Rectangular pipe-jacking tunnels are highly prone to longitudinal deformation under the influence of adjacent engineering activities,uneven foundation settlement,and changes in surface loads.These problems may lead to...Rectangular pipe-jacking tunnels are highly prone to longitudinal deformation under the influence of adjacent engineering activities,uneven foundation settlement,and changes in surface loads.These problems may lead to structural damage at the joints of rectangular pipe-jacking tunnels,potentially triggering engineering disasters.In response to these situations,this paper experimentally studies the effects of different foundation conditions and steel sleeve ring design parameters on their shear stiffness and rotational stiffness.It reveals three stages of joint failure:gap closure,steel sleeve ring stress,and deformation failure.A three-dimensional refined numerical simulation method is adopted to study the deformation and failure characteristics of joints under different foundation strengths and steel sleeve ring design parameters,analyze the mechanical performance of the joints of rectangular pipe-jacking tunnels,and verify the reliability of the experimental results.Based on the experimental and numerical simulation results,considering the nonlinear characteristics of the joints of rectangular pipe-jacking tunnels,a shell-joint theoretical model is constructed.Precise simulation is achieved through the combination of‘rotation+shear’dynamic elements,and the stiffness matrix at the joints and the calculation method of mechanical elements are derived.The shell-joint theoretical model is used to compare and verify the results of the joint tests of rectangular pipe-jacking tunnels,confirming the accuracy and practicality of the shell-joint theoretical model.展开更多
This study quantitatively examined the fluid energy evolution and dissipation process near narrow gaps formed between multiple floating rectangular structures under wave-induced gap resonance conditions.Given the limi...This study quantitatively examined the fluid energy evolution and dissipation process near narrow gaps formed between multiple floating rectangular structures under wave-induced gap resonance conditions.Given the limited understanding of gap resonance mechanisms through fluid energy analysis,a numerical wave flume based on theδ-LES-Smoothed Particle Hydrodynamics(SPH)approach was developed to investigate how incident wave and structural parameters influence the temporal evolution of fluid energy components.The findings reveal that for two floating boxes,the fluid energy dissipation within one wave period in the gap region between the boxes constitutes 81%of the total fluid energy dissipation in the fluid domain.This proportion remains consistent across varying incident wave heights under gap resonance conditions.The temporal distribution of fluid energy dissipation rate shows two peak values within one wave period,exhibiting significant waveform asymmetry.Additionally,in three-box configurations,the two narrow gap regions serve as primary zones of fluid energy dissipation,with energy dissipation patterns closely resembling those observed in the single gap region.Through comprehensive analysis of fluid energy evolution,this research advances the fundamental understanding of gap resonance mechanisms.展开更多
Fluid dynamic research on rectangular and trapezoidal fins is aimed at increasing heat transfer by means of large surfaces.The trapezoidal cavity form is compared with its thermal and flow performance,and it is reveal...Fluid dynamic research on rectangular and trapezoidal fins is aimed at increasing heat transfer by means of large surfaces.The trapezoidal cavity form is compared with its thermal and flow performance,and it is revealed that trapezoidal fins tend to be more efficient,particularly when material optimization is critical.Motivated by the increasing need for sustainable energy management,this work analyses the thermal performance of inclined trapezoidal and rectangular porous fins utilising a unique hybrid nanofluid.The effectiveness of nanoparticles in a working fluid is primarily determined by their thermophysical properties;hence,optimising these properties can significantly improve overall performance.This study considers the dispersion of Graphene Oxide(GO)and Molybdenum Disulfide in the base fluid,engine oil.Temperature profiles are analysed by altering the radiative,porosity,wet porous,and angle of inclination parameters.Surface and contour plots are constructed by using the Lobatto IIIa Collocation Method with BVP5C solver in MATLAB and Gradient Descent Optimisation to predict the combined heat transfer rate.According to the study,fluid temperature consistently decreases when the angle of inclination,wet porous parameter,porosity parameter,and radiative parameter increase,suggesting significantly improved heat dissipation.The trapezoidal fin consistently exhibits a superior heat transfer mechanism than a rectangular fin.It is found that the trapezoidal fin transmits heat at a rate that is 0.05%higher than that of the rectangular fin.Validation of the present study is done through the comparison of previous studies.This research provides useful design insights for sophisticated engineering uses,including electrical cooling devices,heat exchangers,radiators,and solar heaters.展开更多
Elevated,rectangular water tanks are an essential component of the water supply network and for emergency water storage.However,determining the dynamic response from seismic loads will require accurate estimates of th...Elevated,rectangular water tanks are an essential component of the water supply network and for emergency water storage.However,determining the dynamic response from seismic loads will require accurate estimates of their natural frequencies to help avoid damage or failure.Several numerical and analytical methodologies depend on assumptions that may not account for the complexity of fluid-structure interaction regarding rectangular geometries,indicating a strong need for solid experimental validation.This study pioneers the application of Digital Image Correlation(DIC),a non-contact optical technique,to measure the natural frequencies of a small-scale acrylic and Teflon tank,addressing this gap with a novel experimental approach.The method includes DIC using a high-speed camera,image analyzed by MATLAB,frequency analysis by Continuous Wavelet Transformation(CWT),and Fast Fourier Transformation(FFT);ANSYS finite element analysis,simplified models based on Eurocode and the Egyptian Code of Practice(ECP).Study results indicate that DIC is critical for attaining high accuracy,with maximum error differing by 2.92% for impulsive and 4.55%for convective frequencies from ANSYS and provides a better measure of dynamic response compared to contact-based measurements.Impulsive frequency decreased from 5.8724 Hz to 4.0085 Hz,and sloshing increased from 1.00 Hz to 1.84 Hz,as the water cover height varied from 0 cm to 9.8 cm.The Eurocode and ECP models describe acceptable errors of 7.36% and 9.21%,respectively.DIC showed higher accuracy,making it a useful tool for seismic design.This study improves the safety and reliability of designs for elevated water tanks in seismic regions with elevated seismic risk.展开更多
The sedimentation of a rectangular particle falling in a two-dimensional channel filled with Newtonian fluid was simulated with finite element arbitrary Lagrangian-Eulerian domain method.The numerical procedure was va...The sedimentation of a rectangular particle falling in a two-dimensional channel filled with Newtonian fluid was simulated with finite element arbitrary Lagrangian-Eulerian domain method.The numerical procedure was validated by comparison of the simulation results with existing numerical work.Morea over,good agreement was obtained between the simulation results and experimental measurements performed in the current study.The equilibrium position,stable orientation and drag coefficient ofa rect-angular particle for different particle Reynolds numbers(Rep)were studied.The results show that there is a critical particle Reynolds number for the preferred orientation of a rectangular particle falling in a Newtonian fluid.When Rep is smaller than the critical value,the particle fails with its long side parallel to gravity;otherwise the particle fails with its long side perpendicular to gravity.The critical particle Reynolds number is a decreasing function of the blockage ratio and aspect ratio.The distributions of pressure and shear stress on rectangular particle surface were analyzed.Moreover,the drag coefficient of the rectangular particle decreases as Rep or the blockage ratio increases;however,it appears to be independent of aspect ratio.展开更多
The natural frequencies, complex modes and critical speeds of an axially moving rectangular plate, which is partially immersed in a fluid and subjected to a pretension, are investigated. The effects of free surface wa...The natural frequencies, complex modes and critical speeds of an axially moving rectangular plate, which is partially immersed in a fluid and subjected to a pretension, are investigated. The effects of free surface waves, compressibility and viscidity of the fluid are neglected in the analysis. The subsection functions are used to describe the discontinuous characteristics of the system due to partial immersion. The classical thin plate theory is adopted to formulate the equations of motion of a vibrating plate. The velocity potential and Bernoulli's equation are used to describe the fluid pressure acting on the moving plate. The effect of fluid on the vibrations of the plate may be equivalent to the added mass on the plate. The effects of distance ratio, moving speed, immersed-depth ratio, boundary conditions, stiffness ratio and aspect ratio of the plate as well as the fluid-plate density ratios on the free vibrations of the moving plate-fluid system are investigated.展开更多
In this paper, we present the electromagnetic analysis of a rectangular cavity partially filled with a left-handed material slab. Our theoretical investigation shows that there exist novel resonant modes in the cavity...In this paper, we present the electromagnetic analysis of a rectangular cavity partially filled with a left-handed material slab. Our theoretical investigation shows that there exist novel resonant modes in the cavity, and such a cavity becomes a subwavelength cavity. The eigenvalue equation of the cavity is derived and the resonant frequencies of the novel modes are calculated by using numerical simulation. We also discuss the stability of the novel resonant modes and show the best condition under which a useful rectangular cavity of subwavelength dimensions with tolerable stability is obtained.展开更多
A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximat...A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.展开更多
Determining earth pressure on jacked pipes is essential for ensuring lining safety and calculating jacking force,especially for deep-buried pipes.To better reflect the soil arching effect resulting from the excavation...Determining earth pressure on jacked pipes is essential for ensuring lining safety and calculating jacking force,especially for deep-buried pipes.To better reflect the soil arching effect resulting from the excavation of rectangular jacked pipes and the distribution of the earth pressure on jacked pipes,we present an analytical solution for predicting the vertical earth pressure on deep-buried rectangular pipe jacking tunnels,incorporating the tunnelling-induced ground loss distribution.Our proposed analytical model consists of the upper multi-layer parabolic soil arch and the lower friction arch.The key parameters(i.e.,width and height of friction arch B and height of parabolic soil arch H 1)are determined according to the existing research,and an analytical solution for K l is derived based on the distribution characteristics of the principal stress rotation angle.With consideration for the transition effect of the mechanical characteristics of the parabolic arch zone,an analytical solution for soil load transfer is derived.The prediction results of our analytical solution are compared with tests and simulation results to validate the effectiveness of the proposed analytical solution.Finally,the effects of different parameters on the soil pressure are discussed.展开更多
Rectangular explosive charges are usually used in military or civilian explosive transportation and storage.The effects of shape parameters and detonation positions on the peak overpressure and maximum impulse of blas...Rectangular explosive charges are usually used in military or civilian explosive transportation and storage.The effects of shape parameters and detonation positions on the peak overpressure and maximum impulse of blasts lack comprehensive investigation,which is significant for the design of blast-resistant structures.In this paper,the side-length ratio of the rectangle,orientation,and detonation position of the charge are chosen as controlling parameters to investigate their influence on blast loads in the scaled distances of the gauges ranging from 0.63 to 10.54 m/kg1/3 with well validated 3D numerical simulations.The results show that there is a large difference in the near-field spatial distribution of the blast load of the rectangular charge;if the blast load of the rectangular charge is simply evaluated with the spherical charge,the maximum peak overpressure(maximum impulse)will be underestimated by a factor of 7.46(4.84).This must be taken seriously by blast-resistant structure designers.With the increase in the scaled distance,when the critical scaled distance is greater than 6.32(7.38)m/kg1/3,the influence of the charge shape on the maximum peak overpressure(maximum impulse)of the spatial blast load can be ignored.In general,the impact of detonation of the charge at the end on the maximum peak overpressure is greater compared with central detonation,but for the impact of the maximum impulse,it is necessary to pay attention to the side-length ratio of the rectangular charge and the specific detonation position on the end face.Furthermore,the structural response of steel plates placed at different azimuths under the blast load of a rectangular charge is preliminarily analyzed,and the results show that the deformation and energy of the plates are consistent with the distribution of the blast load.These analysis results provide a reference for the explosion protection design in near-field air explosions.展开更多
To investigate groundwater influence on stability and rockburst mechanism of deep hard-rock rectangular tunnels,water-immersed treatment and uniaxial compressive acoustic emission(AE)experiments were conducted on rect...To investigate groundwater influence on stability and rockburst mechanism of deep hard-rock rectangular tunnels,water-immersed treatment and uniaxial compressive acoustic emission(AE)experiments were conducted on rectangular tunnel specimens.Energy dissipation characteristics,AE evolution characteristics and damage evolution characteristics of rectangular tunnels were analysed under waterimmersed condition.Under water-immersed condition,tunnel specimens were quite sensitive to water.Average peak stress and average peak strain energy exhibited negative exponential decay with waterimmersed time.Among them,after 12 d of water immersion,average peak stress of specimens decreased by 28%.Average total strain energy decreased by 70%.Average elastic strain energy decreased by 71%and average dissipated strain energy decreased by 68%.After 62 d of water immersion,average peak stress of specimens decreased by 34%.Average total strain energy decreased by 78%.Average elastic strain energy decreased by 79%and average dissipated strain energy decreased by 75%.Water weakened bonding among mineral particles.Moreover,it undermined load-bearing capacity and diminished energystorage properties.Under high stress,massive releasable elastic strain energy stored in natural specimens within pre-peak stage may abruptly release after peak stress.This caused rapid crack development and connection in specimens.During accumulation and release of elastic strain energy,initial failure typically occurred at sidewalls.This failure location was not affected by water.Compared with natural specimens,Specimens immersed in water for 62 d had the lowest peak values of cumulative amplitude,cumulative AE energy and cumulative AE count.After 62 d of water immersion,peak values of cumulative amplitude,cumulative AE energy and cumulative AE count of specimens decreased by 84%,97%and 99%.Compared with AE damage model,fitting degree of energy damage model was higher.For natural specimens,fitting degree of energy damage model was 0.96.For specimens immersed in water for 12 d,fitting degree of energy damage model was 0.96.For specimens immersed in water for 62 d,fitting degree of energy damage model was 0.72.Therefore,an energy damage model had more remarkable applicability and reliability.By establishing dynamic mapping relationship between energy and damage in the model,accuracy of rockburst early warning has been significantly improved.This provided scientific basis for support structure design of rectangular tunnels and regulation of high strain energy.展开更多
This study investigates the nonlinear dynamic properties of rotating functionally graded sandwich rectangular plates in a thermal environment.The nonlinear vibration equations for a rotating metal-ceramic functionally...This study investigates the nonlinear dynamic properties of rotating functionally graded sandwich rectangular plates in a thermal environment.The nonlinear vibration equations for a rotating metal-ceramic functionally graded sandwich rectangular plate in a thermal environment are derived using classical thin plate theory and Hamilton’s principle,considering geometric nonlinearity,temperature-dependent material properties,and power law distribution of components through the thickness.With cantilever boundary conditions,the flexural nonlinear differential equations of the rectangular sandwich plate are obtained via the Galerkin method.Since the natural vibration differential equations exhibit nonlinear characteristics,the multiscale method is employed to derive the expression for nonlinear natural frequency.An example analysis reveals how the natural frequency of a functionally graded sandwich rectangular plate varies with rotational speed and temperature.Results show that the nonlinear/linear frequency ratio increases with rotational angular velocity Ω and thickness-to-length ratio h/a,follows a cosine-like periodic pattern with the setting angle,and shows a sharp decrease followed by a rapid increase with increasing width-to-length ratio b/a.The derived analytical solutions for nonlinear frequency provide valuable insights for assessing the dynamic characteristics of functionally graded structures.展开更多
The growing need for enhanced heat dissipation is compelling the development of more effective heat exchangers.Innovation inspired by nature bionics,four types of leaf-shaped pin fins were proposed and four combinatio...The growing need for enhanced heat dissipation is compelling the development of more effective heat exchangers.Innovation inspired by nature bionics,four types of leaf-shaped pin fins were proposed and four combinations of them were considered.The leaf-shaped design of the cooling pin fin enhances uniformity and synergy,effectively creating an optimized flow path that boosts cooling performance.Eight three-dimensional conjugate heat transfer models in staggered arrangement were developed using ANSYS-Fluent software.Aluminum6061material was used as the heat sinkmaterial and single-phase liquid water flowed through the rectangular channel where the Reynolds(Re)number varies from 40 to 100.Using the same boundary conditions as the software simulations,two leaf-shaped channels were printed to validate numerical models.Velocity field and temperature differences of the eight proposed leaf-shaped pin fins configurations were discussed by comparison with cylindrical pin fins.Based on the findings of this study,at a Reynolds number of 80,the Leaf B Staggered Array(LBSA)records a maximum temperature that is 0.72 K lower than that of the cylindrical pin fins arrangement.Additionally,the LBSA exhibits a reduction in the friction factor by approximately 33.3%relative to the circular pin fins array under the same Re.This implies that the design of LBSA has been optimized to provide better heat dissipation performance while maintaining lower energy consumption.Furthermore,the LBSA demonstrates the most favorable thermal-hydraulic performance index(TPI),which is 1.18 times higher than that of the circular pin fins arrangement at Re=80.The temperature reduction and friction factor reduction of the lobed channel is more pronounced than that of the conventional cooling channel,highlighting its potential to increase heat transfer efficiency and reduce energy consumption in practical applications.展开更多
The behavior of single-phase flow and conjugate heat transfer in micro-channel heat sinks(MCHS)subjected to auniform heat flux is investigated by means of numerical simulations.Various geometrical configurations areex...The behavior of single-phase flow and conjugate heat transfer in micro-channel heat sinks(MCHS)subjected to auniform heat flux is investigated by means of numerical simulations.Various geometrical configurations areexamined,particularly,the combinations of rectangular solid and perforated blocks,used to create a disturbancein the flow.The analysis focuses on several key aspects and related metrics,including the temperature distribution,the mean Fanning friction factor,the pressure drop,the Nusselt number,and the overall heat transfer coefficientacross a range of Reynolds numbers(80–870).It is shown that the introduction of such blocks significantlyenhances the heat transfer performances of the MCHS compared to the straight-through flow channel.Specifically,a case is found where the Nusselt number increases by 2.3 times relative to the reference case.The integrationof perforated blocks facilitates the generation of vorticity within the channel,promoting the mixing of coldand hot fluids.Notably,MCHS incorporating perforated rectangular blocks exhibit more pronounced heat transferbenefits at Reynolds numbers smaller than 400.展开更多
The implementation of multifunctional metasurfaces through loading diodes has extremely high costs,while increasing the number of channels in the element through polarization multiplexing technology is limited.This pa...The implementation of multifunctional metasurfaces through loading diodes has extremely high costs,while increasing the number of channels in the element through polarization multiplexing technology is limited.This paper proposes a dual-band five-channel(DBFC)1-bit surface,which expands the polarization independent(PD)channels through rotating array.The polarization-independent metasurface element consists of three layers of metal,with the top layer comprising three rectangular patches oriented in the x-direction,the middle layer featuring a Jerusalem cross structure with accompanying resonators,and the bottom layer being a metal ground plane.The middle layer element can easily independently provide the required 1-bit reflection phases for two orthogonal polarizations in every frequency.The rectangular patches in the x-direction on the top layer do not contribute to the phase of y-polarization.By rotating the upper layer dielectric array 90°,the rectangular patches change to the y-direction.Under y-polarized illumination,the current distribution in the middle layer is shielded,providing a fifth set of polarization independent phases.The proposed 1-bit DBFC metasurface array has advantages in terms of structure and cost,while enhancing the utilization rate of the metasurface array.It has high application potential in microwave imaging,wireless power transmission,and other projects.展开更多
The hydroforming experiment of aluminum tubular part with rectangular section was carried out to investigate influence of axial feeding on thickness distribution and calibration pressure of the corner.Thickness distri...The hydroforming experiment of aluminum tubular part with rectangular section was carried out to investigate influence of axial feeding on thickness distribution and calibration pressure of the corner.Thickness distribution and relation between corner radius and internal pressure were analyzed.The influence of lubricant was discussed.Microstructure and hardness of different region were observed.It is shown that thickness reduction in the transition region between the corner and center region is the biggest.Friction condition has influence both on the thickness distribution and calibration pressure of the corner.As the increase of the axial feeding,the calibration pressure is decreased.There is only little change for the microstructure,but the hardness is increased by 23.3% for the transition region.展开更多
Designing thin-walled plate structures is challenging due to their susceptibility to various forms of structural instability.In addition,the substantial computational cost of finite element analyses,especially in opti...Designing thin-walled plate structures is challenging due to their susceptibility to various forms of structural instability.In addition,the substantial computational cost of finite element analyses,especially in optimization scenarios,underscores the need for efficient and reliable surrogate models.To address this challenge,the present study employs machine learning(ML)techniques to predict the buckling response of thin plates under complex boundary conditions.Four ML models,including XGBoost,CatBoost,Light GBM,and Random Forest,are developed to predict the buckling coefficient based on input features,including aspect ratio,boundary condition,and compressive loading pattern.The training data for these models is generated using the finite integral transform method.Model performance is rigorously evaluated,with all four algorithms demonstrating strong predictive capabilities.Among them,XGBoost demonstrates the superior predictive performance,achieving an R2 value of 0.99.To gain deeper insights into feature influence,SHAP analysis is conducted,revealing that the aspect ratio has the greatest influence on buckling coefficient,followed by boundary conditions and compressive loading.By adopting gradient-boosting approaches,the proposed framework demonstrates improved generalization and reduced overfitting,with potential applicability to structural optimization.The results suggest that integrating machine learning with structural analysis can serve as a computationally effcient approach for the design and optimization of thin-walled plates.展开更多
Functionally graded magneto-electro-elastic materials(FG-MEE)are highly valuable for intelligent applications,such as deformation control and active driving,because of their superior multi-physics coupling properties....Functionally graded magneto-electro-elastic materials(FG-MEE)are highly valuable for intelligent applications,such as deformation control and active driving,because of their superior multi-physics coupling properties.The metallic porous materials have attracted attention due to their low density and strong energy absorption capabilities.A sandwich configuration is proposed,consisting of FG-MEE top and bottom layers with an intermediate porous aluminum section as the core.Within the FSDT framework and Hamilton’s variational approach,we model free vibration dynamics under spatially inhomogeneous electromagnetic potentials.Free vibration natural frequencies are determined through Navier’s solution technique with assumed simply-supported edges.By comparing with existing literature,the present model demonstrates reliable and accurate performance.Numerical results research the impacts of geometric parameters,BaTiO3-CoFe2O4volume fraction index,layer thickness ratio,magnetic potential,and electric potential on the natural vibration of FG-MEE sandwich porous plates.This work provides a foundation for further research on such structures,and its findings may aid in the optimization and design of intelligent structures made of FG-MEE.展开更多
A liquid sloshing experimental rig driven by a wave-maker is designed and built to study liquid sloshing problems in a rectangular liquid tank with perforated baffle. A series of experiments are conducted in this expe...A liquid sloshing experimental rig driven by a wave-maker is designed and built to study liquid sloshing problems in a rectangular liquid tank with perforated baffle. A series of experiments are conducted in this experimental rig to estimate the free surface fluctuation and pressure distribution by changing external excitation frequency of the shaking table. An in-house CFD code is also used in this study to simulate the liquid sloshing in three-dimensional (3D) rectangular tank with perforated baffle. Good agreements of free surface elevation and pressure between the numerical results and the experimental data are obtained and presented. Spectral analysis of the time history of free surface elevation is conducted by using the fast Fourier transformation.展开更多
Isolated pillars in underground mines are subjected to uniaxial stress,and the load bearing cross-section of pillars is commonly rectangularly shaped.In addition,the uniaxial compression test(UCT)is widely used for de...Isolated pillars in underground mines are subjected to uniaxial stress,and the load bearing cross-section of pillars is commonly rectangularly shaped.In addition,the uniaxial compression test(UCT)is widely used for determining the basic mechanical properties of rocks and revealing the mechanism of isolated pillar disasters under unidimensional stress.The shape effects of rock mechanical properties under uniaxial compression are mainly quantitatively reflected in the specific shape ratios of rocks.Therefore,it is necessary to study the detailed shape ratio effects on the mechanical properties of rectangular prism rock specimens and isolated pillars under uniaxial compressive stress.In this study,granite,marble and sandstone rectangular prism specimens with various height to width ratios(r)and width to thickness ratios(u)were prepared and tested.The study results show that r and u have a great influence on the bearing ability of rocks,and thin or high rocks have lower uniaxial compressive strength.Reducing the level of r can enhance the u effect on the strength of rocks,and increasing the level of u can enhance the r effect on the strength of rocks.The lateral strain on the thickness side of the rock specimen is larger than that on the width side,which implies that crack growth occurs easily on the thickness side.Considering r and u,a novel strength prediction model of isolated pillars was proposed based on the testing results,and the prediction model was used for the safety assessment of 179 isolated pillars in the Xianglu Mountain Tungsten Mine.展开更多
基金financial support provided by the National Natural Science Foundation of China(Grant Nos.51868062 and 52168060)by the Innovation Scholarship for Doctoral Students of Beijing University of Technology.
摘要Rectangular pipe-jacking tunnels are highly prone to longitudinal deformation under the influence of adjacent engineering activities,uneven foundation settlement,and changes in surface loads.These problems may lead to structural damage at the joints of rectangular pipe-jacking tunnels,potentially triggering engineering disasters.In response to these situations,this paper experimentally studies the effects of different foundation conditions and steel sleeve ring design parameters on their shear stiffness and rotational stiffness.It reveals three stages of joint failure:gap closure,steel sleeve ring stress,and deformation failure.A three-dimensional refined numerical simulation method is adopted to study the deformation and failure characteristics of joints under different foundation strengths and steel sleeve ring design parameters,analyze the mechanical performance of the joints of rectangular pipe-jacking tunnels,and verify the reliability of the experimental results.Based on the experimental and numerical simulation results,considering the nonlinear characteristics of the joints of rectangular pipe-jacking tunnels,a shell-joint theoretical model is constructed.Precise simulation is achieved through the combination of‘rotation+shear’dynamic elements,and the stiffness matrix at the joints and the calculation method of mechanical elements are derived.The shell-joint theoretical model is used to compare and verify the results of the joint tests of rectangular pipe-jacking tunnels,confirming the accuracy and practicality of the shell-joint theoretical model.
基金supported by the New Cornerstone Science Foundation through the XPLORER PRIZE,the National Natural Science Foundation of China(Grant No.52471307)the Fundamental Research Funds for the Central Universities(Grant No.202562012).
摘要This study quantitatively examined the fluid energy evolution and dissipation process near narrow gaps formed between multiple floating rectangular structures under wave-induced gap resonance conditions.Given the limited understanding of gap resonance mechanisms through fluid energy analysis,a numerical wave flume based on theδ-LES-Smoothed Particle Hydrodynamics(SPH)approach was developed to investigate how incident wave and structural parameters influence the temporal evolution of fluid energy components.The findings reveal that for two floating boxes,the fluid energy dissipation within one wave period in the gap region between the boxes constitutes 81%of the total fluid energy dissipation in the fluid domain.This proportion remains consistent across varying incident wave heights under gap resonance conditions.The temporal distribution of fluid energy dissipation rate shows two peak values within one wave period,exhibiting significant waveform asymmetry.Additionally,in three-box configurations,the two narrow gap regions serve as primary zones of fluid energy dissipation,with energy dissipation patterns closely resembling those observed in the single gap region.Through comprehensive analysis of fluid energy evolution,this research advances the fundamental understanding of gap resonance mechanisms.
基金supported by the“Regional Innovation System&Education(RISE)”through the Seoul RISE Center,funded by the Ministry of Education(MOE)and the Seoul Metropolitan Government(2025-RISE-01-027-04).
摘要Fluid dynamic research on rectangular and trapezoidal fins is aimed at increasing heat transfer by means of large surfaces.The trapezoidal cavity form is compared with its thermal and flow performance,and it is revealed that trapezoidal fins tend to be more efficient,particularly when material optimization is critical.Motivated by the increasing need for sustainable energy management,this work analyses the thermal performance of inclined trapezoidal and rectangular porous fins utilising a unique hybrid nanofluid.The effectiveness of nanoparticles in a working fluid is primarily determined by their thermophysical properties;hence,optimising these properties can significantly improve overall performance.This study considers the dispersion of Graphene Oxide(GO)and Molybdenum Disulfide in the base fluid,engine oil.Temperature profiles are analysed by altering the radiative,porosity,wet porous,and angle of inclination parameters.Surface and contour plots are constructed by using the Lobatto IIIa Collocation Method with BVP5C solver in MATLAB and Gradient Descent Optimisation to predict the combined heat transfer rate.According to the study,fluid temperature consistently decreases when the angle of inclination,wet porous parameter,porosity parameter,and radiative parameter increase,suggesting significantly improved heat dissipation.The trapezoidal fin consistently exhibits a superior heat transfer mechanism than a rectangular fin.It is found that the trapezoidal fin transmits heat at a rate that is 0.05%higher than that of the rectangular fin.Validation of the present study is done through the comparison of previous studies.This research provides useful design insights for sophisticated engineering uses,including electrical cooling devices,heat exchangers,radiators,and solar heaters.
摘要Elevated,rectangular water tanks are an essential component of the water supply network and for emergency water storage.However,determining the dynamic response from seismic loads will require accurate estimates of their natural frequencies to help avoid damage or failure.Several numerical and analytical methodologies depend on assumptions that may not account for the complexity of fluid-structure interaction regarding rectangular geometries,indicating a strong need for solid experimental validation.This study pioneers the application of Digital Image Correlation(DIC),a non-contact optical technique,to measure the natural frequencies of a small-scale acrylic and Teflon tank,addressing this gap with a novel experimental approach.The method includes DIC using a high-speed camera,image analyzed by MATLAB,frequency analysis by Continuous Wavelet Transformation(CWT),and Fast Fourier Transformation(FFT);ANSYS finite element analysis,simplified models based on Eurocode and the Egyptian Code of Practice(ECP).Study results indicate that DIC is critical for attaining high accuracy,with maximum error differing by 2.92% for impulsive and 4.55%for convective frequencies from ANSYS and provides a better measure of dynamic response compared to contact-based measurements.Impulsive frequency decreased from 5.8724 Hz to 4.0085 Hz,and sloshing increased from 1.00 Hz to 1.84 Hz,as the water cover height varied from 0 cm to 9.8 cm.The Eurocode and ECP models describe acceptable errors of 7.36% and 9.21%,respectively.DIC showed higher accuracy,making it a useful tool for seismic design.This study improves the safety and reliability of designs for elevated water tanks in seismic regions with elevated seismic risk.
基金the financial support from the Natural Science Fund Project of Chongqing Committee of Science and Technology(No.CSTC.2006BA3023)
摘要The sedimentation of a rectangular particle falling in a two-dimensional channel filled with Newtonian fluid was simulated with finite element arbitrary Lagrangian-Eulerian domain method.The numerical procedure was validated by comparison of the simulation results with existing numerical work.Morea over,good agreement was obtained between the simulation results and experimental measurements performed in the current study.The equilibrium position,stable orientation and drag coefficient ofa rect-angular particle for different particle Reynolds numbers(Rep)were studied.The results show that there is a critical particle Reynolds number for the preferred orientation of a rectangular particle falling in a Newtonian fluid.When Rep is smaller than the critical value,the particle fails with its long side parallel to gravity;otherwise the particle fails with its long side perpendicular to gravity.The critical particle Reynolds number is a decreasing function of the blockage ratio and aspect ratio.The distributions of pressure and shear stress on rectangular particle surface were analyzed.Moreover,the drag coefficient of the rectangular particle decreases as Rep or the blockage ratio increases;however,it appears to be independent of aspect ratio.
基金Project supported by the National Natural Science Foundation of China(Nos.11302046 and 11172063)
摘要The natural frequencies, complex modes and critical speeds of an axially moving rectangular plate, which is partially immersed in a fluid and subjected to a pretension, are investigated. The effects of free surface waves, compressibility and viscidity of the fluid are neglected in the analysis. The subsection functions are used to describe the discontinuous characteristics of the system due to partial immersion. The classical thin plate theory is adopted to formulate the equations of motion of a vibrating plate. The velocity potential and Bernoulli's equation are used to describe the fluid pressure acting on the moving plate. The effect of fluid on the vibrations of the plate may be equivalent to the added mass on the plate. The effects of distance ratio, moving speed, immersed-depth ratio, boundary conditions, stiffness ratio and aspect ratio of the plate as well as the fluid-plate density ratios on the free vibrations of the moving plate-fluid system are investigated.
摘要In this paper, we present the electromagnetic analysis of a rectangular cavity partially filled with a left-handed material slab. Our theoretical investigation shows that there exist novel resonant modes in the cavity, and such a cavity becomes a subwavelength cavity. The eigenvalue equation of the cavity is derived and the resonant frequencies of the novel modes are calculated by using numerical simulation. We also discuss the stability of the novel resonant modes and show the best condition under which a useful rectangular cavity of subwavelength dimensions with tolerable stability is obtained.
摘要A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.
基金Project(2022YJS073)supported by the Fundamental Research Funds for the Central Universities,ChinaProject(2024YFE0198500)supported by the National Key Research and Development Program of China:Intergovernmental International Science and Technology Innovation CooperationProject(U2469207)supported by the National Natural Science Foundation Railway Innovation and Development Joint Fund Project,China。
摘要Determining earth pressure on jacked pipes is essential for ensuring lining safety and calculating jacking force,especially for deep-buried pipes.To better reflect the soil arching effect resulting from the excavation of rectangular jacked pipes and the distribution of the earth pressure on jacked pipes,we present an analytical solution for predicting the vertical earth pressure on deep-buried rectangular pipe jacking tunnels,incorporating the tunnelling-induced ground loss distribution.Our proposed analytical model consists of the upper multi-layer parabolic soil arch and the lower friction arch.The key parameters(i.e.,width and height of friction arch B and height of parabolic soil arch H 1)are determined according to the existing research,and an analytical solution for K l is derived based on the distribution characteristics of the principal stress rotation angle.With consideration for the transition effect of the mechanical characteristics of the parabolic arch zone,an analytical solution for soil load transfer is derived.The prediction results of our analytical solution are compared with tests and simulation results to validate the effectiveness of the proposed analytical solution.Finally,the effects of different parameters on the soil pressure are discussed.
基金supported by the National Science Foundation of China(Grant No.14102428)the Fundamental Research Funds for the Central Universities(Grant Nos.WK2090000019 and YD2480002002)the Open Research Fund of Anhui Province Key Laboratory of Green Building and Assembly Construction,Anhui Institute of Building Research&Design(Grant No.2021-JKYL-005).
摘要Rectangular explosive charges are usually used in military or civilian explosive transportation and storage.The effects of shape parameters and detonation positions on the peak overpressure and maximum impulse of blasts lack comprehensive investigation,which is significant for the design of blast-resistant structures.In this paper,the side-length ratio of the rectangle,orientation,and detonation position of the charge are chosen as controlling parameters to investigate their influence on blast loads in the scaled distances of the gauges ranging from 0.63 to 10.54 m/kg1/3 with well validated 3D numerical simulations.The results show that there is a large difference in the near-field spatial distribution of the blast load of the rectangular charge;if the blast load of the rectangular charge is simply evaluated with the spherical charge,the maximum peak overpressure(maximum impulse)will be underestimated by a factor of 7.46(4.84).This must be taken seriously by blast-resistant structure designers.With the increase in the scaled distance,when the critical scaled distance is greater than 6.32(7.38)m/kg1/3,the influence of the charge shape on the maximum peak overpressure(maximum impulse)of the spatial blast load can be ignored.In general,the impact of detonation of the charge at the end on the maximum peak overpressure is greater compared with central detonation,but for the impact of the maximum impulse,it is necessary to pay attention to the side-length ratio of the rectangular charge and the specific detonation position on the end face.Furthermore,the structural response of steel plates placed at different azimuths under the blast load of a rectangular charge is preliminarily analyzed,and the results show that the deformation and energy of the plates are consistent with the distribution of the blast load.These analysis results provide a reference for the explosion protection design in near-field air explosions.
基金funded by the National Science and Technology Major Project(No.2025ZD1700904)the National Natural Science Foundation of China(Nos.52174093 and 52034009)+1 种基金Fundamental Research Funds for the Central Universities(No.2023ZKPYNY03)Fundamental Research Funds for the Central Universities(Ph.D.Top Innovative Talents Fund of CUMTB)(No.BBJ2025002)。
摘要To investigate groundwater influence on stability and rockburst mechanism of deep hard-rock rectangular tunnels,water-immersed treatment and uniaxial compressive acoustic emission(AE)experiments were conducted on rectangular tunnel specimens.Energy dissipation characteristics,AE evolution characteristics and damage evolution characteristics of rectangular tunnels were analysed under waterimmersed condition.Under water-immersed condition,tunnel specimens were quite sensitive to water.Average peak stress and average peak strain energy exhibited negative exponential decay with waterimmersed time.Among them,after 12 d of water immersion,average peak stress of specimens decreased by 28%.Average total strain energy decreased by 70%.Average elastic strain energy decreased by 71%and average dissipated strain energy decreased by 68%.After 62 d of water immersion,average peak stress of specimens decreased by 34%.Average total strain energy decreased by 78%.Average elastic strain energy decreased by 79%and average dissipated strain energy decreased by 75%.Water weakened bonding among mineral particles.Moreover,it undermined load-bearing capacity and diminished energystorage properties.Under high stress,massive releasable elastic strain energy stored in natural specimens within pre-peak stage may abruptly release after peak stress.This caused rapid crack development and connection in specimens.During accumulation and release of elastic strain energy,initial failure typically occurred at sidewalls.This failure location was not affected by water.Compared with natural specimens,Specimens immersed in water for 62 d had the lowest peak values of cumulative amplitude,cumulative AE energy and cumulative AE count.After 62 d of water immersion,peak values of cumulative amplitude,cumulative AE energy and cumulative AE count of specimens decreased by 84%,97%and 99%.Compared with AE damage model,fitting degree of energy damage model was higher.For natural specimens,fitting degree of energy damage model was 0.96.For specimens immersed in water for 12 d,fitting degree of energy damage model was 0.96.For specimens immersed in water for 62 d,fitting degree of energy damage model was 0.72.Therefore,an energy damage model had more remarkable applicability and reliability.By establishing dynamic mapping relationship between energy and damage in the model,accuracy of rockburst early warning has been significantly improved.This provided scientific basis for support structure design of rectangular tunnels and regulation of high strain energy.
基金supported by the National Natural Science Foundation of China(No.11772090).
摘要This study investigates the nonlinear dynamic properties of rotating functionally graded sandwich rectangular plates in a thermal environment.The nonlinear vibration equations for a rotating metal-ceramic functionally graded sandwich rectangular plate in a thermal environment are derived using classical thin plate theory and Hamilton’s principle,considering geometric nonlinearity,temperature-dependent material properties,and power law distribution of components through the thickness.With cantilever boundary conditions,the flexural nonlinear differential equations of the rectangular sandwich plate are obtained via the Galerkin method.Since the natural vibration differential equations exhibit nonlinear characteristics,the multiscale method is employed to derive the expression for nonlinear natural frequency.An example analysis reveals how the natural frequency of a functionally graded sandwich rectangular plate varies with rotational speed and temperature.Results show that the nonlinear/linear frequency ratio increases with rotational angular velocity Ω and thickness-to-length ratio h/a,follows a cosine-like periodic pattern with the setting angle,and shows a sharp decrease followed by a rapid increase with increasing width-to-length ratio b/a.The derived analytical solutions for nonlinear frequency provide valuable insights for assessing the dynamic characteristics of functionally graded structures.
基金supported by the Shandong Provincial Natural Science Foundation,China(Grant ZR2024ME136).
摘要The growing need for enhanced heat dissipation is compelling the development of more effective heat exchangers.Innovation inspired by nature bionics,four types of leaf-shaped pin fins were proposed and four combinations of them were considered.The leaf-shaped design of the cooling pin fin enhances uniformity and synergy,effectively creating an optimized flow path that boosts cooling performance.Eight three-dimensional conjugate heat transfer models in staggered arrangement were developed using ANSYS-Fluent software.Aluminum6061material was used as the heat sinkmaterial and single-phase liquid water flowed through the rectangular channel where the Reynolds(Re)number varies from 40 to 100.Using the same boundary conditions as the software simulations,two leaf-shaped channels were printed to validate numerical models.Velocity field and temperature differences of the eight proposed leaf-shaped pin fins configurations were discussed by comparison with cylindrical pin fins.Based on the findings of this study,at a Reynolds number of 80,the Leaf B Staggered Array(LBSA)records a maximum temperature that is 0.72 K lower than that of the cylindrical pin fins arrangement.Additionally,the LBSA exhibits a reduction in the friction factor by approximately 33.3%relative to the circular pin fins array under the same Re.This implies that the design of LBSA has been optimized to provide better heat dissipation performance while maintaining lower energy consumption.Furthermore,the LBSA demonstrates the most favorable thermal-hydraulic performance index(TPI),which is 1.18 times higher than that of the circular pin fins arrangement at Re=80.The temperature reduction and friction factor reduction of the lobed channel is more pronounced than that of the conventional cooling channel,highlighting its potential to increase heat transfer efficiency and reduce energy consumption in practical applications.
基金funded by the Project of the Hubei Provincial Department of Science and Technology(Grant No.2022CFB957)the Project of Hubei Engineering University of Teaching Research(Grant No.JY2024032)+1 种基金Ministry of Education University-Industry Cooperation Collaborative Education Project(Grant No.220903584161245)College Students’Innovation and Entrepreneurship Training Program(Grant Nos.DC2024031,DC2024032).
摘要The behavior of single-phase flow and conjugate heat transfer in micro-channel heat sinks(MCHS)subjected to auniform heat flux is investigated by means of numerical simulations.Various geometrical configurations areexamined,particularly,the combinations of rectangular solid and perforated blocks,used to create a disturbancein the flow.The analysis focuses on several key aspects and related metrics,including the temperature distribution,the mean Fanning friction factor,the pressure drop,the Nusselt number,and the overall heat transfer coefficientacross a range of Reynolds numbers(80–870).It is shown that the introduction of such blocks significantlyenhances the heat transfer performances of the MCHS compared to the straight-through flow channel.Specifically,a case is found where the Nusselt number increases by 2.3 times relative to the reference case.The integrationof perforated blocks facilitates the generation of vorticity within the channel,promoting the mixing of coldand hot fluids.Notably,MCHS incorporating perforated rectangular blocks exhibit more pronounced heat transferbenefits at Reynolds numbers smaller than 400.
摘要The implementation of multifunctional metasurfaces through loading diodes has extremely high costs,while increasing the number of channels in the element through polarization multiplexing technology is limited.This paper proposes a dual-band five-channel(DBFC)1-bit surface,which expands the polarization independent(PD)channels through rotating array.The polarization-independent metasurface element consists of three layers of metal,with the top layer comprising three rectangular patches oriented in the x-direction,the middle layer featuring a Jerusalem cross structure with accompanying resonators,and the bottom layer being a metal ground plane.The middle layer element can easily independently provide the required 1-bit reflection phases for two orthogonal polarizations in every frequency.The rectangular patches in the x-direction on the top layer do not contribute to the phase of y-polarization.By rotating the upper layer dielectric array 90°,the rectangular patches change to the y-direction.Under y-polarized illumination,the current distribution in the middle layer is shielded,providing a fifth set of polarization independent phases.The proposed 1-bit DBFC metasurface array has advantages in terms of structure and cost,while enhancing the utilization rate of the metasurface array.It has high application potential in microwave imaging,wireless power transmission,and other projects.
基金Funded by the National Natural Science Foundation of China(50525516)
摘要The hydroforming experiment of aluminum tubular part with rectangular section was carried out to investigate influence of axial feeding on thickness distribution and calibration pressure of the corner.Thickness distribution and relation between corner radius and internal pressure were analyzed.The influence of lubricant was discussed.Microstructure and hardness of different region were observed.It is shown that thickness reduction in the transition region between the corner and center region is the biggest.Friction condition has influence both on the thickness distribution and calibration pressure of the corner.As the increase of the axial feeding,the calibration pressure is decreased.There is only little change for the microstructure,but the hardness is increased by 23.3% for the transition region.
基金funding from the Deanship of Graduate Studies and Scientific Research,Jazan University,Saudi Arabia,through Project Number:JU-202503221-DGSSR-RP-2025.
摘要Designing thin-walled plate structures is challenging due to their susceptibility to various forms of structural instability.In addition,the substantial computational cost of finite element analyses,especially in optimization scenarios,underscores the need for efficient and reliable surrogate models.To address this challenge,the present study employs machine learning(ML)techniques to predict the buckling response of thin plates under complex boundary conditions.Four ML models,including XGBoost,CatBoost,Light GBM,and Random Forest,are developed to predict the buckling coefficient based on input features,including aspect ratio,boundary condition,and compressive loading pattern.The training data for these models is generated using the finite integral transform method.Model performance is rigorously evaluated,with all four algorithms demonstrating strong predictive capabilities.Among them,XGBoost demonstrates the superior predictive performance,achieving an R2 value of 0.99.To gain deeper insights into feature influence,SHAP analysis is conducted,revealing that the aspect ratio has the greatest influence on buckling coefficient,followed by boundary conditions and compressive loading.By adopting gradient-boosting approaches,the proposed framework demonstrates improved generalization and reduced overfitting,with potential applicability to structural optimization.The results suggest that integrating machine learning with structural analysis can serve as a computationally effcient approach for the design and optimization of thin-walled plates.
基金The financial support of the National Natural Science Foundation of China through Grant Nos.12272056,11872127.
摘要Functionally graded magneto-electro-elastic materials(FG-MEE)are highly valuable for intelligent applications,such as deformation control and active driving,because of their superior multi-physics coupling properties.The metallic porous materials have attracted attention due to their low density and strong energy absorption capabilities.A sandwich configuration is proposed,consisting of FG-MEE top and bottom layers with an intermediate porous aluminum section as the core.Within the FSDT framework and Hamilton’s variational approach,we model free vibration dynamics under spatially inhomogeneous electromagnetic potentials.Free vibration natural frequencies are determined through Navier’s solution technique with assumed simply-supported edges.By comparing with existing literature,the present model demonstrates reliable and accurate performance.Numerical results research the impacts of geometric parameters,BaTiO3-CoFe2O4volume fraction index,layer thickness ratio,magnetic potential,and electric potential on the natural vibration of FG-MEE sandwich porous plates.This work provides a foundation for further research on such structures,and its findings may aid in the optimization and design of intelligent structures made of FG-MEE.
基金supported by the China Postdoctoral Science Foundation(Grant No.2012M511192)the National Natural Science Foundation of China(Grant Nos.51209080 and 51061130547+5 种基金Open Fund of State Key Laboratory of Coastaland Off shore Engineering(Grant No.LP1207the Open Fund of State Key Laboratory of Hydraulics and Mountain River Engineering(Grant No.1213)Qing Lan Project and 333 Project of Jiangsu Province(Grant No.BRA2012130)the Fundamental Research Funds for the Central Universities(Hohai University,Grant No.2012B06514the 111 Project(Grant No.B12032)Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120181110084)
摘要A liquid sloshing experimental rig driven by a wave-maker is designed and built to study liquid sloshing problems in a rectangular liquid tank with perforated baffle. A series of experiments are conducted in this experimental rig to estimate the free surface fluctuation and pressure distribution by changing external excitation frequency of the shaking table. An in-house CFD code is also used in this study to simulate the liquid sloshing in three-dimensional (3D) rectangular tank with perforated baffle. Good agreements of free surface elevation and pressure between the numerical results and the experimental data are obtained and presented. Spectral analysis of the time history of free surface elevation is conducted by using the fast Fourier transformation.
基金funded by the National Natural Science Foundation of China(Nos.51774326,42177164,41807259,and41702350)Hunan Young Talent(No.2021RC3007)+2 种基金the open fund of Mining Disaster Prevention and Control Ministry Key Laboratory at Shandong University of Science and Technology(No.MDPC201917)the Fundamental Research Funds for the Central Universities of Central South University(No.2019zzts668)the Innovation-Driven Project of Central South University(No.2020CX040)。
摘要Isolated pillars in underground mines are subjected to uniaxial stress,and the load bearing cross-section of pillars is commonly rectangularly shaped.In addition,the uniaxial compression test(UCT)is widely used for determining the basic mechanical properties of rocks and revealing the mechanism of isolated pillar disasters under unidimensional stress.The shape effects of rock mechanical properties under uniaxial compression are mainly quantitatively reflected in the specific shape ratios of rocks.Therefore,it is necessary to study the detailed shape ratio effects on the mechanical properties of rectangular prism rock specimens and isolated pillars under uniaxial compressive stress.In this study,granite,marble and sandstone rectangular prism specimens with various height to width ratios(r)and width to thickness ratios(u)were prepared and tested.The study results show that r and u have a great influence on the bearing ability of rocks,and thin or high rocks have lower uniaxial compressive strength.Reducing the level of r can enhance the u effect on the strength of rocks,and increasing the level of u can enhance the r effect on the strength of rocks.The lateral strain on the thickness side of the rock specimen is larger than that on the width side,which implies that crack growth occurs easily on the thickness side.Considering r and u,a novel strength prediction model of isolated pillars was proposed based on the testing results,and the prediction model was used for the safety assessment of 179 isolated pillars in the Xianglu Mountain Tungsten Mine.