Equation Method Research Articles

Equivalent Circuit of a Stacked Piezoelectric Cymbal Vibrator.

In order to provide a convenient and fast calculation method, the equivalent circuit of a novel stacked piezoelectric cymbal vibrator is studied. The equivalent circuit model of the piezoelectric stack is derived by combining the equivalent circuit models of the thin piezoelectric disk and electrode. The equivalent circuit of the cymbal structure is then derived. The equivalent circuit model of the stacked piezoelectric cymbal vibrator is further proposed. The output axial displacements and output forces of the cymbal vibrator under different excitation voltages are investigated using the equivalent circuit model. The effectiveness of the equivalent circuit has been verified by comparing it with the finite element method. Furthermore, the equivalent circuit method has a much faster calculation speed than the finite element method.

Have Climate Factor Changes Jeopardized the Value of Qinghai Grassland Ecosystem Services within the Grass–Animal Balance?

Internal and external environmental changes have led to changes in the service value of plateau ecosystems. Plateau ecosystems are facing a risk of falling into “recession”. Meanwhile, climate change has become an important factor affecting the service value of plateau grassland ecosystems. In this paper, from the perspective of how changes in climate factors inhibit the value of ecosystem services of plateau grasslands, we adopt the equivalent factor method to measure the value of grassland ecosystem services in eight municipal levels in Qinghai Province from 2000 to 2021. We also construct a fixed utility model to test how changes in climate factors affect the value of ecosystem services and use the grass–animal balance as a mediating effect model for the test. The results of the study showed that (1) the increase in temperature and precipitation among the changes in climate factors significantly suppresses the ecosystem service value of grassland in the plateau. (2) The mediation test shows that the grass–livestock balance helped suppress the effects of climate factor changes on the ecological service value of plateau grassland. (3) The heterogeneity test shows that the area containing the Three-River-Source National Park is more resistant to climate factor changes. Climate factor changes have a greater impact on the ecosystem service value of plateau grassland in high altitude areas and have a significant positive effect on sustained low grassland carrying pressure index status. Therefore, in the protection of plateau grassland ecosystems, we should pay attention to the inputs in the ecosystems as well as appropriate grazing. At the same time, this study can provide a reference value for the decision-making with respect to ecological natural resources protection or restoration in plateau grassland under the effects of climate factors.

Attribution of climate change and human activities to spatiotemporal changes of ecological service value in Yunnan Province of China

Quantifying the influence of climate change and human activities on spatiotemporal changes of regional ecological service value (ESV) can provide key information for regional ecosystem protection. However, few studies have distinguished the contributions of climate change and human activities to the total ESV. In this study, Yunnan Province in Southwest China with high biodiversity and ESV was selected as a representative region for the attribution analysis of ESV changes. The Carnegie-Ames Stanford Approach (CASA) was used to calculate the vegetation net primary productivity (NPP), and improved equivalent factor method was used to calculate ESVs of different ecosystem service functions directly from NPP. Then, the multi-factor attribution analysis method was used to quantify the contribution rates of climate change and human activities to changes in ESV. Results show that the ESV in Yunnan Province increased by 12.9 % in 2000–2019 compared to 1980–1999 without considering economic development. Land use and cover change (LUCC) is the main cause for the increase in ESV with the contribution rate of 92.3 %, while that of climate change is only 7.7 %. Major components of ESV change are ESV changes in forests, grasslands, and farmland, which are all mainly caused by LUCC with the contribute rates of over 80 %. ESVs in different cities differ greatly, where the ESV and ESV per unit area in Pu'er City are 5.3 and 2.6 times as those in Zhaotong City, respectively. LUCC is also the main cause of ESV changes in all cities, with contributions rates generally exceeding 80 %. When considering economic development, the ESV in Yunnan has increased by 336.2 % in these two periods. Contribution rate of economic development to ESV increase in Yunnan is 80.3 %, while that of climate change and LUCC is only 19.7 %. The speed of ecological construction in Yunnan Province is far slower than that of economic development, and appropriate measures should be taken to improve the ecological services in the future.

Ecosystem service value and ecological compensation in Qilian Mountain National Park: Implications for ecological conservation strategies

Qilian Mountain National Park (QMNP) is a critical ecological barrier and water conservation area in northwestern China. Its diverse ecosystems provide significant ecosystem services, yet the valuation of these services and their dynamic responses to land use/cover (LULC) changes and ecological protection measures require detailed investigation. This study employs an improved equivalent factor method, tailored to the specific ecosystem types and LULC patterns of QMNP, to evaluate the ecosystem service value (ESV) across different LULC types. Using an elasticity analysis model, the sensitivity of ESV to LULC changes from 1990 to 2022 was quantitatively assessed. The results indicate that the ESV of QMNP increased from 46.13 billion RMB to 50.97 billion RMB between 1990 and 2022, mostly due to the growth of grassland and forest areas. The primary route for increasing the region’s ESV is the conversion of desert to grassland, and this should be a major area of emphasis for next ecological conservation initiatives. Regulating services form the core of the ESV in QMNP, with climate and hydrological regulation contributing significantly to the overall ESV. Maintaining the stability of forest, wetland, and water body areas is crucial for sustaining the total ESV of QMNP. Through the application of carbon emission coefficients and ESV methods, the average range for long-term ecological compensation standards in QMNP is expected to be between 3.78 billion RMB and 28.28 billion RMB annually. Additionally, we explore the impacts of ongoing ecological protection mechanisms on enhancing ESV. There is a pressing need to formulate integrated policy frameworks that balance ecological conservation with sustainable economic development. The study also highlights the necessity of strengthening the protection and foundational research of grasslands and water bodies to enhance the ESV of QMNP. These insights serve as a foundation for potential planning and management strategies in QMNP, aiming to maintain and enhance its ecosystem functions and services, thereby contributing to broader regional and global ecological stability.

Addressing magnetometer inconsistencies in drone-borne total field gradiometer surveys: case study from Rånbogen, Arctic Norway

SUMMARY Inconsistencies between (lightweight optical pumped) magnetometers in total field gradiometer surveys can introduce instrument-dependent responses, complicating geological interpretation. Here, we present an equivalent source-based processing method that combines equivalent sources with kernel regression to eliminate these instrument-dependent responses. We evaluate the method using a drone-borne triangular gradiometer survey from Rånbogen, Arctic Norway. The Rånbogen survey exhibits instrument-dependent responses in the measured total field differences, likely resulting from differences in the magnetometer’s heading error and the complexities from the induced field from the system itself. A synthetic gradiometer survey was generated to test the method, where different nonlinear synthetic heading errors were added to the synthetic magnetometer readings. The equivalent source-based processing method effectively removed these heading errors while constructing an equivalent source model that fits the actual underlying synthetic model. Furthermore, applying the method to the Rånbogen survey removes the data’s correlation to its orientation, thereby minimizing the effect of the instrument-dependent response. The method condenses the gradiometer data to a single equivalent source surface where the derivatives of the total field can be calculated to facilitate interpretation. The results suggest that the equivalent source-based method removes the inconsistencies between the magnetometers in a total field gradiometer survey, allowing for drone-borne gradiometer systems with multiple lightweight magnetometers.

Thermal calculation and experimental study of a double-disk magnetic coupler

Aiming to tackle the difficulties and inaccuracies in calculating the temperature field of double-disk magnetic coupler, a novel thermal calculation method is proposed, integrating the equivalent thermal network method and CFD method. This approach deviates from traditional methods that substitute empirical formulas with rotational speed. An equivalent thermal network model is established to ascertain the temperature rise at each network node. Additionally, a fluid-solid coupling model is constructed, and the impact of uneven air temperature distribution on air density, specific heat capacity, dynamic viscosity, and thermal conductivity is analyzed using the least squares method. The results reveal that after incorporating variable temperature air physical properties, the high-temperature area of the copper conductor decreases, the calculated temperature rise aligns closer to actual values, and air friction loss on the copper surface is reduced by 6.5 %. Experimental verification, conducted on a 55 kW double-disk magnetic coupler, demonstrates maximum errors of 8.86 % and 6.53 % when comparing experimental values to those calculated by the equivalent thermal network method and CFD method, respectively, thereby validating the proposed method. This research provides a theoretical reference for thermal calculations in double-disk magnetic coupler.

Coordinated frequency control strategy for modern power system considering engagement willingness

The large scale integration of renewable energy sources (RES) is posing unprecedented challenges to the frequency stability of modern power systems, with system inertia being the primary concern. Under such a landscape, this paper introduces a coordinated control strategy aiming at enhancing frequency stability by swiftly adjusting the power output of flexible resources to mitigate power imbalances and further dampen frequency fluctuations. Firstly, a communication-free center of inertia (COI) frequency estimation method is proposed. An equivalent inertia estimation method tailored for modern power systems is then developed by exploiting the correlation between synchronous inertia and active power fluctuations. By integrating the COI frequency variation rate with the estimated equivalent inertia, the imbalance power is calculated and compensated through the proposed coordinated control strategy. In this work, two typical flexible resources including photovoltaic (PV) generation and electric vehicles (EVs) are modeled and integrated into the testing system in PSCAD/EMTDC. Considering the contradiction between maximizing generation profit and reducing power output to mitigate frequency variation, the Corporate Social Responsibility (CSR) of renewable Generation Companies (GENCOs) is modeled to sketch their willingness of engaging into frequency support. Moreover, the frequency modulation potential of EVs in both commercial and residential areas are quantified for practical implementation. The simulations results successfully validate the effectiveness of the proposed control strategy.

Experimental study and life prediction for aero-engine turbine blade considering creep-fatigue interaction effect

As an important failure form of the turbine blade, creep-fatigue interaction damage affects the safe operation and maintenance strategy of aero-engine, and has been the focus of scientific research and the academic community. Firstly, based on the Kachanov-Rabotnov-Lemaitre continuum damage mechanics theory and the nonlinear symmetry of creep damage and fatigue damage, a creep-fatigue life prediction model is constructed considering the interaction effect in this paper. Then, based on the thermal-fluid–solid multi-physical field coupling numerical simulation of the turbine blade, the equivalent method of creep-fatigue load spectrum was explored according to the equal damage criterion and linear damage rule, and the creep-fatigue interaction test of smooth samples of the blade material was conducted to analyze the creep-fatigue fracture morphology. Finally, the stress term in the creep-fatigue life prediction model of blade material is modified by the correction factor α, and the modified creep-fatigue life prediction model of the turbine blade is constructed considering the interaction effect. The results show that the modified creep-fatigue life prediction model considering the interaction effect has a high life prediction ability with an error of 3.9%. The above research has important scientific research value for the life extension design of turbine blades and the improvement of aero-engine maintenance strategy.

Stress-induced warpage estimation of advanced semiconductor copper interconnect processes

The growth of the semiconductor industry is driven by the demand for electronic products and high transistor density. However, complex manufacturing processes generate residual stress and result in wafer warpage. Therefore, mastering wafer warpage has become a crucial challenge. This study proposes a process-oriented simulation methodology with simulation-based equivalent material method to overcome the difficulty of finite element modeling and the substantial amount of computation time. Three different methodologies, including volume percentage, representative volume element, and Timoshenko bi-material approach, are discussed due to the estimation of residual stress for equivalent material. In addition, each methodology is validated through process-oriented simulations and comparison with measurement data. The Timoshenko bi-material approach is efficient in predicting warpage in the back end of line (BEOL) interconnects and provides a comprehensive understanding of the warpage variation that occurs during different stages of BEOL.

A study on fresh, mechanical, and thermal properties of limestone calcined clay cement (LC3) blended with cementitious materials

In light of environmental concerns about cement manufacture, limestone and thermally activated kaolinitic clays are being explored as supplementary cementitious materials with the potential to reduce CO2 emissions and energy usage. The use of calcined clay and limestone for clinker replacement to create a tertiary blend called limestone calcined clay cement (LC3) is one of the most promising emerging technologies for meeting environmental requirements. This paper reports on the evaluation of the fresh-state and hardened properties of cementitious pastes and self-compacting concretes (SCC) prepared using the concrete equivalent mortar method made with LC3 systems containing 30%, 35%, and 40% metakaolin (LC-30MK, LC-35MK, and LC-40MK) in comparison with ordinary Portland cement (OPC). Paste and concrete equivalent mortar specimens were prepared to investigate water demand, setting time, and workability (mini-slump flow test). Also, the compressive strength and drying shrinkage after 7 and 28 days, as well as thermal conductivity after one year of curing, were examined. The obtained results showed that the incorporation of metakaolin resulted in increased water demand to reach normal consistency. The setting time of LC3 mixtures also increased, while the same workability behavior was observed for all mixtures. LC-30MK can provide compressive strength that is comparable to OPC, especially after the first few days of curing. However, the compressive strengths of LC-35MK and LC-40MK are lower than those of OPC. Nevertheless, they demonstrate noteworthy strength characteristics. All LC3 mixtures exhibited relatively low drying shrinkage and reduced thermal conductivity compared to the OPC mixture.

Vibration suppression in SDOF systems coupled to a nonlinear energy sink under colored noise

This study analyzes the stochastic vibration suppression and optimization of the single-degree-of-freedom (SDOF) system equipped with the cubic stiffness nonlinear energy sink (NES) under colored noise excitation. Two theoretical methods are proposed: an integrated method (denoted as EL-ELM) that combines evolutionary Lyapunov theory with the equivalent linearization method, and the other is an empirical formula. Using EL-ELM, the coupled nonlinear system is simplified to an equivalent linear stochastic system, allowing for a theoretical analysis of the impact of NES structural parameters on suppression performance and the precise determination of optimal parameter configurations for the best suppression effects. Subsequently, based on the results from the EL-ELM and the response data, an empirical formula has been developed that clearly describes the comprehensive laws governing the optimal NES parameters as they vary with vibration system parameters and stochastic excitation. Through error analysis and comparison of the two methods, it is found that the empirical formula significantly outperforms EL-ELM in terms of accuracy and computational cost, but it is contingent on solid prior knowledge. This study explores the influence of NES structural parameters on the system’s dynamic response and energy, further validating the effectiveness of the proposed methods in identifying optimal structural parameters. The phenomenon of targeted energy transfer (TET) under different NES structural parameters is also explained. The methodologies introduced in this study have strengthened the theory of vibration suppression. Specifically, the empirical formula excels in accuracy and computational efficiency by effectively using prior knowledge. The EL-ELM method, owing to its theoretical insights, is vital for analyzing complex stochastic nonlinear models. Combining these approaches offers guidance for advancing vibration control in theoretical and practical domains.

An effective and efficient approach for smoke control in underground parking garages

Underground parking garages are enclosed spaces not directly exposed to the exterior. A smoke control system is typically required to facilitate occupants’ safe evacuation/relocation and assist in firefighting/rescue. Currently, there is a lack of guidelines for designing such systems in primary codes/standards. Only a limited number of local authorities have developed amendments to address this issue. These amendments either rely on outdated approaches, such as air change method, or simply repurpose carbon monoxide ventilation systems for smoke control without conducting additional engineering analysis and providing justification. The intent of this study is to examine the adopted approaches and explore an effective and efficient approach for garage smoke control. According to the study’s findings, it is discovered that garage floor height significantly impacts the performance of smoke control system. Additionally, structural components (beams) also influence the performance of smoke control system. Moreover, this study derives a linear equation to ascertain available safe egress time (ASET) when utilizing the carbon monoxide ventilation system or typical air change methods. Taking cost into consideration, the study concludes that for effective and cost-efficient smoke control in large underground garages, employing a carbon monoxide ventilation system is preferable to the traditional or equivalent air change method.

Load resistance of masonry infilled panels for steel frames to mitigate progressive collapse caused by middle column missing

The load resistance of masonry infilled panels in upgrading the steel frame to mitigate progressive collapse was quantified experimentally and analytically in the current study. Four 1/2-scale steel subframes were tested, including two bare subframes without infilled panels for reference and two infilled subframes to assess the effects of infilled panels. Two types of connection were investigated in current study: welded connection and top and seat angle connection. The test result showed that infilled panels provided a greater improvement in initial stiffness and peak load of the steel subframe with top and seat angle connections compared to the infilled steel subframe with welded connections. On the premise that the connections retained their integrity, the strut mechanism of infilled panels could change from a diagonal strut mechanism forming in the whole panel to an off-diagonal strut mechanism formed in the remaining intact corner region with increasing vertical deflection. A novel equivalent multi-strut modelling method was proposed for the prediction of the infilled panel behavior with an acceptable level of accuracy. This model incorporates the shifts in the position of plastic hinges, which were influenced by the specific types of connection and the load-resisting mechanisms of the infilled panel. The analysis result demonstrated that the model slightly overestimated the load resistance of infilled panels within the steel frame with simple connections and slightly underestimated the load resistance of infilled panels within steel frame with semi-rigid or rigid connections.

Impact of freeze recovery method on high-speed fracture in metal cylindrical shells

The freeze recovery method (FRM) is a crucial approach for investigating the high-speed fracture process of metal cylindrical shells under explosive loading. However, the precise impacts of the recovery process on the deformation and fracture behavior of such shells remain unclear, significantly constraining the widespread application of this method in high-speed fracture studies. This paper quantitatively evaluates the effects of the expansion contour, fracture mode, and damage state of intermediate shells at different stages of fracture development using a crack evolution simulation method and nondestructive crack detection technique. The recovered shell contour can effectively represent the free expansion contour of the shell at the equivalent moment, with an error of less than 4%. Impact induces tensile cracks on the outer wall of the shell, which leads to changes in the local fracture mode. A method of crack elimination and equivalence in the damage statistics of the recovered shell is proposed to address this effect. The recovered shell can characterize the damage evolution during free expansion at the equivalent moment after eliminating the influence of excess tensile cracks. Based on the principle of stress analysis and energy conservation, the formation mechanism of tensile cracks in the outer wall of the shell is explored, and the correlation between tensile cracks and recovery time is elucidated. The study shows that the impact of fracture damage caused by freezing recovery is gradually reduced over time. The improved freezing recovery method based on the hard recovery principle is successfully used to recover the multistage intermediate shell, meeting the demand for obtaining the transient physical model in the high-speed fracture field.

Low-Frequency Sound-Insulation Performance of Labyrinth-Type Helmholtz and Thin-Film Compound Acoustic Metamaterial.

This paper presents a type of acoustic metamaterial that combines a labyrinth channel with a Helmholtz cavity and a thin film. The labyrinth-opening design and thin-film combination contribute to the metamaterial's exceptional sound-insulation performance. After comprehensive research, it is observed that in the frequency range of 20-1200 Hz, this acoustic metamaterial exhibits multiple sound-insulation peaks, showing a high overall sound-insulation quality. Specifically, the first sound-insulation peak is 26.3 Hz, with a bandwidth of 13 Hz and giving a transmission loss of 56.5 dB, showing excellent low-frequency sound-insulation performance. To further understand the low-frequency sound-insulation mechanism, this paper uses the equivalent model method to conduct an acoustic-electrical analogy, construct an equivalent model of the acoustic metamaterial, and delve into the sound-insulation mechanism at the first sound-insulation peak. To confirm the validity of the theoretical calculations, physical experiments are carried out by 3D printing experimental samples. The analysis of the experimental data has yielded results that are consistent with the simulation data, providing empirical evidence for the accuracy of the theoretical model. The material has significant practical application value. Finally, various factors are studied in depth based on the established equivalent model, which can provide valuable insights for the design and practical engineering application of acoustic metamaterials.

Research on multi-heat source arrangement optimization based on equivalent heat source method and reconstructed variational autoencoder

The variational autoencoder (VAE) architecture has significant advantages in predictive image generation. This study proposes a novel RFCNN-βVAE model, which combines residual-connected fully connected neural networks with VAE to handle multi-heat source arrangements. By integrating analytical solutions, polynomial fitting, and temperature field superposition, we accurately simulated the temperature rise distribution of a single heat source. We further explored the use of multiple equivalent heat sources to replace adiabatic boundary conditions. This enables the analytical method to effectively solve the two-dimensional conjugate convective heat transfer problem, providing a reliable alternative to traditional numerical solutions. Our results show that the model achieved high predictive accuracy. By adjusting the β parameter, we balanced reconstruction accuracy and latent space generalization. During the stable phase of the multi-heat source optimization iteration, 73.4% of the results outperformed the dense dataset benchmark, indicating that the model successfully optimized heat source coordinates and minimized peak temperature rise. This validates the feasibility and effectiveness of deep learning in thermal management system design. This research lays the groundwork for optimizing complex thermal environments and contributes valuable perspectives on the effective design of systems with multiple thermal sources or for applications like multi-beam lighting equalization.

Experiment and analysis on seismic performance of a self-centering Y-eccentrically braced frames structure

Conventional eccentrically braced frames (EBFs) exhibit significant residual deformations following major earthquakes, necessitating costly repairs for the damaged structures. This study proposed a novel self-centering Y-eccentrically braced frames (SC-YEBFs) system to enhance the seismic resilience. A theoretical mechanical model which takes into account its components is formulated to predict the lateral load behavior of SC-YEBFs. The pseudo-static experiments were conducted on four specimens, and the resulting observations and analyses demonstrate that the shear links effectively function as ductile fuses, dissipating a significant portion of the input energy to safeguard the main frame from damage. Furthermore, the self-centering joint exhibits a hinge-like behavior with remarkable self-centering characteristics. The structural reparability of all specimens was found to be exceptional during major seismic events. By increasing the initial prestress and sectional area of steel strands, the self-centering performance can be further enhanced. The damaged shear links could be easily detached by loosening bolts, and the consideration of prestress loss is nonnegligible to ensure an exceptional self-centering performance. The proposed theoretical model predicted the mechanical properties of SC-YEBFs, including lateral stiffness, energy dissipation, and self-centering mechanism, through a comparison with experimental results. Moreover, the theoretical model was utilized to propose an equivalent simulation method for simulating self-centering joint and shear link using Connector function in ABAQUS software, while establishing a simplified frame finite element model for further analysis.

Multi-Scale Analysis of Ecosystem Service Trade-Offs/Synergies in the Yangtze River Delta

The transformation of ecosystem structure leads to changes in ecosystem services (ESs) and their relationship. However, most research in this area has focused on particular scales and timeframes, often overlooking the significance of spatial and temporal variations. Therefore, we used the equivalent value method to evaluate seven typical ESs in the Yangtze River Delta (YRD) between 2000 and 2020: food production (FP), water supply (WS), climate regulation (CR), environmental purification (EP), soil conservation (SC), biodiversity maintenance (BM), and aesthetic landscape (AL). We further employed the Spearman correlation coefficient and bivariate Moran’s I to evaluate the relationship of ESs and their spatial heterogeneity at grid, township, county and city scales. Our results show that (1) All ESs except AL exhibited a fluctuating upward trend from 2000 to 2020, resulting in a total increase in ecosystem service (ES) value of RMB 650.63 billion. (2) Approximately 70% of the ES pairs demonstrated a synergistic relationship, with the exception of FP and other ESs, which mainly showed a trade-off. (3) With the scale increased from grid to city level, the degree of trade-off between FP and other ESs strengthened at different levels, while the synergy degree of among other ESs gradually decreased. (4) The relationship between ESs demonstrated strong spatial heterogeneity, with FP and other ESs exhibiting trade-offs primarily in the northern and southern YRD, while other ES pairs exhibited mostly synergy in these regions. This study provides scientific information for governments to optimize land use distribution and improve ESs.

Performance analysis of multi-stack fuel cell systems for large buildings using electricity and heat

The fuel cell market, which utilizes hydrogen as a fuel for zero-carbon power generation to address global warming, continues to grow steadily. In the building sector, where small-scale fuel cells of 10 kW or less have been predominant, there is increasing interest in scaling up fuel cells to increase deployment and reduce system costs. The multi-stack fuel cell system (MFCS), which consists of connecting multiple modules, is one method of configuring large-scale fuel cell systems, offering advantages in system efficiency, durability, and cost. The objective of this paper is to compare and analyze the behavior of the MFCS according to different operation strategies. In particular, it compares the Equivalent operation method, which behaves similarly to the single-stack fuel cell system (SFCS), with others (Daisy-Chain, Electrical Optimization). Unlike previous studies that only focused on the electrical efficiency of MFCS, this study analyzed thermal energy, which is indispensable in building applications, to maximize the effects of MFCS. Simulation of operation strategies based on the electricity and heat demand of a specific residence showed that MFCS outperformed the SFCS in terms of electrical and heat efficiency, hydrogen consumption, degradation, and operating costs.

Analysis of the overall structural strength and optimization recommendations for ultra-large container ships based on the improved equivalent design wave method

Ultra-large container ships face challenges in structural strength under complex sea conditions. The traditional equivalent design wave method inadequately considers nonlinear wave effects, leading to inaccuracies in strength assessments. This article improves the method by incorporating nonlinear wave effects and optimizing wave spectrum parameters to better simulate structural responses. A study on a container ship, using refined wave load calculations and finite element analysis, focusing on stress distribution in critical hull areas. The findings show that the enhanced method more accurately reflects real loading conditions, confirming the ship’s structural soundness and offering optimization suggestions for improved safety and longevity.