We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensiti...We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensities.To account for these variations,we utilized a Monte Carlo Simulation(MCS)technique coupled with the finite difference code FLAC^(3D),to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system(GSIs)and subjected to different states of static loading.To quantify the severity of damage within the rock mass,we selected one stress-based(brittle shear ratio(BSR))and one strain-based failure criterion(plastic damage index(PDI)).Based on these criteria,we then developed fragility curves.Additionally,we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass.The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel.Therefore,we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state.Our method is a numerically developed,multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels.展开更多
de Casteljau算法可以递推地定义一条具有限个控制顶点的Bzier曲线,在此基础上文中提出了基于de Casteljau算法的Poisson细分曲线逼近算法,Poisson曲线完全具备了Bzier曲线的重要性质,并且比Bzier曲线有更广泛的应用范围。最后还...de Casteljau算法可以递推地定义一条具有限个控制顶点的Bzier曲线,在此基础上文中提出了基于de Casteljau算法的Poisson细分曲线逼近算法,Poisson曲线完全具备了Bzier曲线的重要性质,并且比Bzier曲线有更广泛的应用范围。最后还给出了n阶Poisson曲线的细分。展开更多
To realize the high precision and real-time interpolation of the NURBS （non-uniform rational B-spline） curve, a kinetic model based on the modified sigmoid function is proposed. The constraints of maximum feed rate,...To realize the high precision and real-time interpolation of the NURBS （non-uniform rational B-spline） curve, a kinetic model based on the modified sigmoid function is proposed. The constraints of maximum feed rate, chord error, curvature radius and interpolator cycle are discussed. This kinetic model reduces the cubic polynomial S-shape model and the trigonometry function S-shape model from 15 sections into 3 sections under the precondition of jerk, acceleration and feedrate continuity. Then an optimized Adams algorithm using the difference quotient to replace the derivative is presented to calculate the interpolator cycle parameters. The higher-order derivation in the Taylor expansion algorithm can be avoided by this algorithm. Finally, the simplified design is analyzed by reducing the times of computing the low-degree zero-value B-spline basis function and the simplified De Boor-Cox recursive algorithm is proposed. The simulation analysis indicates that by these algorithms, the feed rate is effectively controlled according to tool path. The calculated amount is decreased and the calculated speed is increased while the machining precision is ensured. The experimental results show that the target parameter can be correctly calculated and these algorithms can be applied to actual systems.展开更多
A technique of shape modification and deformation for parametric curvesthrough cosine extension function (CEF) is presented. First, a special extension function isdefined, based on which a shape operator matrix is con...A technique of shape modification and deformation for parametric curvesthrough cosine extension function (CEF) is presented. First, a special extension function isdefined, based on which a shape operator matrix is constructed. Then combining such matrix with thecenter of extension and principal directions, two kinds of deformation matrices are defined.Finally, curve deformation is achieved through multiplying its position vector in a local coordinatesystem by deformation matrix or adding the multiplication of a vector field and quasi-deformationmatrix to its position vector in the original coordinate system. Since CEF contains several variableparameters, each of which generates a different effect of shape modification such as controllingthe degree of continuity of the modified part of curve with the unchanged part, ideal deformationeffects can be got fairly and easily. Examples of theoretical analysis show that the method ispotentially useful for geometric modeling, computer graphics and so on.展开更多
This article studies the existence of analytic invariant curves for a nonlinear second order difference equation which was modeled from macroeconomics of the business cycle. The author not only discusses the case of t...This article studies the existence of analytic invariant curves for a nonlinear second order difference equation which was modeled from macroeconomics of the business cycle. The author not only discusses the case of the eigenvalue off the unit circle S^1 and the case on S^1 with the Diophantine condition but also considers the case of the eigenvalue at a root of the unity, which obviously violates the Diophantine condition.展开更多
The relationship between trace elements in coal and organic functional groups of coal, also some of aromatic structure, was investigated by using curve fitting of infrared spectra. Cluster analysis was also performed ...The relationship between trace elements in coal and organic functional groups of coal, also some of aromatic structure, was investigated by using curve fitting of infrared spectra. Cluster analysis was also performed according to the degree of affinity of organic groups to the trace elements. The results show that there is a possibility that trace elements, especially LREE, were bound to peripheral organic functional groups of middle rank coal macromolecule. The most possible functional group that binds trace element is the hydroxyl, and to the less degree, the asymmetric -CH3 and 〉CH2 stretching, -CH3 stretching, etc. The degree of affinity of trace elements to different functional groups varies. The tendency obeys the natural structural changing law of trace elements-- the periodic law. The deviation of some trace elements from this regular trend is attributed to the deviation of intrinsic ＂confusion degree＂ （conventional molar entropy） of the matter system of coal basin, which is affected by the inner and outer factors during the evolution.展开更多
Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and repr...Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.展开更多
AIM:To generate phasic and tonic stress-strain curves for evaluation of intestinal smooth muscle function in type 2 diabetic rats during active and passive conditions.METHODS:Seven diabetic Goto-Kakizaki(GK)male rats,...AIM:To generate phasic and tonic stress-strain curves for evaluation of intestinal smooth muscle function in type 2 diabetic rats during active and passive conditions.METHODS:Seven diabetic Goto-Kakizaki(GK)male rats,32-wk old(GK group),and 9 age-matched normal Wistar rats(Normal group)were included in the study.Jejunal segments were distended up to a pressure of10 cm H2O in an organ bath containing 37℃Krebs solution with addition of carbachol(CA).The pressure and outer diameter changes were synchronously recorded.Passive conditions were obtained using calcium-free Krebs solution containing ethylene glycol tetraacetic acid and papaverine.Total phasic,tonic and passive circumferential stress and strain were computed from the diameter and pressure data with reference to the zero-stress state geometry.The active phasic and tonic stresses were defined as the total phasic and tonic stresses minus the passive stress.RESULTS:Diabetes increased jejunal mucosa and muscle layer thicknesses compared to the Normal group(mucosa,755.8±63.3 vs 633.1±59.1μm,P<0.01;muscle,106.3±12.9 vs 85.2±11.7μm,P<0.05).The pressure and stress thresholds were decreased in the GK group after CA application compared to distensions without CA application(pressure,1.01±0.07vs 1.99±0.19 cmH2O,P<0.01;stress,0.11±0.01vs 0.24±0.02 kPa,P<0.01).CA application did not change the pressure and stress threshold in the Normal group(pressure,2.13±0.32 vs 2.34±0.32 cm H2O,P>0.05;stress,0.25±0.03 vs 0.35±0.06 kPa,P>0.05).The amplitude of total phasic,total tonic,active phasic and active tonic circumferential stresses did not differ for the distensions without CA application between the GK group and the Normal group.However,the total phasic and total tonic stresses increased after CA application in the GK group compared those in the Normal group.When normalized to muscle layer thickness,the amplitude of active stresses before CA application was lowest in the GK group compared with the Normal group.No difference was found during CA application.CONCLUSION:The stress generated by intestinal muscle normalized to the muscle layer thickness was lowest in GK rats compared to normal rats whereas the response to CA stimulation was preserved.展开更多
This paper presents a procedure to develop fragility curves of structures equipped with TMD considering multiple failure functions.The failure criteria considered are maximum inter-story drift ratio as a safety criter...This paper presents a procedure to develop fragility curves of structures equipped with TMD considering multiple failure functions.The failure criteria considered are maximum inter-story drift ratio as a safety criterion,maximum absolute acceleration as a convenience criterion and TMD stroke length.The relationship between intensity measure and responses of the structure was assumed to follow the power-law model,and a regression analysis was used to estimate its properties.A nonlinear eight-story shear building subjected to near-fault earthquakes was used for the numerical studies.Fragility curves using multiple and single failure functions for an uncontrolled structure and a structure equipped with optimal TMDs were developed.Numerical analysis showed that using multiple failure functions led to increasing the fragility when compared with using the single failure function for both the uncontrolled and controlled structures.However,TMDs slightly reduced the seismic fragility and have the capability to improve the reliability of the structure.Also,it was found that the fragility was significantly influenced by the values of the capacity thresholds of both the acceleration of the structure and TMD stroke length,which should be selected by considering the target performance and application of the structure and control device.展开更多
In this paper we propose a construction method of the planar cubic algebraic splinecurve with endpoint interpolation conditions and a specific analysis of its properties. Thepiecewise cubic algebraic curve has G2 cont...In this paper we propose a construction method of the planar cubic algebraic splinecurve with endpoint interpolation conditions and a specific analysis of its properties. Thepiecewise cubic algebraic curve has G2 continuous contact with the control polygon at twoendpoints and is G2 continuous between each segments of itself. The process of this method issimple and clear, and provides a new way of thinking to design implicit curves.展开更多
基金funding received by a grant from the Natural Sciences and Engineering Research Council of Canada(NSERC)(Grant No.CRDPJ 469057e14).
文摘We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensities.To account for these variations,we utilized a Monte Carlo Simulation(MCS)technique coupled with the finite difference code FLAC^(3D),to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system(GSIs)and subjected to different states of static loading.To quantify the severity of damage within the rock mass,we selected one stress-based(brittle shear ratio(BSR))and one strain-based failure criterion(plastic damage index(PDI)).Based on these criteria,we then developed fragility curves.Additionally,we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass.The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel.Therefore,we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state.Our method is a numerically developed,multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels.
基金The Doctoral Fund of Ministry of Education of China(No.20090092110052)the Natural Science Foundation of Higher Education Institutions of Jiangsu Province(No.12KJA460002)College Industrialization Project of Jiangsu Province(No.JHB2012-21)
文摘To realize the high precision and real-time interpolation of the NURBS （non-uniform rational B-spline） curve, a kinetic model based on the modified sigmoid function is proposed. The constraints of maximum feed rate, chord error, curvature radius and interpolator cycle are discussed. This kinetic model reduces the cubic polynomial S-shape model and the trigonometry function S-shape model from 15 sections into 3 sections under the precondition of jerk, acceleration and feedrate continuity. Then an optimized Adams algorithm using the difference quotient to replace the derivative is presented to calculate the interpolator cycle parameters. The higher-order derivation in the Taylor expansion algorithm can be avoided by this algorithm. Finally, the simplified design is analyzed by reducing the times of computing the low-degree zero-value B-spline basis function and the simplified De Boor-Cox recursive algorithm is proposed. The simulation analysis indicates that by these algorithms, the feed rate is effectively controlled according to tool path. The calculated amount is decreased and the calculated speed is increased while the machining precision is ensured. The experimental results show that the target parameter can be correctly calculated and these algorithms can be applied to actual systems.
文摘A technique of shape modification and deformation for parametric curvesthrough cosine extension function (CEF) is presented. First, a special extension function isdefined, based on which a shape operator matrix is constructed. Then combining such matrix with thecenter of extension and principal directions, two kinds of deformation matrices are defined.Finally, curve deformation is achieved through multiplying its position vector in a local coordinatesystem by deformation matrix or adding the multiplication of a vector field and quasi-deformationmatrix to its position vector in the original coordinate system. Since CEF contains several variableparameters, each of which generates a different effect of shape modification such as controllingthe degree of continuity of the modified part of curve with the unchanged part, ideal deformationeffects can be got fairly and easily. Examples of theoretical analysis show that the method ispotentially useful for geometric modeling, computer graphics and so on.
基金supported by the Fund of Educational Reform Project of Guangxi Province of China (200710961)the Scientific Research Foundation of the Education Department of Guangxi Province of China (200707MS112)+1 种基金the Natural Science Fund of Hechi University (2006N001)the fund of Key discipline of applied mathematics of Hechi University (200725)
文摘This article studies the existence of analytic invariant curves for a nonlinear second order difference equation which was modeled from macroeconomics of the business cycle. The author not only discusses the case of the eigenvalue off the unit circle S^1 and the case on S^1 with the Diophantine condition but also considers the case of the eigenvalue at a root of the unity, which obviously violates the Diophantine condition.
基金supported by the National Science Foundation of China(Nos.41172143 and 40872101)Developmental Plan of Basic Research on Natural Science of Shanxi Province(20012JM5005)Science Research Plan of Shanxi education department(12JK0483)
文摘The relationship between trace elements in coal and organic functional groups of coal, also some of aromatic structure, was investigated by using curve fitting of infrared spectra. Cluster analysis was also performed according to the degree of affinity of organic groups to the trace elements. The results show that there is a possibility that trace elements, especially LREE, were bound to peripheral organic functional groups of middle rank coal macromolecule. The most possible functional group that binds trace element is the hydroxyl, and to the less degree, the asymmetric -CH3 and 〉CH2 stretching, -CH3 stretching, etc. The degree of affinity of trace elements to different functional groups varies. The tendency obeys the natural structural changing law of trace elements-- the periodic law. The deviation of some trace elements from this regular trend is attributed to the deviation of intrinsic ＂confusion degree＂ （conventional molar entropy） of the matter system of coal basin, which is affected by the inner and outer factors during the evolution.
文摘Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.
文摘AIM:To generate phasic and tonic stress-strain curves for evaluation of intestinal smooth muscle function in type 2 diabetic rats during active and passive conditions.METHODS:Seven diabetic Goto-Kakizaki(GK)male rats,32-wk old(GK group),and 9 age-matched normal Wistar rats(Normal group)were included in the study.Jejunal segments were distended up to a pressure of10 cm H2O in an organ bath containing 37℃Krebs solution with addition of carbachol(CA).The pressure and outer diameter changes were synchronously recorded.Passive conditions were obtained using calcium-free Krebs solution containing ethylene glycol tetraacetic acid and papaverine.Total phasic,tonic and passive circumferential stress and strain were computed from the diameter and pressure data with reference to the zero-stress state geometry.The active phasic and tonic stresses were defined as the total phasic and tonic stresses minus the passive stress.RESULTS:Diabetes increased jejunal mucosa and muscle layer thicknesses compared to the Normal group(mucosa,755.8±63.3 vs 633.1±59.1μm,P<0.01;muscle,106.3±12.9 vs 85.2±11.7μm,P<0.05).The pressure and stress thresholds were decreased in the GK group after CA application compared to distensions without CA application(pressure,1.01±0.07vs 1.99±0.19 cmH2O,P<0.01;stress,0.11±0.01vs 0.24±0.02 kPa,P<0.01).CA application did not change the pressure and stress threshold in the Normal group(pressure,2.13±0.32 vs 2.34±0.32 cm H2O,P>0.05;stress,0.25±0.03 vs 0.35±0.06 kPa,P>0.05).The amplitude of total phasic,total tonic,active phasic and active tonic circumferential stresses did not differ for the distensions without CA application between the GK group and the Normal group.However,the total phasic and total tonic stresses increased after CA application in the GK group compared those in the Normal group.When normalized to muscle layer thickness,the amplitude of active stresses before CA application was lowest in the GK group compared with the Normal group.No difference was found during CA application.CONCLUSION:The stress generated by intestinal muscle normalized to the muscle layer thickness was lowest in GK rats compared to normal rats whereas the response to CA stimulation was preserved.
文摘This paper presents a procedure to develop fragility curves of structures equipped with TMD considering multiple failure functions.The failure criteria considered are maximum inter-story drift ratio as a safety criterion,maximum absolute acceleration as a convenience criterion and TMD stroke length.The relationship between intensity measure and responses of the structure was assumed to follow the power-law model,and a regression analysis was used to estimate its properties.A nonlinear eight-story shear building subjected to near-fault earthquakes was used for the numerical studies.Fragility curves using multiple and single failure functions for an uncontrolled structure and a structure equipped with optimal TMDs were developed.Numerical analysis showed that using multiple failure functions led to increasing the fragility when compared with using the single failure function for both the uncontrolled and controlled structures.However,TMDs slightly reduced the seismic fragility and have the capability to improve the reliability of the structure.Also,it was found that the fragility was significantly influenced by the values of the capacity thresholds of both the acceleration of the structure and TMD stroke length,which should be selected by considering the target performance and application of the structure and control device.
基金Supported by the National Key Basic Research Project of China (No. 2004CB318000)the NSF of China(No. 60533060/60872095)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education (No.20060358055)the Subject Foundation in Ningbo University(No. xkl09046)
文摘In this paper we propose a construction method of the planar cubic algebraic splinecurve with endpoint interpolation conditions and a specific analysis of its properties. Thepiecewise cubic algebraic curve has G2 continuous contact with the control polygon at twoendpoints and is G2 continuous between each segments of itself. The process of this method issimple and clear, and provides a new way of thinking to design implicit curves.
