Table of Content

25 January 2024, Volume 52 Issue 1

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Contents



2024, 52(1):  0. 

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Structural Fatigue and Damage

Test and Bearing Capacity Calculation Method of Concrete-Filled CFRP-Stainless Steel Sandwich Tube Columns Under Axial Compression



CHEN Zongping, QIN Weiheng, LIANG Yuhan, et al.

2024, 52(1):  1-14.  doi:10.12141/j.issn.1000-565X.220773

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In order to enhance the bearing capacity and durability of thin-walled stainless steel structures, a kind of seawater sea sand concrete-filled CFRP-stainless steel sandwich tube structure, that is, in which the inner and outer walls of stainless steel tube were pasted with CFRP (Carbon Fiber-Reinforced Polymer) composite constrained seawater sea sand concrete, was designed. Then, monotonic static axial compression tests were carried out on 18 short column specimens, with the number of pasting layers and pasting methods of CFRP as the variation parameters. The failure process and morphology of the specimens were observed, the load-displacement curves and material strain distribution data were obtained, and the variation law of the axial compression mechanical properties of the specimens was analyzed. The results show that: (1) the internal and external CFRP can effectively improve the bearing capacity and deformation capacity of the structure; (2) the failure modes of the specimens without CFRP and the specimens with internal CFRP are both shear damage, but the shear damage will change to waist drum damage with the increase of the number of external CFRP layers; (3) with the same pasting methods, the bearing capacity, deformation capacity and energy dissipation capacity of the specimens increase non-linearly with the increase of the number of CFRP layers; and (4) with the same pasting layers, the mechanical properties of the specimens with internal CFRP are better than those with external CFRP, and the ultimate bearing capacity of the specimen with one or two internal CFRP layer respectively increases by 5.6% or 6.7%, as compared with that of the specimen with external CFRP, and the energy dissipation capacity of the specimen with one internal CFRP layer is equivalent to that of the specimen with two external CFRP layers. Moreover, the strain analysis results show that CFRP and stainless steel have good cooperative performance before the specimen is damaged. Finally, based on the limit equilibrium method and by considering the strain hardening effect of stainless steel, a formula for calculating the ultimate axial compressive bearing capacity was proposed and 73 sample data were collected for verification, finding that the calculated values accord well with the test ones.

Seismic Performance Analysis of Welded Multi-Cavity Double Steel Plate-Concrete Composite Shear Wall



DING Faxing, CAI Yongqiang, WANG Liping, et al.

2024, 52(1):  15-25.  doi:10.12141/j.issn.1000-565X.220828

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Most double steel plate-concrete composite shear walls use bolted or welded ribs to make the steel plate and concrete work together. However, this connection method may lead to low integrality and plastic deformation efficiency, as well as complex fabrication. Welded multi-cavity double steel plate-concrete composite shear walls are able to avoid these problems effectively. In order to investigate the seismic performance of welded multi-cavity double steel plate-concrete composite shear wall, a three-dimension solid-shell model of composite shear wall is established by using the constrained concrete true triaxial plasticity-damage constitutive model and the steel elastoplastic hybrid strengthening-ductile damage constitutive model. The hysteresis curve, skeleton curve, stiffness degradation curve, elastic stiffness, bearing capacity, cumulative energy dissipation, equivalent damping viscosity coefficient and ductility coefficient obtained by the model are in good agreement with the existing quasi-static test results. The analysis results show that: (1) the axial compression ratio has little effect on the elastic stiffness and bearing capacity of the composite shear wall model, while the stiffness and bearing capacity of the composite shear wall model decrease linearly with the increase of shear span ratio; (2) the axial compression ratio has little effect on the total plastic energy dissipation of the composite shear wall model, while the shear span ratio has a greater effect, and the total plastic energy dissipation of the shear wall decreases with the increase of shear span ratio; and (3) both the axial compression ratio and the shear span ratio do not change the energy dissipation allocation mechanism of each component of the shear wall model, which means that the energy dissipation of the composite shear wall model is mainly due to the outer steel plate and the inner partition.

Optimal Design of Steel-SFRC Composite Deck of Continuous Steel Girder



XU Chen, XU Qindong, SUN Xuxia, et al.

2024, 52(1):  26-37.  doi:10.12141/j.issn.1000-565X.220840

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In order to investigate the optimization design method of medium and large span continuous steel girder steel fiber reinforced concrete (SFRC) composite bridge deck, the study used SFRC to replace C50 concrete pavement in the original design, and established SFRC composite bridge deck steel box girder segment model by Abaqus for parameter analysis. And the influence characteristics of SFRC plate thickness, steel roof thickness and reinforcement ratio on the bending stiffness and steel structure stress of the main beam were investigated. The study is based on the cracking characteristics of SFRC obtained by the combination of SFRC composite plate partial tension test and numerical simulation and the existing continuous steel girder structural characteristics. On this basis, the main girder elastic bending stiffness and key cross-section stress were taken as the constraints, and the upper structural self-weight and material cost were taken as the optimization objectives to optimize the mid-span 50 m and 80 m continuous steel girders. Finally, based on the variable optimization results, Midas was used to establish a bar model considering SFRC cracking in the negative moment region to verify the reasonableness of the optimization results. The results show that the finite element analysis method of plastic damage introduced in the paper is reliable, and the relationship between the SFRC crack width and the tensile damage factor can characterize the SFRC cracking state. The 80~120 mm thick SFRC layer on the continuous steel girder increases the elastic bending stiffness of the main girder by 17%~24% after participating in the force; the bending stiffness of the main girder decreases by 13%~20% when the width of the SFRC crack reaches 0.20 mm; the stress of the steel roof plate decreases by 7%~12%, and the negative bending capacity of the main girder does not change significantly. Increasing the thickness of top plate and reinforcement ratio can effectively improve the stress of steel roof. Through the optimization analysis of SFRC layer thickness, reinforcement ratio, steel roof and roof stiffener size, compared with the original design, the optimized steel consumption of 50 m and 80 m continuous steel girders with SFRC deck panels is reduced by 13% and 6% respectively, the weight of the superstructure is reduced by 12% and 6% respectively, and the cost of the material is reduced by 14% and 9% respectively. The optimized design process and optimization results can be used for the design of the continuous steel girder in SFRC deck panels. The optimized design process and optimization results can provide reference for the popularization and application of SFRC composite bridge deck in continuous steel girder.

Study on Whole-Process Mechanical Behavior of Novel Spread Slab Beam Bridges



JIANG Dongqi, WU Hao, FAN Jin

2024, 52(1):  38-51.  doi:10.12141/j.issn.1000-565X.220770

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To study the whole-process structural performance of new spread slab beam bridges, this paper investigated the damage development and failure mechanisms from construction to in-service stages with beam clear spacing, beam number and prestressing steel arrangement as key parameters. The nonlinear numerical analyses were preformed on the bridge system with using ABAQUS software. Research outcome indicates that the beam failure and mixed beam-slab failure are two main failure patterns for this new bridge system. When the beam clear spacing is small, the deformation of all beams is consistent, and the ultimate strength is relatively higher, which is prone to the failure of beams. On the contrary, when the beam clear spacing is large, the transverse load transfer capacity is relatively weaker and the deformation-lag effect exists among different slab beams, resulting in the mixed beam-slab failure. For spread slab beam bridge cases with similar bridge width and span length, a relatively larger beam spacing value is unfavorable for the transverse load sharing, and the ultimate strength of the entire bridge system may be significantly reduced by 40%~50%. The bearing capacity of bridge cases with less beam numbers can be improved by increasing the prestressing steel amount, and the ultimate strength of a single slab beam may be increased by 10%~30%. However, the camber issue at the precasting stage should be handled with caution in the design. Compared with the integral casting concrete beam bridge, this composite beam bridge system is different in the displacement and stress responses obtained from the whole-process analysis, but their difference in the ultimate strength is small. In general, the new spread slab beam bridge system shows good strength and deformation capability, and the characteristics of light weight, low profile and easy construction, owning a good application prospect in China.

Study on Area-Loss Limit of Cable-Strut Structures Considering Different Failure Modes



DENG Manyu, YUAN Xingfei, DONG Yongcan

2024, 52(1):  52-61.  doi:10.12141/j.issn.1000-565X.220661

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Corrosion of cable-strut structures during long-term service life will cause cross-sectional area loss of steel members, which will lead to redistribution of internal force and affect safety performance of the structure. This paper established three failure modes including member strength failure mode, cable relaxation failure mode and node deformation failure mode based on the reliability theory and structural limit state, and further obtained reliability limit control inequalities under critical states of different failure modes. Through mechanical derivation, it derived the formula for the members’ internal force variation as well as nodal displacement variation of cable-strut structure due to variation of cross-sectional area. Based on the formula, the influence coefficient matrix in the reliability limit control inequality can be calculated. By introducing the corrosion model of steel and combining it with nonlinear programming, it proposed the method to determine the members’ area-loss limit of cable-strut structure. The numerical example of a Levy cable dome was carried out and the calculated area-loss limits were compared with the current limit in specification. The result shows that the calculated area-loss limit of most members in the cable-strut structure under the strength failure mode and deformation failure mode is higher than the durability specification limit, but the area-loss limit under the relaxation failure model is smaller than the durability limit. If the structure is designed and maintained according to this limit value, the cable relaxation failure may occur. The safety specification limit is strict for steel cable members, but it is the same as durability specification limit for steel bar members. Therefore, the area-loss limit under three failure modes and specification limits should be considered comprehensively and the final limit should be controlled according to the most stringent results.

Mechanical Properties Degradation Under Fatigue Loading in Pultruded Unidirectional Glass Fiber Reinforced Polymer Composites



HE Jiapeng, ZHANG Jinyu, CHEN Zhangxing, et al.

2024, 52(1):  62-71.  doi:10.12141/j.issn.1000-565X.220760

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Pultruded glass fiber reinforced polymer (GFRP) composites are extensively applied in the field of ultra-high voltage power transmission due to their excellent electrical and mechanical properties, and the design considering its performance degradation characteristics under fatigue loading is the key to the application. This study carried out static load tests and fatigue tests under different conditions with the pultruded unidirectional GFRP. A fatigue life prediction model was established based on a piecewise linear constant life diagram determined by S-N curves. According to the stiffness degradation law under different stress ratios, a modified damage accumulation model based on the improved trigonometric function was presented to describe the nonlinear stiffness degradation process under both tension-tension and tension-compression fatigue loads. The correlation model between residual strength and residual stiffness was established to predict the strength degradation precisely. The results show that the stiffness degradation processes of GFRP under tension-tension and tension-compression fatigue loads are significantly different. The model proposed in the paper can accurately predict the residual strength under the two conditions. Under compression-compression fatigue load, there are two different patterns for the stiffness degradation processes, and the residual strength test shows that the strength within the first 70% fatigue life does not exhibit a significant degradation.The prediction model for the residual strength and residual stiffness of GFRP under different fatigue loading provides a guide for the durability design of GFRP.

Traffic & Transportation Engineering

Traffic Boundary Control Strategy Based on Macroscopic Fundamental Diagram Under Different Rainfall



ZHAO Xiaomei, HAO Guoyu, NIU Xiaojing, et al.

2024, 52(1):  72-82.  doi:10.12141/j.issn.1000-565X.220721

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Adverse weather such as rain and snow often aggravates urban traffic congestion, and large cities such as Beijing and Tianjin often experience multi section regional traffic congestion under rainfall conditions. Therefore, based on the real traffic data of the road network in the central and suburban area of Tianjin, with the macroscopic fundamental diagram model as the research foundation, the paper compared the time series and the macroscopic fundamental diagram changes of road network traffic flow for different rainfall and road networks. It analyzed the impact of different rainfall on the traffic status of the road network in the central and suburban area of Tianjin. The dynamic evolution models of the road network were constructed based on the change law in macroscopic traffic flow of the road network in the central and suburban area under different rainfall, and their parameters were also calibrated and validated. Aiming at solving the regional congestion problem of the road network, the control strategies of the road network in the central area and the suburban area under different rainfall conditions were designed based on the perimeter control of macroscopic fundamental diagram. The effectiveness of different control strategies was verified through simulation experiments, and feasible strategies were proposed to alleviate road network congestion in central and suburban areas. The simulation results show that: under light rain conditions, the traffic status between the central area and the suburban area is more balanced and the road network regulation effect is better when the transfer proportion of traffic flow from the suburban area to the central area is reduced within the range of 9% to 50%; under the condition of heavy rain, the traffic status of the central area and the suburban area is more balanced and the road network regulation effect is better when the reduction is controlled within the range of 23% to 50%. This shows that the control strategy can alleviate the traffic congestion of the road network and ensure the stable operation of the road network traffic system.

Analyzing and Modeling of Multi-Class E-Bikes Violation Behaviors at Signalized Intersection



DONG Chunjiao, LU Yuxiao, MA Sheqiang, et al.

2024, 52(1):  83-89.  doi:10.12141/j.issn.1000-565X.220785

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The e-bike violations have significant impacts on traffic efficiency and safety at signalized intersections, and they are important safety control objects. Based on the data of 9 726 non-motor vehicles at signalized intersections obtained by video survey method, the research compared and analyzed the characteristics of violation behaviors of three types of non-motor vehicles under the influence of riders’ personal attributes and time-space scenes. Considering 14 factors as covariables, including rider’s personal attributes, signalized intersection characteristics and traffic flow characteristics, a multi-category violation model of e-bikes based on multiple Logistic regression was developed to reveal the mechanism of e-bikes running red lights, occupying motor lanes, waiting for crossing lines and reverse riding at signalized intersections. The results show that: the overall violation rate of e-bikes at signalized intersections is 44.01%, which is 1.21 times that of traditional bicycles; the model middle-aged and elderly e-bike riders are more likely to commit four kinds of violations than young ones; female cyclists are more likely to cross the line waiting and reverse cycling, while male cyclists are more likely to occupy the motorway. The addition of coordinators can effectively reduce the red light running, line crossing and reverse riding behaviors of e-bikes at signalized intersections, but might increase the possibility of e-bikes occupying the motorway. Setting the exclusive phase of left turn can effectively reduce the occupation of motor vehicle lane, line crossing waiting and reverse riding behavior of e-bikes.

Influence of Alignment Indexes of Highway Turning Section on Safety Performance of Concrete Guardrail



YANG Yonghong, TANG Zude, WANG Chun, et al.

2024, 52(1):  90-99.  doi:10.12141/j.issn.1000-565X.220789

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The alignment design indexes of highway turning section have important influences on the safety performance of guardrail. In this paper, based on the finite element software LS-DYNA widely used in the field of highway side safety, a complex collision test model of truck and concrete guardrail is established, and simulation and vehicle tests are performed to comparatively verify the effectiveness of the model. Detailed animation describing the collision of vehicle to guardrail is obtained by simulation, which directly exhibits the safety performance of the guardrail in flat curve section. Then, the traffic lane radius, the superelevation value and the vehicle speed are used as variables to investigate and quantify the influence of main alignment indexes on the safety performance of concrete guardrail. The results show that, when the traffic lane radius is close to the ultimate minimum radius corresponding to the design velocity, the roll-over-angle of the vehicle increases, and the vehicle easily crashes to the guardrail and rolls over; that a superelevation value of 6% of the traffic lane is the critical point for the safety performance of concrete guardrail; that when the superelevation value is more than 6%, the height of the vehicle climbing along the collision surface of the guardrail may increase, and the vehicle is more likely to roll over, so that the combination of large superelevation (above 6%) and small ultimate minimum radius should be avoided during the highway design; and that, on the curve section, the collision speed has a significant impact on the safety performance of guardrail. For the integral van, the risk of rollovers significantly increases when the vehicle speed reaches 90 km/h. This research lays a theoretical foundation for the alignment safety design of highway curve sections.

Point Cloud Classification Based on Offset Attention Mechanism and Multi-Feature Fusion



TIAN Sheng, SONG Lin, ZHAO Kailong

2024, 52(1):  100-109.  doi:10.12141/j.issn.1000-565X.220545

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3D point cloud has received great attention due to the fact that they are less affected by natural weather conditions such as fog, rain and snow, and it is widely used in a variety of fields such as transportation, energy and healthcare. Point cloud classification aims to classify the categories of 3D point cloud data to provide information to decision makers in different fields and to enable the development of solutions, so it’s significant for automated driving, fault diagnosis and medical image analysis. The application of point cloud classification is promising, but it still faces many challenges. Due to the characteristics of point cloud such as disorder, sparseness and finiteness, traditional image processing and computer vision methods can not be directly applied to point cloud data analysis. The direct use of convolutional neural network can not effectively extract point cloud features; the feature extraction in some models is insufficient, and the local and global information is not effectively utilized, which may lead to the loss of important feature information. Aiming at these problems, a multi-feature fusion module combining local and global features of point cloud was proposed, and combined with the offset attention mechanism, the multi-feature fusion module was embedded to realize the extraction of deeper point cloud features. At the same time, the residual structure was introduced to make full use of the shallow extracted features to prevent the loss of shallow features caused by the overdepth of network. Training and testing were performed on ModelNet40 and ScanObjectNN classification datasets, and ablation studies and partial data visualization of the experiments were performed. The experimental results show that the overall classification accuracy of this model on ModelNet40 is 93.6%, which improves the overall classification accuracy by 4.4, 0.7 and 0.4 percentage points compared with PointNet, LDGCNN and PCT models, respectively. The overall accuracy of classification on ScanObjectNN is 83.7%, which is 5.8 and 5.6 percentage points higher than that of PointNet++ and DGCNN, respectively, with higher accuracy and robustness.

Influence of Shapes of Corrugated Steel Plate on Load-Carrying Capacity of Reinforced Concrete Slab Culvert and Arch Effect with Lateral Restraint



LI Baijian, HUANG Yan, FU Xinsha

2024, 52(1):  110-118.  doi:10.12141/j.issn.1000-565X.220748

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To explore the influence of the shape of corrugated steel plate (CSP) on the reinforced concrete (RC) slab culvert rehabilitated with grouted CSP, and the discrimination of arch effect of grout, this paper established 72 numerical models of the rehabilitated system with box, arc and transition shapes of CSPs by combining laboratory test with numerical analysis, based on the laboratory experimental results. The variation law of the load-carrying capacity of the rehabilitated system changed with the shape parameters of CSPs was ascertained. In addition, based on the concept of reasonable arch axis, the formation mechanism of arch effect of grout was also ascertained and verified by five numerical models. The results indicate that, when the radius of the haunch of CSP remained constant, the load-carrying capacity of the rehabilitated system increases upon decreasing of the radius of side walls and crown; when the side walls and crown of CSP remained constant, the load-carrying capacity of the rehabilitated system increases with the increase of the radius of the arch haunches; the most effective way to improve the load-carrying capacity of the rehabilitated system is to increase the radius of the haunches, followed by reducing the radius of the vault and side wall. The arch effect of grout was related to the load types. When the shape of CSP can keep the arch axis continuous and within the rigid angle of grout, the load-carrying capacity of the rehabilitated system is the highest. The structural design of the RC slab culvert rehabilitated with CSP should comprehensively consider the shapes of CSP and the arch effect of grout according to the actual needs of the project, and try to avoid the rehabilitation design close to the original RC slab culvert as far as possible.

Identification of Accident Black Spots Based on Improved Network Kernel Density and Negative Binomial Regression



ZHUANG Yan, DONG Chunjiao, MI Xueyu, et al.

2024, 52(1):  119-126.  doi:10.12141/j.issn.1000-565X.220659

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The existing research on identifying black spots in traffic accidents is mostly based on accident frequency or accident rate, without considering the impact characteristics of traffic accidents on different locations. In order to comprehensively consider the differential effects of traffic accidents in different traffic environments and road network characteristics and to solve the zero inflation problem of zero values far exceeding the classical discrete distribution in traffic accident data, this paper proposed an improved network kernel density estimation method that considers the comprehensive importance of nodes, and identified urban traffic accident black spots based on the zero inflation negative binomial regression model. Firstly, in the topological road network, a comprehensive impact index of accidents was constructed by comprehensively considering the traffic environment and road conditions at the location of the accident, and the accident severity index was embedded into the traditional network kernel density estimation. By generating a smooth density surface on the road network, the spatial aggregation of point events was qualitatively reflected. On this basis, a discrimination model based on zero-inflated negative binomial regression was constructed to clarify the boundary range of accident-prone areas and quantitatively depict the spatial distribution characteristics of accident black spots at different severity levels. Finally, an example analysis was carried out for Huaqiangbei street in Shenzhen. The results show that the search efficiency indexes of the proposed method are all larger than those of the planar kernel density estimation method at the threshold levels of 70%, 80% and 90%. Furthermore, some non-road areas are no longer mistaken, and the accuracy of the model is 3.60%, 5.31% and 7.20% larger than those of the traditional network kernel density method respectively after considering the comprehensive importance of nodes.

Evaluation of Utility and Optimal of Variable Speed Limit Value for Bridge in Foggy Condition



ZHANG Jianhua, ZHAO Xiaohua, OU Jushang, et al.

2024, 52(1):  127-138.  doi:10.12141/j.issn.1000-565X.220765

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To improve the traffic safety of highway bridge sections in foggy environments, this paper considered the influence of variable speed limit signs on driving behavior. To obtain the best effect, it put forward a quantitative evaluation method from the perspective of the obedience effect. Taking E’dong Yangtze River Bridge as the prototype, this paper selected the lowest visibility （100 m） and free flow service level of the bridge in recent years as the test environment. Three speed limit strategies were designed, namely, the control group S_Ⅰ (no speed limit strategy）, the experimental group S_Ⅱ (90~70 km/h speed limit strategy), and the experimental group S_Ⅲ (90~70~50 km/h step-by-step speed limit strategy）. Relying on the driving simulator, the micro-driving behavior data of foggy bridge scenes with different speed limit conditions were realized. The action mechanism of variable speed limit signs and driver characteristics were analyzed from the rapidity, stability, and accuracy of driver response by repeated measure analysis of variance, and the effectiveness of different speed limit strategies was evaluated using the fuzzy comprehensive evaluation method. The results show that the variable speed limit sign can make the driver take deceleration measures earlier, and the vehicle’s stability in the fog area is better. When the visibility is 100 m in fog, the steady-state frequency of 90~70~50 km/h step-by-step speed limiting strategy is more significant, the spatial stability is better, the speed overshoot and the following ratio are more minor, and the response accuracy is higher. The results of the fuzzy comprehensive evaluation show that the 90~70~50 km/h step-by-step speed limit strategy, as the optimal scheme, can effectively improve the adaptability of driving behavior in fog areas, reduce driving risk, and improve the stability of vehicle operation. The research results provide a solution for setting variable speed limit signs for bridges on foggy days and can provide adequate support for the active safety prevention and control of bridges on foggy days.

Physics

A 5D Multi-Stable System with Wide Range of Hyperchaotic States



ZENG Yicheng, LI Wenxuan, SUN Xiaoli

2024, 52(1):  139-146.  doi:10.12141/j.issn.1000-565X.220620

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Large-scale chaotic systems are often used in secure communication and other fields, because they can provide a wider chaotic interval. Most of the existing large-scale chaotic systems are three-dimensional and four-dimensional systems. In order to obtain more chaotic and more complex systems, this study proposed a five-dimensional system with a large range of hyperchaotic states and multiple coexisting attractors. The dynamic characteristics of the five-dimensional system were analyzed by means of coexistence bifurcation diagram, coexistence phase diagram, Lyapunov exponent spectrum and calculation of system divergence. The results show that: the system is a dissipative hyperchaotic system; when the parameters are fixed, the system can produce multiple coexisting attractors only by changing the initial value, and when the parameter d takes different values, the system will produce 12 types of coexistence phenomena, which are period-1 attractor, period-2 attractor, period-4 attractor, quasi-periodic attractor, one-scroll attractor, double-scroll attractor and so on; when the parameter m varies in the range of [0.1, 4 000], the system will always maintain a hyperchaotic state, and when m is in the range of [70, 4 000], the Lyapunov exponent spectrum of the system remains unchanged and maintains a hyperchaotic state with three positive Lyapunov exponents, indicating that the system has an invariant Lyapunov exponent characteristic. FPGA (field programmable gate array) was used to realize the digital circuit, and the experimental results were observed on the oscilloscope, which verified the feasibility of the hyperchaotic system.

Numerical Simulation of Electromechanical Coupling Response of Nano Flexoelectric Structures



HUANG Huaiwei, HUANG Haibo

2024, 52(1):  147-156.  doi:10.12141/j.issn.1000-565X.220835

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At the micro-nano scale, the flexoelectric effect exhibits a higher electromechanical coupling conversion efficiency in comparison with the traditional piezoelectric effect. Therefore, it holds potential applications in the fields of sensing, actuation, and energy harvesting. However, most commercially available finite element analysis software packages lack the flexoelectric constitutive model, rendering it impossible to perform a precise numerical simulation of flexoelectric structures. Therefore, this study incorporated the flexoelectric effect into the calculation model based on the development of Abaqus user-defined element (UEL) subroutine. Additionally, we derived the electromechanical coupling equations of the flexoelectric structure and developed a flexoelectric element in Abaqus, which provides numerical simulation technology for analyzing the structural flexoelectric response. Compared with the traditional mixed finite element method (MFEM), this proposed method has the advantages of easier modeling, high efficiency and low computational cost. And its deflection and electric field strength metrics are closer to the analytical solution than either of the other methods. Then, using this numerical simulation method, this study established a flexoelectric structural response analysis numerical model, conducted force-electromechanical coupling response calculations, and analyzed straight and curved beams under different boundary conditions. The analysis results show the mechanism of the geometric parameters of the beam affects the structural strain gradient, and show that the output voltage can be controlled by controlling the deformation gradient when designing a flexoelectric beam using the same material. It is shown that changing the degree of bending of the beam is effective in increasing the open-circuit voltage of the beam output and reducing the deflection of the beam. The open-circuit voltage of a curved cantilever beam bent downward is greater than the open-circuit voltage of a curved cantilever beam bent upward for the same degree of bending. When the circular arc angle of the upward bending curved beam is 38°, the left edge is a sliding bearing, and the right edge is a hinge bearing, the open-circuit voltage is the maximum, up to 214.07 mV, which is five times more than that of the cantilevered rectangular beam. In addition, by considering the piezoelectric effect alone, the open-circuit voltage will decrease by 89.3% in the same model.