Bailongjiang watershed in southern Gansu province, China, is one of the most landslide-prone regions in China, characterized by very high frequency of landslide occurrence. In order to predict the landslide occurrence...Bailongjiang watershed in southern Gansu province, China, is one of the most landslide-prone regions in China, characterized by very high frequency of landslide occurrence. In order to predict the landslide occurrence, a comprehensive map of landslide susceptibility is required which may be significantly helpful in reducing loss of property and human life. In this study, an integrated model of information value method and logistic regression is proposed by using their merits at maximum and overcoming their weaknesses, which may enhance precision and accuracy of landslide susceptibility assessment. A detailed and reliable landslide inventory with 1587 landslides was prepared and randomly divided into two groups,(i) training dataset and(ii) testing dataset. Eight distinct landslide conditioning factors including lithology, slope gradient, aspect, elevation, distance to drainages,distance to faults, distance to roads and vegetation coverage were selected for landslide susceptibility mapping. The produced landslide susceptibility maps were validated by the success rate and prediction rate curves. The validation results show that the success rate and the prediction rate of the integrated model are 81.7 % and 84.6 %, respectively, which indicate that the proposed integrated method is reliable to produce an accurate landslide susceptibility map and the results may be used for landslides management and mitigation.展开更多
General purpose graphic processing unit (GPU) calculation technology is gradually widely used in various fields. Its mode of single instruction, multiple threads is capable of seismic numerical simulation which has ...General purpose graphic processing unit (GPU) calculation technology is gradually widely used in various fields. Its mode of single instruction, multiple threads is capable of seismic numerical simulation which has a huge quantity of data and calculation steps. In this study, we introduce a GPU-based parallel calculation method of a precise integration method (PIM) for seismic forward modeling. Compared with CPU single-core calculation, GPU parallel calculating perfectly keeps the features of PIM, which has small bandwidth, high accuracy and capability of modeling complex substructures, and GPU calculation brings high computational efficiency, which means that high-performing GPU parallel calculation can make seismic forward modeling closer to real seismic records.展开更多
In this study,to develop a benefit-allocation model,in-depth analysis of a distributed photovoltaic-powergeneration carport and energy-storage charging-pile project was performed;the model was developed using Shapley ...In this study,to develop a benefit-allocation model,in-depth analysis of a distributed photovoltaic-powergeneration carport and energy-storage charging-pile project was performed;the model was developed using Shapley integrated-empowerment benefit-distribution method.First,through literature survey and expert interview to identify the risk factors at various stages of the project,a dynamic risk-factor indicator system is developed.Second,to obtain a more meaningful risk-calculation result,the subjective and objective weights are combined,the weights of the risk factors at each stage are determined by the expert scoring method and entropy weight method,and the interest distribution model based on multi-dimensional risk factors is established.Finally,an example is used to verify the rationality of the method for the benefit distribution of the charging-pile project.The results of the example indicate that the limitations of the Shapley method can be reasonably avoided,and the applicability of the model for the benefit distribution of the charging-pile project is verified.展开更多
We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law ...We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.展开更多
We proposed a practical way for mapping the results of coarse-grained molecular simulations to the observables in hydrogen change experiments.By combining an atomic-interaction based coarse-grained model with an all-a...We proposed a practical way for mapping the results of coarse-grained molecular simulations to the observables in hydrogen change experiments.By combining an atomic-interaction based coarse-grained model with an all-atom structure reconstruction algorithm,we reproduced the experimental hydrogen exchange data with reasonable accuracy using molecular dynamics simulations.We also showed that the coarse-grained model can be further improved by imposing experimental restraints from hydrogen exchange data via an iterative optimization strategy.These results suggest that it is feasible to develop an integrative molecular simulation scheme by incorporating the hydrogen exchange data into the coarse-grained molecular dynamics simulations and therefore help to overcome the accuracy bottleneck of coarse-grained models.展开更多
In order to effectively cope with exponent increase of the complexity faced to the rock mechanics analysis problems and the large incompatibility existing between the information level required to model the rock mass ...In order to effectively cope with exponent increase of the complexity faced to the rock mechanics analysis problems and the large incompatibility existing between the information level required to model the rock mass and engineering and our obtainable information level at hand,the integrated approaches with intelligent characters are proposed. Many previous standard methods,such as precedent type analysis,rock classification,analytic method stress-based,basic numerical methods (BEM,FEM,DEM,hybrid),and their extended numerical methods (fully coupled) to be developed,can be selected respectively or integrated accordingly. It is alternative to develop basic/fully integrated system,and internet-based approaches. These novel methods can also be selected or integrated each other or with the standard methods to perform rock mechanics analysis. Some key techniques to develop these alternative methods are discussed. It may focus in future on developing fully integrated systems and internet-based approaches. Developing an environmental,virtual facility/space shall be firstly done for this collaborative research on internet.展开更多
Various calibration methods have been propounded to determine profiles of apparent bulk soil electrical conductivity (ECa) and soil electrical conductivity of a saturated soil paste extract (ECe) or a 1:5 soil water e...Various calibration methods have been propounded to determine profiles of apparent bulk soil electrical conductivity (ECa) and soil electrical conductivity of a saturated soil paste extract (ECe) or a 1:5 soil water extract (EC1:5) using an electromagnetic induction instrument (EM38). The modeled coefficients, one of the successful and classical methods hitherto, were chosen to calibrate the EM38 measurements of the inverted salinity profiles of characteristic coastal saline soils at selected sites of Xincao Farm, Jiangsu Province, China. However, this method required three parameters for each depth layer. An integration approach, based on an exponential decay profile model, was proposed and the model was fitted to all the calibration sites. The obtained model can then be used to predict EC1:5 at a certain depth from electromagnetic measurements made using the EM38 device positioned in horizontal and vertical positions at the soil surface. This exponential decay model predicted the EC1:5 well according to the results of a one-way analysis of variance, and the further comparison indicated that the modeled coefficients appeared to be slightly superior to, but not statistically different from, this exponential decay model. Nevertheless, this exponential decay model was more significant and practical because it depended on less empirical parameters and could be used to perform point predictions of EC1:5 continuously with depth.展开更多
The selection of suitable models and solutions is a fundamental requirement for con-ducting energy flow analysis in integrated energy systems(IES).However,this task is challenging due to the vast number of existing mo...The selection of suitable models and solutions is a fundamental requirement for con-ducting energy flow analysis in integrated energy systems(IES).However,this task is challenging due to the vast number of existing models and solutions,making it difficult to comprehensively compare scholars'studies with current work.In this paper,we aim to address this issue by presenting a comprehensive overview of mainstream IES models and clarifying their relationships,thereby providing guidance for scholars in selecting appro-priate models.Additionally,we introduce several widely used solvers for solving algebraic and differential equations,along with their detailed implementations in the energy flow analysis of IES.Furthermore,we conduct extensive testing and demonstration of these models and methods in various cases to establish benchmarking datasets.To facilitate reproducibility,verification and comparisons,we provide open‐source access to these datasets,including system data,analysis settings and implementations of the various solvers in the mainstream models.Scholars can utilise the provided datasets to reproduce the results,verify the findings and perform comparative analyses.Moreover,they have the flexibility to customise these settings according to their specific requirements.展开更多
Submarine landslides can cause severe damage to marine engineering structures. Their sliding velocity and runout distance are two major parameters for quantifying and analyzing the risk of submarine landslides.Current...Submarine landslides can cause severe damage to marine engineering structures. Their sliding velocity and runout distance are two major parameters for quantifying and analyzing the risk of submarine landslides.Currently, commercial calculation programs such as BING have limitations in simulating underwater soil movements. All of these processes can be consistently simulated through a smoothed particle hydrodynamics(SPH) depth integrated model. The basis of the model is a control equation that was developed to take into account the effects of soil consolidation and erosion. In this work, the frictional rheological mode has been used to perform a simulation study of submarine landslides. Time-history curves of the sliding body's velocity, height,and length under various conditions of water depth, slope gradient, contact friction coefficient, and erosion rate are compared; the maximum sliding distance and velocity are calculated; and patterns of variation are discussed.The findings of this study can provide a reference for disaster warnings and pipeline route selection.展开更多
In order to process different kinds of observing data with different precisions, a new solution model of nonlinear dynamic integral least squares adjustment was put forward, which is not dependent on their derivatives...In order to process different kinds of observing data with different precisions, a new solution model of nonlinear dynamic integral least squares adjustment was put forward, which is not dependent on their derivatives. The partial derivative of each component in the target function is not computed while iteratively solving the problem. Especially when the nonlinear target function is more complex and very difficult to solve the problem, the method can greatly reduce the computing load.展开更多
In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic ...In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic problems. The advantage of this class of method is such that the amount of work calculating one integration with parameters becomes that of two interpolations, when the system of nonlinear equations is solved on the right hand side function. The other class of method is the equivalence substitution method for avoiding calculating derivative on the right hand side function. In order to avoid calculation derivatives, two equivalence substitution methods are proposed here. The application instances of some special effect of the equivalence substitution methods are given.展开更多
Mathematical modeling of surface deformations caused by underground mining operation is commonly carried out with use of empirical,numerical or stochastic models.One of the most frequently applied model for prediction...Mathematical modeling of surface deformations caused by underground mining operation is commonly carried out with use of empirical,numerical or stochastic models.One of the most frequently applied model for prediction of ground deformation in many countries is Knothe model.The model developed by Knothe belongs to the stochastic methods and is based on the influence function.In China a prediction method named Probability Integration Method(PIF)was established by Liu Baochen and Liao Guohua based on the stochastic medium theory.Modified version of that model allows to predict ground movements caused by mining operation in extremely complex technical and geological conditions.That model is commonly applied for coal,metal ore and salt deposits.The article presents several modifications of the mathematical model used in China and Poland.This model is very widespread in the world,therefore the generalizations proposed in the article can be implemented for the purposes of prediction surface deformations for various types of deposits in many countries.The presented generalizations were then tested on specific examples of coal mining,copper ore mining and rock salt deposit.The obtained results indicate high efficiency of methods based on the influence function in complex geological and mining conditions.展开更多
Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along...Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along the radial and circumferential directions,we propose nonlocal integral polar models in this work.The proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular microplates.The governing differential equations and boundary conditions(BCs)as well as constitutive constraints are deduced.It is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are neglected.Meanwhile,the purely strain-and stress-driven nonlocal integral polar models are ill-posed,because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive constraints.Several nominal variables are introduced to simplify the mathematical expression,and the general differential quadrature method(GDQM)is applied to obtain the numerical solutions.The results from the current models(CMs)are compared with the data in the literature.It is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models,respectively.The proposed two-phase local/nonlocal integral polar models(TPNIPMs)may provide an efficient method to design and optimize the plate-like structures for microelectro-mechanical systems.展开更多
In this paper,we propose general strain-and stress-driven two-phase local/nonlocal piezoelectric integral models,which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of n...In this paper,we propose general strain-and stress-driven two-phase local/nonlocal piezoelectric integral models,which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of nanostructures.The nonlocal piezoelectric model is transformed from integral to an equivalent differential form with four constitutive boundary conditions due to the difficulty in solving intergro-differential equations directly.The nonlocal piezoelectric integral models are used to model the static bending of the Euler-Bernoulli piezoelectric beam on the assumption that the nonlocal elastic and piezoelectric parameters are coincident with each other.The governing differential equations as well as constitutive and standard boundary conditions are deduced.It is found that purely strain-and stress-driven nonlocal piezoelectric integral models are ill-posed,because the total number of differential orders for governing equations is less than that of boundary conditions.Meanwhile,the traditional nonlocal piezoelectric differential model would lead to inconsistent bending response for Euler-Bernoulli piezoelectric beam under different boundary and loading conditions.Several nominal variables are introduced to normalize the governing equations and boundary conditions,and the general differential quadrature method(GDQM)is used to obtain the numerical solutions.The results from current models are validated against results in the literature.It is clearly established that a consistent softening and toughening effects can be obtained for static bending of the Euler-Bernoulli beam based on the general strain-and stress-driven local/nonlocal piezoelectric integral models,respectively.展开更多
基金supported by the Project of the 12th Five-year National Sci-Tech Support Plan of China(2011BAK12B09)China Special Project of Basic Work of Science and Technology(2011FY110100-2)
文摘Bailongjiang watershed in southern Gansu province, China, is one of the most landslide-prone regions in China, characterized by very high frequency of landslide occurrence. In order to predict the landslide occurrence, a comprehensive map of landslide susceptibility is required which may be significantly helpful in reducing loss of property and human life. In this study, an integrated model of information value method and logistic regression is proposed by using their merits at maximum and overcoming their weaknesses, which may enhance precision and accuracy of landslide susceptibility assessment. A detailed and reliable landslide inventory with 1587 landslides was prepared and randomly divided into two groups,(i) training dataset and(ii) testing dataset. Eight distinct landslide conditioning factors including lithology, slope gradient, aspect, elevation, distance to drainages,distance to faults, distance to roads and vegetation coverage were selected for landslide susceptibility mapping. The produced landslide susceptibility maps were validated by the success rate and prediction rate curves. The validation results show that the success rate and the prediction rate of the integrated model are 81.7 % and 84.6 %, respectively, which indicate that the proposed integrated method is reliable to produce an accurate landslide susceptibility map and the results may be used for landslides management and mitigation.
基金supported by the National Natural Science Foundation of China (Nos 40974066 and 40821062)National Basic Research Program of China (No 2007CB209602)
文摘General purpose graphic processing unit (GPU) calculation technology is gradually widely used in various fields. Its mode of single instruction, multiple threads is capable of seismic numerical simulation which has a huge quantity of data and calculation steps. In this study, we introduce a GPU-based parallel calculation method of a precise integration method (PIM) for seismic forward modeling. Compared with CPU single-core calculation, GPU parallel calculating perfectly keeps the features of PIM, which has small bandwidth, high accuracy and capability of modeling complex substructures, and GPU calculation brings high computational efficiency, which means that high-performing GPU parallel calculation can make seismic forward modeling closer to real seismic records.
基金Supported by Science and Technology Foundation of SGCC Research and development of key models for decision support of energy internet companies(NO.SGSDJY00GPJS1900057).
文摘In this study,to develop a benefit-allocation model,in-depth analysis of a distributed photovoltaic-powergeneration carport and energy-storage charging-pile project was performed;the model was developed using Shapley integrated-empowerment benefit-distribution method.First,through literature survey and expert interview to identify the risk factors at various stages of the project,a dynamic risk-factor indicator system is developed.Second,to obtain a more meaningful risk-calculation result,the subjective and objective weights are combined,the weights of the risk factors at each stage are determined by the expert scoring method and entropy weight method,and the interest distribution model based on multi-dimensional risk factors is established.Finally,an example is used to verify the rationality of the method for the benefit distribution of the charging-pile project.The results of the example indicate that the limitations of the Shapley method can be reasonably avoided,and the applicability of the model for the benefit distribution of the charging-pile project is verified.
基金Project supported by the National Natural Science Foundation of China(No.12172169)the Natural Sciences and Engineering Research Council of Canada(No.NSERC RGPIN-2023-03227)。
文摘We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.
基金the National Natural Science Foundation of China(Grant Nos.11974173 and 11934008)the HPC Center of Nanjing University。
文摘We proposed a practical way for mapping the results of coarse-grained molecular simulations to the observables in hydrogen change experiments.By combining an atomic-interaction based coarse-grained model with an all-atom structure reconstruction algorithm,we reproduced the experimental hydrogen exchange data with reasonable accuracy using molecular dynamics simulations.We also showed that the coarse-grained model can be further improved by imposing experimental restraints from hydrogen exchange data via an iterative optimization strategy.These results suggest that it is feasible to develop an integrative molecular simulation scheme by incorporating the hydrogen exchange data into the coarse-grained molecular dynamics simulations and therefore help to overcome the accuracy bottleneck of coarse-grained models.
基金Nature Science Foundation of China under Grant no.50179034.
文摘In order to effectively cope with exponent increase of the complexity faced to the rock mechanics analysis problems and the large incompatibility existing between the information level required to model the rock mass and engineering and our obtainable information level at hand,the integrated approaches with intelligent characters are proposed. Many previous standard methods,such as precedent type analysis,rock classification,analytic method stress-based,basic numerical methods (BEM,FEM,DEM,hybrid),and their extended numerical methods (fully coupled) to be developed,can be selected respectively or integrated accordingly. It is alternative to develop basic/fully integrated system,and internet-based approaches. These novel methods can also be selected or integrated each other or with the standard methods to perform rock mechanics analysis. Some key techniques to develop these alternative methods are discussed. It may focus in future on developing fully integrated systems and internet-based approaches. Developing an environmental,virtual facility/space shall be firstly done for this collaborative research on internet.
基金Project supported by the Knowledge Innovation Program of the Chinese Academy of Sciences (No. KZCX2-YW-406-3)the National Key Basic Research Support Foundation (NKBRSF) of China (No. 2005CB121108).
文摘Various calibration methods have been propounded to determine profiles of apparent bulk soil electrical conductivity (ECa) and soil electrical conductivity of a saturated soil paste extract (ECe) or a 1:5 soil water extract (EC1:5) using an electromagnetic induction instrument (EM38). The modeled coefficients, one of the successful and classical methods hitherto, were chosen to calibrate the EM38 measurements of the inverted salinity profiles of characteristic coastal saline soils at selected sites of Xincao Farm, Jiangsu Province, China. However, this method required three parameters for each depth layer. An integration approach, based on an exponential decay profile model, was proposed and the model was fitted to all the calibration sites. The obtained model can then be used to predict EC1:5 at a certain depth from electromagnetic measurements made using the EM38 device positioned in horizontal and vertical positions at the soil surface. This exponential decay model predicted the EC1:5 well according to the results of a one-way analysis of variance, and the further comparison indicated that the modeled coefficients appeared to be slightly superior to, but not statistically different from, this exponential decay model. Nevertheless, this exponential decay model was more significant and practical because it depended on less empirical parameters and could be used to perform point predictions of EC1:5 continuously with depth.
基金The National Science Fund for Distinguished Young Scholars,Grant/Award Number:52325703IEEE Power and Energy Society Working Group on Test Systems for Economic Analysis。
文摘The selection of suitable models and solutions is a fundamental requirement for con-ducting energy flow analysis in integrated energy systems(IES).However,this task is challenging due to the vast number of existing models and solutions,making it difficult to comprehensively compare scholars'studies with current work.In this paper,we aim to address this issue by presenting a comprehensive overview of mainstream IES models and clarifying their relationships,thereby providing guidance for scholars in selecting appro-priate models.Additionally,we introduce several widely used solvers for solving algebraic and differential equations,along with their detailed implementations in the energy flow analysis of IES.Furthermore,we conduct extensive testing and demonstration of these models and methods in various cases to establish benchmarking datasets.To facilitate reproducibility,verification and comparisons,we provide open‐source access to these datasets,including system data,analysis settings and implementations of the various solvers in the mainstream models.Scholars can utilise the provided datasets to reproduce the results,verify the findings and perform comparative analyses.Moreover,they have the flexibility to customise these settings according to their specific requirements.
基金The Specialized Research Fund for the Doctoral Program of Higher Education under contract No.20120041130002the National Key Project of Science and Technology under contract No.2011ZX 05056-001-02the Fundamental Research Funds for the Central Universities under contract No.DUT14ZD220
文摘Submarine landslides can cause severe damage to marine engineering structures. Their sliding velocity and runout distance are two major parameters for quantifying and analyzing the risk of submarine landslides.Currently, commercial calculation programs such as BING have limitations in simulating underwater soil movements. All of these processes can be consistently simulated through a smoothed particle hydrodynamics(SPH) depth integrated model. The basis of the model is a control equation that was developed to take into account the effects of soil consolidation and erosion. In this work, the frictional rheological mode has been used to perform a simulation study of submarine landslides. Time-history curves of the sliding body's velocity, height,and length under various conditions of water depth, slope gradient, contact friction coefficient, and erosion rate are compared; the maximum sliding distance and velocity are calculated; and patterns of variation are discussed.The findings of this study can provide a reference for disaster warnings and pipeline route selection.
文摘In order to process different kinds of observing data with different precisions, a new solution model of nonlinear dynamic integral least squares adjustment was put forward, which is not dependent on their derivatives. The partial derivative of each component in the target function is not computed while iteratively solving the problem. Especially when the nonlinear target function is more complex and very difficult to solve the problem, the method can greatly reduce the computing load.
基金The project was supported by the National Natural Science Faundation of China
文摘In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic problems. The advantage of this class of method is such that the amount of work calculating one integration with parameters becomes that of two interpolations, when the system of nonlinear equations is solved on the right hand side function. The other class of method is the equivalence substitution method for avoiding calculating derivative on the right hand side function. In order to avoid calculation derivatives, two equivalence substitution methods are proposed here. The application instances of some special effect of the equivalence substitution methods are given.
基金This paper is funded by the national key project"The Belt and Road"talent recruitment project named:Comparison of Mining Subsidence Research in China and Poland(No.G2017001).Part of the research was financed from the Grant for Statutory Research AGH-University of Science and Technology in Krakow,Poland No.16.16.150.545.
文摘Mathematical modeling of surface deformations caused by underground mining operation is commonly carried out with use of empirical,numerical or stochastic models.One of the most frequently applied model for prediction of ground deformation in many countries is Knothe model.The model developed by Knothe belongs to the stochastic methods and is based on the influence function.In China a prediction method named Probability Integration Method(PIF)was established by Liu Baochen and Liao Guohua based on the stochastic medium theory.Modified version of that model allows to predict ground movements caused by mining operation in extremely complex technical and geological conditions.That model is commonly applied for coal,metal ore and salt deposits.The article presents several modifications of the mathematical model used in China and Poland.This model is very widespread in the world,therefore the generalizations proposed in the article can be implemented for the purposes of prediction surface deformations for various types of deposits in many countries.The presented generalizations were then tested on specific examples of coal mining,copper ore mining and rock salt deposit.The obtained results indicate high efficiency of methods based on the influence function in complex geological and mining conditions.
基金Project supported by the National Natural Science Foundation of China(No.12172169)the Research Fund of State Key Laboratory of Mechanicsthe Priority Academic Program Development of Jiangsu Higher Education Institutions of China。
文摘Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along the radial and circumferential directions,we propose nonlocal integral polar models in this work.The proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular microplates.The governing differential equations and boundary conditions(BCs)as well as constitutive constraints are deduced.It is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are neglected.Meanwhile,the purely strain-and stress-driven nonlocal integral polar models are ill-posed,because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive constraints.Several nominal variables are introduced to simplify the mathematical expression,and the general differential quadrature method(GDQM)is applied to obtain the numerical solutions.The results from the current models(CMs)are compared with the data in the literature.It is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models,respectively.The proposed two-phase local/nonlocal integral polar models(TPNIPMs)may provide an efficient method to design and optimize the plate-like structures for microelectro-mechanical systems.
基金the National Natural Science Foundation of China(No.12172169)the Scholarship of the China Scholarship Council(No.202106830093)。
文摘In this paper,we propose general strain-and stress-driven two-phase local/nonlocal piezoelectric integral models,which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of nanostructures.The nonlocal piezoelectric model is transformed from integral to an equivalent differential form with four constitutive boundary conditions due to the difficulty in solving intergro-differential equations directly.The nonlocal piezoelectric integral models are used to model the static bending of the Euler-Bernoulli piezoelectric beam on the assumption that the nonlocal elastic and piezoelectric parameters are coincident with each other.The governing differential equations as well as constitutive and standard boundary conditions are deduced.It is found that purely strain-and stress-driven nonlocal piezoelectric integral models are ill-posed,because the total number of differential orders for governing equations is less than that of boundary conditions.Meanwhile,the traditional nonlocal piezoelectric differential model would lead to inconsistent bending response for Euler-Bernoulli piezoelectric beam under different boundary and loading conditions.Several nominal variables are introduced to normalize the governing equations and boundary conditions,and the general differential quadrature method(GDQM)is used to obtain the numerical solutions.The results from current models are validated against results in the literature.It is clearly established that a consistent softening and toughening effects can be obtained for static bending of the Euler-Bernoulli beam based on the general strain-and stress-driven local/nonlocal piezoelectric integral models,respectively.