A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term ...A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term as a slow-varying parameter,a generalized autonomous fast subsystem can be defined,the equilibrium branches as well as the bifurcations of which can be employed to account for the mechanism of the bursting oscillations by combining the transformed phase portrait introduced.As an example,a typical periodically excited Hartley model is used to demonstrate the validness of the method,in which the exciting frequency is far less than the natural frequency.The equilibrium branches and their bifurcations of the fast subsystem with the variation of the slow-varying parameter are presented.Bursting oscillations for two typical cases are considered,which reveals that,fold bifurcation may cause the the trajectory to jump between different equilibrium branches,while Hopf bifurcation may cause the trajectory to oscillate around the stable limit cycle.展开更多
The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elas...The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.展开更多
Current building design codes allow the appearance of structural and nonstructural damage under design basis earthquakes.The research regarding probabilistic seismic loss estimation in domestic building structure is u...Current building design codes allow the appearance of structural and nonstructural damage under design basis earthquakes.The research regarding probabilistic seismic loss estimation in domestic building structure is urgent.The evaluation in this paper is based on a 11-story reinforced concrete office building,incremental dynamic analysis(IDA)is conducted in Perform 3D program using models capable to simulate all possible limit states up to collapse.Next,the probability distribution of post-earthquake casualties,rebuild costs repair costs and business downtime loss are calculated in PACT software for the studied building considering the modified component vulnerability groups and population flow models.The evaluation procedure can also shed light on other types of buildings in China.For non-typical functional building structures,this article proposes to build a finite element model of structural components and to classify the vulnerability groups based on the construction drawings,and to supply and improve the vulnerability library of appendages in FEMA P-58 according to the actual situation.In this way,the application scope of building seismic performance evaluation can be expanded.展开更多
Investigating the dynamic characteristics of nonlinear models that appear in ocean science plays an important role in our lifetime.In this research,we study some features of the paired Boussinesq equation that appears...Investigating the dynamic characteristics of nonlinear models that appear in ocean science plays an important role in our lifetime.In this research,we study some features of the paired Boussinesq equation that appears for two-layered fluid flow in the shallow water waves.We extend the modified expansion function method(MEFM)to obtain abundant solutions,as well as to find new solutions.By using this newly modified method one can obtain novel and more analytic solutions comparing to MEFM.Also,numerical solutions via the Adomian decomposition scheme are discussed and favorable comparisons with analytical solutions have been done with an outstanding agreement.Besides,the instability modulation of the governing equations are explored through the linear stability analysis function.All new solutions satisfy the main coupled equation after they have been put into the governing equations.展开更多
This paper aims to evaluate the stochastic response of steel columns subjected to blast loads using the modified single degree of freedom(MSDOF)method,which assessed towards the conventional single degree of freedom(S...This paper aims to evaluate the stochastic response of steel columns subjected to blast loads using the modified single degree of freedom(MSDOF)method,which assessed towards the conventional single degree of freedom(SDOF)and the experimentally validated Finite Element(FE)methods(LSDYNA).For this purpose,special atten-tion is given to calculating the response of H-shaped steel columns under blast.The damage amount is determined based on the support rotation criterion,which is expressed as a function of their maximum lateral mid-span dis-placement.To account for uncertainties in input parameters and obtain the failure probability,the Monte Carlo simulation(MCS)method is employed,complemented by the Latin Hypercube Sampling(LHS)method to reduce the number of simulations.A parametric analysis is hence performed to examine the effect of several input pa-rameters(including both deterministic and probabilistic parameters)on the probability of column damage as a function of support rotation.First,the MSDOF method confirms its higher accuracy in estimating the probability of column damage due to blast,compared to the conventional SDOF.The collected results also show that un-certainties of several input parameters have significant effects on the column behavior.In particular,geometric parameters(including cross-sectional characteristics,boundary conditions and column length)have major effect on the corresponding column response,in the same way of input blast load parameters and material properties.展开更多
A simple,yet accurate modi?ed multi-scale method(MMSM)for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is proposed.This method depends on the clas...A simple,yet accurate modi?ed multi-scale method(MMSM)for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is proposed.This method depends on the classical multi-scale method(MSM)and the method of variation of parameters.Assuming that the forced excitation is a constant,one could easily obtain the approximate analytical solution of the simpli?ed system based on the traditional MSM.Then,this solution for the oscillator under forced harmonic excitation could be established after replacing the harmonic excitation by the constant excitation.To certify the correctness and precision of the proposed analytical method,the van der Pol system with two scales subject to slowly periodic excitation is investigated;this system presents rich dynamical phenomena such as spiking(SP),spiking-quiescence(SP-QS),and quiescence(QS)responses.The approximate analytical expressions of the three types of responses are given by the MMSM,and it can be found that the precision of the new analytical method is higher than that of the classical MSM and better than that of the harmonic balance method(HBM).The results obtained by the present method are considerably better than those obtained by traditional methods,quantitatively and qualitatively,particularly when the excitation frequency is far less than the natural frequency of the system.展开更多
Elastic critical buckling load of a column depends on various parameters,such as boundary conditions,material,and crosssection geometry.The main purpose of this work is to present a new method for investigating the bu...Elastic critical buckling load of a column depends on various parameters,such as boundary conditions,material,and crosssection geometry.The main purpose of this work is to present a new method for investigating the buckling load of tapered columns subjected to axial force.The proposed method is based on modified buckling mode shape of tapered structure and perturbation theory.The mode shape of the damaged structure can be expressed as a linear combination of mode shapes of the intact structure.Variations in length in piecewise form can be positive or negative.The method can be used for single-span and continuous columns.Comparison of results with those of finite element and Timoshenko methods shows the high accuracy and efficiency of the proposed method for detecting buckling load.展开更多
In this paper, based on the robust inverse scattering method, we construct two kinds of solutions to the focusing modified Korteweg–de Vries equation. One is the classical soliton solution under the zero background c...In this paper, based on the robust inverse scattering method, we construct two kinds of solutions to the focusing modified Korteweg–de Vries equation. One is the classical soliton solution under the zero background condition and the other one is given through the nonzero background.Especially, for the nonzero background case, we choose a special spectral parameter such that the nonzero background solution is changed into the rational travelling waves. Finally, we also give a simple analysis of the soliton as the time t is large, then we give the comparison between the exact solution and the asymptotic solution.展开更多
This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredepend...This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.展开更多
In this study, we constructed and analysed a mathematical model of COVID-19 in order to comprehend the transmission dynamics of the disease. The reproduction number (R<sub>C</sub>) was calculated via the n...In this study, we constructed and analysed a mathematical model of COVID-19 in order to comprehend the transmission dynamics of the disease. The reproduction number (R<sub>C</sub>) was calculated via the next generation matrix method. We also used the Lyaponuv method to show the global stability of both the disease free and endemic equilibrium points. The results showed that the disease-free equilibrium point is globally asymptotically stable if R<sub>C</sub> R<sub>C</sub> > 1. We further used the Adomian decomposition method and the modified Adomian decomposition method to obtain the solutions of the model. Numerical analysis of the model was done using Sagemath 9.0 software.展开更多
A recently developed backward extrusion method entitled “modified backward extrusion” was presented using an upper bound analysis. For this purpose deformation area was divided into four distinct zones and a kinemat...A recently developed backward extrusion method entitled “modified backward extrusion” was presented using an upper bound analysis. For this purpose deformation area was divided into four distinct zones and a kinematically admissible velocity field for each of them was suggested. Total dissipated power was calculated for the deformation zones and the extrusion power wascomputed. The correlations of important geometrical parameters with extrusion force and dissipated powers were shown. Finding the initial billet size, a challenging area in the modified backward extrusion method, was discussed and the optimum billet radius was obtained, considering the minimum relative extrusion pressure. Finite element analyses were conducted and the results werecompared with the upper bound analysis. Finally, experiments were executed on commercially pure aluminium and a good agreement between upper bound and finite element analyses with experimental values was observed.展开更多
The conventional pseudo-dynamic(CPD)and modified pseudo-dynamic(MPD)methods are invoked to obtain the seismic bearing capacity of strip foundations using the limit equilibrium method,with a two-wedge failure mechanism...The conventional pseudo-dynamic(CPD)and modified pseudo-dynamic(MPD)methods are invoked to obtain the seismic bearing capacity of strip foundations using the limit equilibrium method,with a two-wedge failure mechanism.A spectral version of the conventional pseudo-dynamic method(SPD)is also invoked by considering the ground motion amplification factor,to be a function of the non-dimensional frequencyλ/B and soil damping.Numeric analyses show that bearing capacity results obtained by the MPD and SPD methods are generally consistent.Both experience the same general reduction in bearing capacity with the increase ofλ/B,with successive ups and downs corresponding to soil′s natural frequencies.For 5<λ/B<10,SPD and MPD results fluctuated between falling above and below CPD results.Forλ/B<2.5,SPD and MPD results were consistent with attenuation of the shear wave,while for 10<λ/B,amplification was exhibited.Results obtained by the CPD method monotonically decrease,due to the fact that CPD fails to inherently consider site effects and damping,and instead and relies on a single factor to consider the ground motion amplification.展开更多
An approximate analysis for free vibration of a laminated curved panel(shell)with four edges simply supported(SS2),is presented in this paper.The transverse shear deformation is considered by using a higher-order shea...An approximate analysis for free vibration of a laminated curved panel(shell)with four edges simply supported(SS2),is presented in this paper.The transverse shear deformation is considered by using a higher-order shear deformation theory.For solving the highly coupled partial differential governing equations and associated boundary conditions,a set of solution functions in the form of double trigonometric Fourier series,which are required to satisfy the geometry part of the considered boundary conditions,is assumed in advance.By applying the Galerkin procedure both to the governing equations and to the natural boundary conditions not satisfied by the assumed solution functions,an approximate solution,capable of providing a reliable prediction for the global response of the panel,is obtained.Numerical results of antisymmetric angle-ply as well as symmetric cross-ply and angle-ply laminated curved panels are presented and discussed.展开更多
Due to rainfall infiltration,groundwater activity,geological processes,and natural erosion,soil often exhibits heterogeneity and unsaturation.Additionally,seismic events can compromise slope stability.Existing analyti...Due to rainfall infiltration,groundwater activity,geological processes,and natural erosion,soil often exhibits heterogeneity and unsaturation.Additionally,seismic events can compromise slope stability.Existing analytical solutions typically consider a single failure mode,leading to inaccurate slope stability assessments.This study analyzes the impact of matric suction through three nonlinear shear strength models and adopts a heterogeneous soil model where cohesion linearly increases with depth.An improved pseudo-dynamic method is used to account for seismic effects.Based on a three-dimensional(3D)trumpet-shaped rotational failure mechanism,a new framework is established to analyze the stability of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects.The internal energy dissipation rate and external power at failure are calculated,and the gravity increase method is introduced to derive an explicit expression for the safety factor(F_(s)).The results are compared with previously published results,demonstrating the effectiveness of the proposed method.Sensitivity analyses on different parameters are conducted,discussing the influence of various factors on F s.This study proposes a new formula for calculating the F_(s) of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects,providing a practical application for slope engineering.展开更多
The sliding forms of weak sloped and horizontal subgrades during the sliding process differ.In addition,the sliding form of weakly sloped subgrades exhibits considerable slippage and asymmetry.The accuracy of traditio...The sliding forms of weak sloped and horizontal subgrades during the sliding process differ.In addition,the sliding form of weakly sloped subgrades exhibits considerable slippage and asymmetry.The accuracy of traditional slice methods for computing the stability safety factor of weakly sloped subgrades is insufficient for a subgrade design.In this study,a novel modified Bishop method was developed to improve the accuracy of the stability safety factor for different inclination angles.The instability mechanism of the weakly sloped subgrade was considered in the proposed method using the“influential force”and“additional force”concepts.The“additional force”reflected the weight effect of the embankment fill,whereas the“influential force”reflected the effect of the potential energy difference.Numerical simulations and experimental tests were conducted to evaluate the advantages of the proposed modified Bishop method.Compared with the traditional slice method,the error between the proposed method and the exact value is less than 32.3%in calculating the safety factor.展开更多
Underground engineering,including shield tunnel construction,is a significant contributor to carbon dioxide emissions in infrastructure engineering projects.To better predict and control the carbon emissions associate...Underground engineering,including shield tunnel construction,is a significant contributor to carbon dioxide emissions in infrastructure engineering projects.To better predict and control the carbon emissions associated with shield tunnel construction,this paper presents a novel calculation method:the modified process analysis method based on inputoutput and process analysis methods.To evaluate the effectiveness of the proposed method,a specific shield tunnel construction project was selected as a case study.The modified process analysis method was used to analyze the various factors that influence carbon emissions during the project’s construction phase.In addition,a neural network approach was applied to validate the accuracy of the calculation using the LSTM and BP neural network.The results demonstrate that the proposed method not only combines the strengths of traditional methods but also offers high accuracy and acceptable error rates.Based on these findings,several measures to reduce carbon emissions during shield tunnel construction are suggested,providing valuable insights for reducing CO_(2) emissions associated with infrastructure engineering projects.This study highlights the importance of adopting innovative approaches to reduce carbon emissions and promotes the implementation of sustainable practices in the construction industry.Through the use of advanced analytical methods,such as the proposed modified process analysis method,we can effectively mitigate the environmental impact of construction activities and make significant contributions to the global effort to combat climate change.展开更多
基金supported by the National Natural Science Foundation of China(Grants11632008 and 11872189)
文摘A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term as a slow-varying parameter,a generalized autonomous fast subsystem can be defined,the equilibrium branches as well as the bifurcations of which can be employed to account for the mechanism of the bursting oscillations by combining the transformed phase portrait introduced.As an example,a typical periodically excited Hartley model is used to demonstrate the validness of the method,in which the exciting frequency is far less than the natural frequency.The equilibrium branches and their bifurcations of the fast subsystem with the variation of the slow-varying parameter are presented.Bursting oscillations for two typical cases are considered,which reveals that,fold bifurcation may cause the the trajectory to jump between different equilibrium branches,while Hopf bifurcation may cause the trajectory to oscillate around the stable limit cycle.
基金supported by the Iranian Nanotechnology Development Committee and the University of Kashan(No.363452/10)
文摘The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.
基金This research has been supported by the National Natural ScienceFoundation of China (Grant No. 51778135 )the Natural Science Foundation of JiangsuProvince (Grant No. BK20160207)+1 种基金Aeronautical Science Foundation of China (GrantNo. 20130969010)the Fundamental Research Funds for the Central Universities andPostgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No.KYCX18_0113 and KYLX16_0253).
文摘Current building design codes allow the appearance of structural and nonstructural damage under design basis earthquakes.The research regarding probabilistic seismic loss estimation in domestic building structure is urgent.The evaluation in this paper is based on a 11-story reinforced concrete office building,incremental dynamic analysis(IDA)is conducted in Perform 3D program using models capable to simulate all possible limit states up to collapse.Next,the probability distribution of post-earthquake casualties,rebuild costs repair costs and business downtime loss are calculated in PACT software for the studied building considering the modified component vulnerability groups and population flow models.The evaluation procedure can also shed light on other types of buildings in China.For non-typical functional building structures,this article proposes to build a finite element model of structural components and to classify the vulnerability groups based on the construction drawings,and to supply and improve the vulnerability library of appendages in FEMA P-58 according to the actual situation.In this way,the application scope of building seismic performance evaluation can be expanded.
文摘Investigating the dynamic characteristics of nonlinear models that appear in ocean science plays an important role in our lifetime.In this research,we study some features of the paired Boussinesq equation that appears for two-layered fluid flow in the shallow water waves.We extend the modified expansion function method(MEFM)to obtain abundant solutions,as well as to find new solutions.By using this newly modified method one can obtain novel and more analytic solutions comparing to MEFM.Also,numerical solutions via the Adomian decomposition scheme are discussed and favorable comparisons with analytical solutions have been done with an outstanding agreement.Besides,the instability modulation of the governing equations are explored through the linear stability analysis function.All new solutions satisfy the main coupled equation after they have been put into the governing equations.
文摘This paper aims to evaluate the stochastic response of steel columns subjected to blast loads using the modified single degree of freedom(MSDOF)method,which assessed towards the conventional single degree of freedom(SDOF)and the experimentally validated Finite Element(FE)methods(LSDYNA).For this purpose,special atten-tion is given to calculating the response of H-shaped steel columns under blast.The damage amount is determined based on the support rotation criterion,which is expressed as a function of their maximum lateral mid-span dis-placement.To account for uncertainties in input parameters and obtain the failure probability,the Monte Carlo simulation(MCS)method is employed,complemented by the Latin Hypercube Sampling(LHS)method to reduce the number of simulations.A parametric analysis is hence performed to examine the effect of several input pa-rameters(including both deterministic and probabilistic parameters)on the probability of column damage as a function of support rotation.First,the MSDOF method confirms its higher accuracy in estimating the probability of column damage due to blast,compared to the conventional SDOF.The collected results also show that un-certainties of several input parameters have significant effects on the column behavior.In particular,geometric parameters(including cross-sectional characteristics,boundary conditions and column length)have major effect on the corresponding column response,in the same way of input blast load parameters and material properties.
基金the National Natural Science Foundation of China(Nos.11672191,11772206,and U1934201)the Hundred Excellent Innovative Talents Support Program in Hebei University(No.SLRC2017053)。
文摘A simple,yet accurate modi?ed multi-scale method(MMSM)for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is proposed.This method depends on the classical multi-scale method(MSM)and the method of variation of parameters.Assuming that the forced excitation is a constant,one could easily obtain the approximate analytical solution of the simpli?ed system based on the traditional MSM.Then,this solution for the oscillator under forced harmonic excitation could be established after replacing the harmonic excitation by the constant excitation.To certify the correctness and precision of the proposed analytical method,the van der Pol system with two scales subject to slowly periodic excitation is investigated;this system presents rich dynamical phenomena such as spiking(SP),spiking-quiescence(SP-QS),and quiescence(QS)responses.The approximate analytical expressions of the three types of responses are given by the MMSM,and it can be found that the precision of the new analytical method is higher than that of the classical MSM and better than that of the harmonic balance method(HBM).The results obtained by the present method are considerably better than those obtained by traditional methods,quantitatively and qualitatively,particularly when the excitation frequency is far less than the natural frequency of the system.
文摘Elastic critical buckling load of a column depends on various parameters,such as boundary conditions,material,and crosssection geometry.The main purpose of this work is to present a new method for investigating the buckling load of tapered columns subjected to axial force.The proposed method is based on modified buckling mode shape of tapered structure and perturbation theory.The mode shape of the damaged structure can be expressed as a linear combination of mode shapes of the intact structure.Variations in length in piecewise form can be positive or negative.The method can be used for single-span and continuous columns.Comparison of results with those of finite element and Timoshenko methods shows the high accuracy and efficiency of the proposed method for detecting buckling load.
基金supported by the Natural Science Foundation of Shandong Province(Grant No.ZR2019QD018)National Natural Science Foundation of China(Grant Nos.11975143,12105161,61602188)+1 种基金CAS Key Laboratory of Science and Technology on Operational Oceanography(Grant No.OOST2021-05)Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents(Grant Nos.2017RCJJ068,2017RCJJ069)。
文摘In this paper, based on the robust inverse scattering method, we construct two kinds of solutions to the focusing modified Korteweg–de Vries equation. One is the classical soliton solution under the zero background condition and the other one is given through the nonzero background.Especially, for the nonzero background case, we choose a special spectral parameter such that the nonzero background solution is changed into the rational travelling waves. Finally, we also give a simple analysis of the soliton as the time t is large, then we give the comparison between the exact solution and the asymptotic solution.
基金supported by a grant from the National Science and Technology Council of the Republic of China(Grant Number:MOST 112-2221-E-006-048-MY2).
文摘This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.
文摘In this study, we constructed and analysed a mathematical model of COVID-19 in order to comprehend the transmission dynamics of the disease. The reproduction number (R<sub>C</sub>) was calculated via the next generation matrix method. We also used the Lyaponuv method to show the global stability of both the disease free and endemic equilibrium points. The results showed that the disease-free equilibrium point is globally asymptotically stable if R<sub>C</sub> R<sub>C</sub> > 1. We further used the Adomian decomposition method and the modified Adomian decomposition method to obtain the solutions of the model. Numerical analysis of the model was done using Sagemath 9.0 software.
文摘A recently developed backward extrusion method entitled “modified backward extrusion” was presented using an upper bound analysis. For this purpose deformation area was divided into four distinct zones and a kinematically admissible velocity field for each of them was suggested. Total dissipated power was calculated for the deformation zones and the extrusion power wascomputed. The correlations of important geometrical parameters with extrusion force and dissipated powers were shown. Finding the initial billet size, a challenging area in the modified backward extrusion method, was discussed and the optimum billet radius was obtained, considering the minimum relative extrusion pressure. Finite element analyses were conducted and the results werecompared with the upper bound analysis. Finally, experiments were executed on commercially pure aluminium and a good agreement between upper bound and finite element analyses with experimental values was observed.
文摘The conventional pseudo-dynamic(CPD)and modified pseudo-dynamic(MPD)methods are invoked to obtain the seismic bearing capacity of strip foundations using the limit equilibrium method,with a two-wedge failure mechanism.A spectral version of the conventional pseudo-dynamic method(SPD)is also invoked by considering the ground motion amplification factor,to be a function of the non-dimensional frequencyλ/B and soil damping.Numeric analyses show that bearing capacity results obtained by the MPD and SPD methods are generally consistent.Both experience the same general reduction in bearing capacity with the increase ofλ/B,with successive ups and downs corresponding to soil′s natural frequencies.For 5<λ/B<10,SPD and MPD results fluctuated between falling above and below CPD results.Forλ/B<2.5,SPD and MPD results were consistent with attenuation of the shear wave,while for 10<λ/B,amplification was exhibited.Results obtained by the CPD method monotonically decrease,due to the fact that CPD fails to inherently consider site effects and damping,and instead and relies on a single factor to consider the ground motion amplification.
文摘An approximate analysis for free vibration of a laminated curved panel(shell)with four edges simply supported(SS2),is presented in this paper.The transverse shear deformation is considered by using a higher-order shear deformation theory.For solving the highly coupled partial differential governing equations and associated boundary conditions,a set of solution functions in the form of double trigonometric Fourier series,which are required to satisfy the geometry part of the considered boundary conditions,is assumed in advance.By applying the Galerkin procedure both to the governing equations and to the natural boundary conditions not satisfied by the assumed solution functions,an approximate solution,capable of providing a reliable prediction for the global response of the panel,is obtained.Numerical results of antisymmetric angle-ply as well as symmetric cross-ply and angle-ply laminated curved panels are presented and discussed.
基金Project(51378510)supported by the National Natural Science Foundation of China。
文摘Due to rainfall infiltration,groundwater activity,geological processes,and natural erosion,soil often exhibits heterogeneity and unsaturation.Additionally,seismic events can compromise slope stability.Existing analytical solutions typically consider a single failure mode,leading to inaccurate slope stability assessments.This study analyzes the impact of matric suction through three nonlinear shear strength models and adopts a heterogeneous soil model where cohesion linearly increases with depth.An improved pseudo-dynamic method is used to account for seismic effects.Based on a three-dimensional(3D)trumpet-shaped rotational failure mechanism,a new framework is established to analyze the stability of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects.The internal energy dissipation rate and external power at failure are calculated,and the gravity increase method is introduced to derive an explicit expression for the safety factor(F_(s)).The results are compared with previously published results,demonstrating the effectiveness of the proposed method.Sensitivity analyses on different parameters are conducted,discussing the influence of various factors on F s.This study proposes a new formula for calculating the F_(s) of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects,providing a practical application for slope engineering.
基金This study was sponsored by the National Natural Science Foundation of China(Grant No.51609071)the Fundamental Research Funds for the Central Universities(Nos.B200202087,B200204032).
文摘The sliding forms of weak sloped and horizontal subgrades during the sliding process differ.In addition,the sliding form of weakly sloped subgrades exhibits considerable slippage and asymmetry.The accuracy of traditional slice methods for computing the stability safety factor of weakly sloped subgrades is insufficient for a subgrade design.In this study,a novel modified Bishop method was developed to improve the accuracy of the stability safety factor for different inclination angles.The instability mechanism of the weakly sloped subgrade was considered in the proposed method using the“influential force”and“additional force”concepts.The“additional force”reflected the weight effect of the embankment fill,whereas the“influential force”reflected the effect of the potential energy difference.Numerical simulations and experimental tests were conducted to evaluate the advantages of the proposed modified Bishop method.Compared with the traditional slice method,the error between the proposed method and the exact value is less than 32.3%in calculating the safety factor.
基金supported by the National Natural Science Foundation of China(Grant No.52079128)Anhui province university discipline(professional)top talents academic funding project,project number:gxbjZD2022085.
文摘Underground engineering,including shield tunnel construction,is a significant contributor to carbon dioxide emissions in infrastructure engineering projects.To better predict and control the carbon emissions associated with shield tunnel construction,this paper presents a novel calculation method:the modified process analysis method based on inputoutput and process analysis methods.To evaluate the effectiveness of the proposed method,a specific shield tunnel construction project was selected as a case study.The modified process analysis method was used to analyze the various factors that influence carbon emissions during the project’s construction phase.In addition,a neural network approach was applied to validate the accuracy of the calculation using the LSTM and BP neural network.The results demonstrate that the proposed method not only combines the strengths of traditional methods but also offers high accuracy and acceptable error rates.Based on these findings,several measures to reduce carbon emissions during shield tunnel construction are suggested,providing valuable insights for reducing CO_(2) emissions associated with infrastructure engineering projects.This study highlights the importance of adopting innovative approaches to reduce carbon emissions and promotes the implementation of sustainable practices in the construction industry.Through the use of advanced analytical methods,such as the proposed modified process analysis method,we can effectively mitigate the environmental impact of construction activities and make significant contributions to the global effort to combat climate change.
