stability [
7,
8].
Traditional building materials, particularly carbon steel, are prone to rapid deterioration in marine environments due to their inadequate corrosion resistance [
9]. The aggressive nature of saltwater, coupled with high humidity and fluctuating temperatures, accelerates the corrosion process, undermining the structural integrity and long-term functionality of carbon steel [
10]. In coastal regions, where structures are consistently exposed to harsh environmental conditions, including saline mist and extreme weather events, the degradation of carbon steel is notably accelerated [
11]. This leads to increased maintenance requirements, elevated costs, and potential safety risks. Consequently, the use of carbon steel in such settings has become increasingly untenable due to its relatively short lifespan and the high cost of maintenance, rendering it an impractical solution for coastal construction [
12].
To mitigate these challenges, stainless steel, particularly nickel-saving stainless steel, has emerged as the preferred material in coastal building design due to its superior corrosion resistance, mechanical strength, and cost-effectiveness over the lifecycle of the structure [
13]. Stainless steel’s ability to withstand the corrosive effects of saltwater and other harsh environmental factors is due to the formation of a passive chromium oxide layer that protects the material from further oxidation [
14]. This makes it an ideal choice for coastal structures exposed to continuous and severe marine conditions. Notably, nickel-saving stainless steel grades, such as S22152, offer enhanced corrosion resistance, higher tensile strength, and excellent resistance to localized corrosion, such as pitting and crevice corrosion, all while reducing dependence on costly nickel [
14,
15,
16]. The incorporation of elements like nitrogen and molybdenum, instead of nickel, enhances the material’s performance while simultaneously reducing material costs, making it a more economically viable option compared to conventional stainless steel grades [
17]. Furthermore, stainless steel’s superior weldability ensures strong, durable joints, crucial for maintaining the structural integrity of large-scale coastal installations [
18]. Therefore, the combination of durability, cost efficiency, and fabrication versatility positions nickel-saving stainless steel as the material of choice for sustainable and reliable coastal construction projects.
Despite the widespread recognition of stainless steel’s corrosion resistance, the impact of wind-induced fatigue on stainless steel structures remains an important research topic [
19]. Under wind load, dynamic structures such as the leaves of movable sculptures often experience significant cyclic loading [
20,
21,
22]. This cyclic loading can lead to material fatigue, ultimately affecting the structural safety and functionality [
23]. As a new material, nickel-saving stainless steel S22152 has not been fully studied in the context of wind-induced fatigue, particularly in its performance in real-world engineering applications.
This study focuses on the dynamic sculpture atop the Welcome Tower at Yazhou Bay in Sanya, with an emphasis on the sculpture’s design, material selection, and wind-induced fatigue performance. By utilizing stainless steel materials and incorporating advanced mechanical drive systems, the sculpture achieves a perfect balance between stability under wind loads and dynamic aesthetics. The study conducts detailed wind-induced fatigue damage assessments through wind tunnel testing, numerical simulations, and fatigue analysis, providing an effective design framework and theoretical support for similar future projects.
3. Leaf Structures Scheme
As shown in
Figure 12 and
Figure 13, the sculpture consists of a total of 8 leaves, with the lower 4 being larger and the upper 4 smaller. The movement trajectories of the leaves and collision detection were simulated using Autodesk Revit software.
The design of the leaf structure has two key differences compared to ordinary building structures: First, the leaf structures are mechanically driven and must be as lightweight as possible to reduce the mechanical load. Second, they are situated in an open coastal environment, subject to harsh corrosive conditions.
3.1. Leaf Structure
As shown in
Figure 14, The leaf features a spatial grid structure, with a triangular core at the center and trusses suspending the sides to form its outer profile. At the tip of the leaf, an I-shaped solid web section is used for the overhanging member due to space constraints.
The core area of the leaf contains numerous intersecting nodes, using truncated spherical nodes. The edge nodes have fewer intersecting members, and intersecting nodes are used in these areas, as shown in
Figure 15.
3.2. Structure Material
The sculpture is located outdoors near the coastline, where it is exposed to harsh corrosive conditions. Due to the limited interior space of the leaf, it is impossible to set up a walkway for maintenance. Therefore, ensuring the durability of the leaf structure is crucial.
Three material options were considered: Option 1 involves using aluminum alloy, which is lightweight and has good corrosion resistance. However, its strength significantly decreases after welding, making it unsuitable for wind resistance requirements. Additionally, mechanical connection nodes have poor adaptability to the irregular spatial structure of the project. Option 2 uses ordinary steel with a coating, which is easy to construct but lacks durability, as the coating degrades over time. Option 3 involves stainless steel, which offers both construction convenience and durability but is more expensive. Therefore, nickel-saving stainless steel (S22152/S32001) was selected. This type of stainless steel reduces the nickel content and increases the proportion of other alloys, thereby reducing costs while maintaining strength and corrosion resistance. The pitting corrosion rate of this material is approximately 7.82 g/(mh
2), comparable to that of conventional 304 austenitic stainless steel (Cr18Ni8 type). Thus, stainless steel (S22152/S32001) was chosen as the material for the leaf structure. The chemical composition and mechanical properties of this stainless steel are presented in
Table 2 and
Table 3.
3.3. Economy and Embodied Carbon Emissions Consideration
We also compared the economic costs and embodied carbon emissions of stainless steel and coated steel. Although stainless steel has a higher initial cost during construction, its lower maintenance frequency and longer service life lead to reduced total cost and embodied carbon emissions over the entire lifecycle. Therefore, the use of stainless steel offers better long-term economic and environmental performance. Finally, we chose stainless steel as the structure material of leaves.
4. Wind-Induced Fatigue Damage Calculation
4.1. Wind Tunnel Test Overview
The rigid model pressure wind tunnel test was performed at the TJ-2 Atmospheric Boundary Layer Wind Tunnel Laboratory of the Civil Engineering Disaster Prevention and Mitigation National Key Laboratory at Tongji University. Due to the large size of the model, the lower third of the tower was removed to avoid significantly affecting the overall flow characteristics. The blockage ratio during the wind tunnel test was maintained below 5%, with a calculated value of approximately 3.75%. The geometric scale ratio was 1:50, and the time scale ratio was 1:12.25. The experimental model is shown in
Figure 16.
The silver PTFE mesh membrane covering the leaf surfaces primarily serves decorative and protective purposes. In the 1:50-scale wind-tunnel model, solid surfaces were used instead of perforated membranes to ensure reliable pressure measurements. Although the actual porosity of the membrane was not determined, it may slightly reduce mean and fluctuating pressure coefficients. Therefore, adopting solid surfaces represents a conservative assumption, ensuring that the design wind loads and fatigue analysis reflect the upper-bound aerodynamic condition.
The far-field terrain analysis was performed using topographic and land-use data within a 5 km radius of the site, obtained from GIS and satellite imagery, supplemented by on-site photographs. The analysis identified the surroundings as a coastal urban zone with low- to medium-density buildings and vegetation, corresponding to Class B wind field. The measured wind speed and turbulence intensity profiles during the test were compared with the specifications [
3], where the roughness of the Class B terrain was taken as 0.15, as shown in
Figure 17a. In this comparison,
z represents the relative height of the test point (i.e., the actual height divided by 2.5 m),
U is the measured wind speed at height
z,
Iu is the turbulence intensity at the test point, and
U_
ref is the reference wind speed measured at the reference point. The reference point denotes the location at the reference height (z_ref) used for measuring the reference wind speed (U_ref) in the atmospheric boundary-layer flow. The reference height corresponds to the top of the simulated boundary layer in the wind-tunnel test.
Considering the design standards and testing equipment, the wind tunnel test was conducted with an actual wind speed of 37.25 m/s and a wind speed scale ratio of 1:4.08. The range of wind direction angles was from 0° to 350°, with intervals of 10°, resulting in a total of 36 wind direction angles. The specified 0° wind direction is shown in
Figure 17b. In the subsequent calculations, the wind pressure coefficient time histories at the leaf measurement points under the 36 different wind direction conditions were extracted as input data for the structural stress analysis of the wind load.
It should be noted that the 0° wind direction in the wind tunnel test differs by 152° from the 0° wind direction in the meteorological data. When numerically integrating the joint probability density function of wind speed and wind direction, the wind direction angle range for integration was determined based on the wind direction conditions observed in the wind tunnel test.
4.2. Fatigue Stress Amplitude
In the wind tunnel test, a total of 15,000 data points were recorded at each test point. These data were converted using the time scale ratio to match the wind pressure time history for a 10 min duration in the actual engineering scenario. To optimize computational efficiency, only 1500 data points were selected, corresponding to 1 min of pressure measurement data. An equidistant sampling method was then applied, extracting 300 wind pressure data points from the wind tunnel test to serve as the wind load input, with a time step of 0.2 s.
The basic wind pressure
w0 used in the wind tunnel test was selected based on the 50-year recurrence period for Sanya City, with a value of 0.85 kPa. A total of 36 conditions were calculated based on the experimental setup. The measured wind pressure coefficients were averaged in blocks and converted into surface loads applied to the leaf surfaces. For leaf 1, the calculation model is shown in
Figure 18, where the positions and numbers of some rods are indicated.
The stress time history of the internal stainless steel tubes in the leaves was calculated using SAP 2000. In the SAP 2000 analysis, the root of the leaf was fully fixed to simulate the rigid connection with the mechanical device, while the rods were modeled as pin-connected truss members. The wind pressure time histories obtained from the wind tunnel test were converted into equivalent surface loads and applied to the leaf panels. When the wind speed reached 24 m/s, the maximum instantaneous stress (106 MPa) occurred at the end node of rod 103 on leaf 1, while the maximum stress amplitude, obtained from the stress-time-history analysis, was 132 MPa at the end node of rod 111. Both conditions occurred on leaf 1, which was therefore selected to represent the entire structure in the fatigue-life analysis. Following the maximum stress principle, four critical rods were selected for fatigue analysis: rods 72, 103, 111, and 126. The stress time histories at the nodes of these rods were extracted for further analysis.
Finite element calculations using ABAQUS revealed that the maximum stress at the ball joints, where multiple rods are connected, was approximately 1.5 times greater than the maximum stress in the individual rods. As a result, the stress in the rods was amplified by a factor of 1.5, and the fatigue life of the ball joints was verified. Stress amplitude and mean stress were calculated using the rain-flow counting method [
25].
The basic steps of the rain-flow counting method are as follows: First, the time history data is processed by retaining only the peak and valley values. Next, four consecutive values are extracted in time order, and the difference between the second and third values is compared with the difference between the first and fourth values. If the difference between the second and third values is greater than or equal to the difference between the first and fourth, the average of the second and third values is taken as the mean stress for one stress cycle, and their difference is the stress amplitude for that cycle. The second and third values are then removed from the load time history, and the process is repeated for the next four values. If the difference between the second and third values is smaller than the difference between the first and fourth, the first value is retained, and the next four values are extracted in order, corresponding to values 2, 3, 4, and 5. The process is repeated for all values. Finally, all stress amplitudes and mean stresses from the second step are summarized, and the frequency of each combination of stress amplitude and mean stress is counted. This method is known as the “four-point” rain-flow counting method.
For example, for rod 111, under a 350° wind direction and a wind speed of 23 m/s, its stress time history is shown in
Figure 19. The stress amplitude, mean stress, and number of stress cycles for this condition, calculated using the rain-flow counting method, are shown in
Figure 20 and used for subsequent fatigue calculations.
4.3. Fatigue Life and Calculation Process
The stress amplitude obtained using the rain-flow counting method in
Section 4.2 does not account for the case when the mean stress is zero. The effect of mean stress on the stress amplitude must therefore be considered and corrected. A commonly used correction method is the Goodman correction [
26], which is expressed as:
where
S0 is the corrected stress amplitude,
Sa is the original stress amplitude,
Sm is the mean stress, and
Su is the material’s ultimate tensile strength (620 MPa). After applying the Goodman correction, the corrected stress amplitudes and the corresponding number of stress cycles for each condition were obtained.
The fatigue verification method used in this study is the Miner linear fatigue accumulation theory [
27], which assumes that fatigue damage accumulates linearly. For a component subjected to a constant stress level
S, the number of load cycles until failure is denoted as
N, and the fatigue damage for
n cycles is given by:
The total damage accumulated from different stress levels is the sum of individual damages. The total damage
D is calculated as follows:
When
D = 1, the component reaches fatigue failure. The fatigue life of the welded joints is calculated using the
S-
N curve of stainless steel S22152, which is calculated as follows:
The joint probability distribution formula for wind speed and wind direction is as follows:
where
a,
b,
c,
d,
e, and
f represent the fitting coefficients.
Table 4 lists the values of each coefficient for this fifth-order polynomial fit.
To calculate the joint probability of wind speed and wind direction, the wind speed and wind direction were divided into discrete intervals. In the wind tunnel test, the wind directions were divided into 36 groups with an interval of 10°. For the wind speed, the range of 0–24 m/s was divided into 12 groups, with an interval of 2 m/s. The probability density function was then divided into 12 × 36 sections, and numerical integration was performed for each area to obtain the joint probability density of wind speed and wind direction.
For the fatigue analysis, each rod was also divided into 12 × 36 conditions. Using SAP 2000, the stress time histories were calculated, and the stress amplitude, mean stress, and number of stress cycles were further obtained using the rain-flow counting method. For each condition, the cumulative fatigue damage was calculated using the Miner formula. The cumulative damage was then multiplied by the probability of each condition’s occurrence. The results for all 12 × 36 conditions were summed to obtain the total cumulative fatigue damage for a single rod within 1 min. This value was then multiplied by 60 × 24 × 365 to obtain the annual cumulative fatigue damage, and the reciprocal of this value was taken to calculate the fatigue life. Based on these steps, the fatigue life for the four rod connection nodes was obtained, as shown in
Table 5. It is evident that the most unfavorable fatigue life is 380 years, during which no fatigue damage occurs.
5. Conclusions
This study focuses on the design, material selection, and fatigue analysis of a dynamic movable sculpture at the top of the Welcome Tower in Yazhou Bay Bougainvillea Park, Sanya. The sculpture, driven by mechanical systems, consists of eight movable leaves that transform into five distinct shapes. The design addresses the challenges of the harsh coastal environment by using nickel-saving stainless steel (S22152/S32001), chosen for its durability and corrosion resistance. A comprehensive mechanical system enables the leaves to perform functions such as rising, opening and closing, and rotating, all driven by a hydraulic system. To withstand wind loads, the sculpture incorporates safety mechanisms, including horizontal safety rods and locking devices for added stability in high wind conditions.
The fatigue analysis of the sculpture was conducted using wind tunnel test data, numerical simulations, and the rain-flow counting method. The study found that the maximum stress at the ball joints, where the rods are connected, was approximately 1.5 times that of the individual rods. The Goodman correction was applied to adjust the stress amplitude for mean stress effects, and the Miner linear fatigue accumulation theory was used to calculate the fatigue damage. The analysis revealed that the most unfavorable fatigue life for the sculpture’s components is 380 years, indicating that the structure will not experience fatigue damage during its expected lifespan. This research provides valuable insights into the design and material selection for dynamic sculptures in coastal environments, ensuring their long-term stability and resilience to wind-induced fatigue.