Equation Method Research Articles

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.

Probabilistic study on non-stationary extreme response of transmission tower under moving downburst impact

Localized severe non-synoptic winds, such as downbursts and tornadoes, cause frequent structural failures of the electric transmission lines worldwide. This paper aims to develop an analytical approach to evaluate the extreme non-stationary dynamic response of transmission towers under downbursts in frequency domain. First, the empirical models of time-varying mean wind and non-stationary fluctuating wind of moving downbursts are introduced to deduce the transient wind loads on transmission towers in time domain. The closed-form frequency domain solutions of non-stationary fluctuating downburst wind-induced response of transmission towers are derived based on the pseudo excitation method. Furthermore, through the up-crossing extreme value theory, the probability distribution of the non-stationary extreme response is studied. Finally, the peak factors of the non-stationary and the equivalent stationary theoretical methods are compared based on the proposed equivalent stationary extreme value distribution for engineering application. The proposed theoretical framework is validated by stochastic sampling simulation and finite element analysis. It is found that the proposed theoretical framework can accurately assess the extreme value responses of transmission towers under non-stationary moving downbursts.

Multiband electromagnetically induced transparency-like on metamaterials

In recent years, the electromagnetically induced transparency-like (EIT-like) of metamaterials has been widely concerned due to obtain high Q, which has potential applications in the field of sensing and slow light. In this paper, an EIT-like metamaterial structure in the microwave band was investigated, which can realize to multi-band EIT-like phenomena. The equivalent circuit method and the electric field distribution are used to study the EIT -like effect’ mechanism, and the multi-band EIT-like phenomenon is discussed by analyzing its structural parameters. The results show that the multi-band EIT in the proposed structure is obtained by coupling multiple bright modes to multiple dark modes. The change of transmission spectrum is discussed by changing the environmental permittivity. The results have potential applications in areas such as refractive index sensing, filters.

Simulating the effects of geometric imperfections on the buckling of axially compressed cylindrical shells through reducing localized stiffness

Thin-walled cylindrical shells are prone to buckling under axial compression. The load-carrying capacity of the shells can thus be significantly reduced. It's well known that the buckling loads of axially compressed cylindrical shells are quite sensitive to the initial geometric imperfections. Even though the magnitudes of these imperfections are relatively small, the corresponding buckling loads can be significantly reduced compared to the perfect shells. In this paper, the effects of geometric imperfections on the buckling loads are equivalently simulated by reducing localized stiffness of the cylindrical shells. Firstly, the method for simulating the effects of geometric imperfections on the buckling loads of cylindrical shells is introduced in detail. Then, the proposed method is used to simulate the effects of single dimple imperfection and multiple dimple imperfections on the buckling loads of cylindrical shells. Results show that the buckling loads and load-displacement curves of the shells with single and multiple dimple imperfections can both be well simulated by the localized stiffness reduction method. Furthermore, the measured geometric imperfections from manufactured cylindrical shells are investigated. The numerical results simulated by the proposed method are also verified by the shell models with real measured geometric imperfections and the experimental results from the literature. The applicability and reliability of the proposed equivalent method in dealing with complex imperfection configurations can thus be validated. Results show that the proposed equivalent method is suitable for simulating various geometric imperfections of the cylindrical shells. It is promising to be applied as an efficient tool to quantify the imperfection sensitivity of buckling loads and provide a new solution for buckling analysis of cylindrical shells.

A Grouping and Aggregation Modeling Method of Induction Motors for Transient Voltage Stability Analysis

Induction motors are the most common type of motor in power systems, constituting approximately 70–90% of the dynamic loads, making them significant contributors to system dynamics. In transient voltage stability analysis, dynamic equivalent models are commonly used to simplify the representation of a group of induction motors. This paper presents a method for the grouping and aggregation of induction motors at a common bus. Firstly, grouping rules are provided for clustering induction motors into several subgroups based on the mechanical principles of rotor force and motion, and aggregation rules are provided for aggregating a motor subgroup into a single-unit model based on the relationship between voltage drop and power transmission in distribution networks. Secondly, guided by the grouping rules, high-speed remaining electromagnetic torque and low-speed remaining electromagnetic torque are defined as new clustering indicators, and an adaptive K-means clustering method using silhouette coefficient verification is introduced to obtain the optimal motor subgroups. Thirdly, guided by the aggregation rules, a dynamic equivalent method is further introduced to obtain the equivalent single-unit model from a motor subgroup. Lastly, a transient voltage stability simulation in a typical distribution network is presented to illustrate that the proposed clustering and equivalent methods are more reasonable, accurate, and effective than traditional methods, as the obtained model has better dynamic characteristics and can more accurately reproduce the process of voltage collapse.

Assessing the equivalent spring modelling method of CFS elements encased in ultra-lightweight concrete

An efficient finite element approach was recently developed to analyse encased cold-formed steel (CFS) structures. This new technique replaced encasing material with unidirectional springs, analogous to the Winkler foundation concept, to shorten the analysis time while ensuring accuracy and reliability in predicting the structural behaviour of encased CFS components. In this paper, the validity, and limitations of the simplified spring model to represent outstanding plates were assessed. The investigation demonstrated that the simplified spring model could effectively predict the ultimate load for a wide range of ultra-lightweight concrete moduli (50-250 MPa) with an acceptable error. The analysis indicated that plate elements initially in cross-section class 4 without encasing material become at least class 3, or better as a consequence of encasing. Previously reported experiments were used to evaluate the performance of the ESM. The analysis demonstrated that the ESM can accurately predict the local failure ultimate load of encased CFS sections with an acceptable error percent and significantly less computational effort than a 3D solid model.

A reconstruction method for harmonic measurement in distribution networks based on equivalent harmonic source approach

Abstract In recent years, with a large number of nonlinear devices connected to the distribution network, harmonic problems have been inevitably generated during operation, which makes harmonic problems more complex in the distribution network. However, it is important to master the real-time harmonic level of the distribution network for the analysis and management of the harmonic problems in the grid. However, because of economic reasons and decentralized nodes, it is impractical to install a harmonic measurement device at each node in engineering. Moreover, it is important to know how to measure harmonics at important nodes in a distribution network using a limited number of measurement devices. Therefore, a harmonic measurement reconstruction method for distribution networks is proposed based on the equivalent harmonic source method. This method aims to obtain more harmonic source state information with a minimum economic cost. First, a mathematical model of the harmonic currents is established. Subsequently, an equivalent harmonic source method is proposed, and a harmonic reconstruction model based on the equivalent harmonic source method is presented. Finally, an example of an IEEE 14-node distribution network is used to verify the effectiveness of the equivalent harmonic source method.

Numerical simulation of the dynamic interaction characteristics between Wood’s metal and water under coolant injection mode

The accident of the steam generator tube rupture in the lead-bismuth-cooled fast reactor or the core meltdown in the light water reactor may cause violent heat and mass transfer between the melt and the coolant, potentially further damaging the reactor. Therefore, it is essential to study the corresponding mechanisms. In this study, numerical simulations are utilized to investigate the dynamic interactions between Wood’s metal and subcooled water in the coolant injection (CI) mode, focusing on jet behavior and critical cavity parameter changes. By analyzing these factors, this research aims to clarify the interfacial evolution and interaction mechanisms between the melt, water, and air, thereby tackling the problem of inadequate observation in experiments. A user-defined function (UDF) was employed to simulate the flow characteristics of the melt during the solidification process. This approach effectively addressed the limitation of Fluent’s inherent solidification model, where the fluid no longer participates in turbulent velocity calculations after solidification. In addition, an equivalence method was proposed according to the characteristics of two-dimensional simulations in Fluent. Comparisons with Cheng’s experimental results show that the equivalent model can accurately predict jet penetration characteristics while significantly reducing the demand for computational resources. According to this equivalence method, this research developed a new correlation for predicting the maximum jet penetration depth in the CI mode. The above results provide new perspectives for understanding the dynamic interactions between metals and coolants, which is significant for the application and optimization of technologies in the nuclear field.