The aim of this study is to evaluate the uncertainty of 2πα and 2πβ surface emission rates using the windowless multiwire proportional counter method.This study used the Monte Carlo method (MCM) to validate the co...The aim of this study is to evaluate the uncertainty of 2πα and 2πβ surface emission rates using the windowless multiwire proportional counter method.This study used the Monte Carlo method (MCM) to validate the conventional Guide to the Expression of Uncertainty in Measurement (GUM) method.A dead time measurement model for the two-source method was established based on the characteristics of a single-channel measurement system,and the voltage threshold correction factor measurement function was indirectly obtained by fitting the threshold correction curve.The uncertainty in the surface emission rate was calculated using the GUM method and the law of propagation of uncertainty.The MCM provided clear definitions for each input quantity and its uncertainty distribution,and the simulation training was realized with a complete and complex mathematical model.The results of the surface emission rate uncertainty evaluation for four radioactive plane sources using both methods showed the uncertainty’s consistency E_(n)<0.070 for the comparison of each source,and the uncertainty results of the GUM were all lower than those of the MCM.However,the MCM has a more objective evaluation process and can serve as a validation tool for GUM results.展开更多
The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy.At low temperatures,theoretical predictio...The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy.At low temperatures,theoretical predictions[Phys.Rev.A 72053604(2005)]and[arXiv:0706.1609]indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering.However,due to ergodic difficulties faced by Monte Carlo methods at low temperatures,this topological phase has not been numerically explored.We propose a linear cluster updating Monte Carlo method,which flips spins without rejection in the anisotropy limit but does not change the energy.Using this scheme and conventional Monte Carlo methods,we succeed in revealing the nature of topological phases with half-vortices and domain walls.In the constructed global phase diagram,Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier.We also propose and explore a wide range of quantities,including magnetism,superfluidity,specific heat,susceptibility,and even percolation susceptibility,and obtain consistent and reliable results.Furthermore,we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes,as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections.The critical exponents of different types of phase transitions are reasonably fitted.The results are useful to help cold atom experiments explore the half-vortex topological phase.展开更多
In public health,simulation modeling stands as an invaluable asset,enabling the evaluation of new systems without their physical implementation,experimentation with existing systems without operational adjustments,and...In public health,simulation modeling stands as an invaluable asset,enabling the evaluation of new systems without their physical implementation,experimentation with existing systems without operational adjustments,and testing system limits without real-world repercussions.In simulation modeling,the Monte Carlo method emerges as a powerful yet underutilized tool.Although the Monte Carlo method has not yet gained widespread prominence in healthcare,its technological capabilities hold promise for substantial cost reduction and risk mitigation.In this review article,we aimed to explore the transformative potential of the Monte Carlo method in healthcare contexts.We underscore the significance of experiential insights derived from simulated experimentation,especially in resource-constrained scenarios where time,financial constraints,and limited resources necessitate innovative and efficient approaches.As public health faces increasing challenges,incorporating the Monte Carlo method presents an opportunity for enhanced system construction,analysis,and evaluation.展开更多
An approach for generating test problems by a computer using the Monte Carlo method based upon user-given characterizations is described.A single point X~* is prespocified by the user to be a solution of the test prob...An approach for generating test problems by a computer using the Monte Carlo method based upon user-given characterizations is described.A single point X~* is prespocified by the user to be a solution of the test problems.The approach is flex- ible enough to specify function values,gradients,Hesse,degeneracy degree and ill- conditioned degree at the point X~*.Other numerical features such as indefiniteness, convexity are also under user's control.展开更多
After the trajectory simulation model of rudder control rocket with six degrees of freedom is established by Matlab/ Simulink, the simulated targeting of rudder control rocket with rudder angle error and starting cont...After the trajectory simulation model of rudder control rocket with six degrees of freedom is established by Matlab/ Simulink, the simulated targeting of rudder control rocket with rudder angle error and starting control moment error is carried out respectively by means of Monte Carlo method and the distribution of impact points of rudder control rocket is counted from all the successful subsamples. In the case of adding interference errors associated with rudder angle error and starting time error, the simulation analysis of impact point dispersion is done and its lateral and longitudinal correction abilities at different targeting angles are simulated to identify the effects of these factors on characteristics and control precision of the rudder control rocket, which provides the relevant reference for high-precision design of rudder control system.展开更多
Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random error...Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.展开更多
The conduct mechanism of the doped polymer is considered. In an asymmetrysystem composed of high polymer and doping conductive matte, chain or congeries framework will beformed between the conductive particles to impr...The conduct mechanism of the doped polymer is considered. In an asymmetrysystem composed of high polymer and doping conductive matte, chain or congeries framework will beformed between the conductive particles to improve the conductance characteristic. In thisprocession, the conductive particles interact to each other. In this paper, we describe theconductance of the doped polymer by Monte Carlo method. The results accord with the experimentsquite well. It can be concluded that there is an evident change of doped polymer from nonconductorto metal.展开更多
Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the resul...Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on ＂The Guide to the Expression of Uncertainty in Measurement（GUM）＂. In order to compute spatial straightness error（SSE） accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization（QPSO） is proposed to solve the minimum zone SSE and Monte Carlo Method（MCM） is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function（PDF） for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine（CMM） is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.展开更多
A two-dimensional （2D） full band self-consistent ensemble Monte Carlo （MC） method for solving the quantum Boltzmann equation, including collision broadening and quantum potential corrections, is developed to exten...A two-dimensional （2D） full band self-consistent ensemble Monte Carlo （MC） method for solving the quantum Boltzmann equation, including collision broadening and quantum potential corrections, is developed to extend the MC method to the study of nano-scale semiconductor devices with obvious quantum mechanical （QM） effects. The quantum effects both in real space and momentum space in nano-scale semiconductor devices can be simulated. The effective mobility in the inversion layer of n and p channel MOSFET is simulated and compared with experimental data to verify this method. With this method 50nm ultra thin body silicon on insulator MOSFET are simulated. Results indicate that this method can be used to simulate the 2D QM effects in semiconductor devices including tunnelling effect.展开更多
It can be difficult to calculate some under-sampled regions in global Monte Carlo radiation transport calculations. The global variance reduction(GVR) method is a useful solution to the problem of variance reduction e...It can be difficult to calculate some under-sampled regions in global Monte Carlo radiation transport calculations. The global variance reduction(GVR) method is a useful solution to the problem of variance reduction everywhere in a phase space. In this research, a GVR procedure was developed and applied to the Chinese Fusion Engineering Testing Reactor(CFETR). A cylindrical CFETR model was utilized for comparing various implementations of the GVR method to find the optimum.It was found that the flux-based GVR method could ensure more reliable statistical results, achieving an efficiency being 7.43 times that of the analog case. A mesh tally of the scalar neutron flux was chosen for the GVR method to simulate global neutron transport in the CFETR model.Particles distributed uniformly in the system were sampled adequately through ten iterations of GVR weight window.All voxels were scored, and the average relative error was 2.4% in the ultimate step of the GVR iteration.展开更多
In loosely coupled or large-scale problems with high dominance ratios,slow fission source convergence can take extremely long time,reducing Monte Carlo(MC)criticality calculation efficiency.Although various accelerati...In loosely coupled or large-scale problems with high dominance ratios,slow fission source convergence can take extremely long time,reducing Monte Carlo(MC)criticality calculation efficiency.Although various acceleration methods have been developed,some methods cannot reduce convergence times,whereas others have been limited to specific problem geometries.In this study,a new fission source convergence acceleration(FSCA)method,the forced propagation(FP)method,has been proposed,which forces the fission source to propagate and accelerate fission source convergence.Additionally,some stabilization techniques have been designed to render the method more practical.The resulting stabilized method was then successfully implemented in the MC transport code,and its feasibility and effectiveness were tested using the modified OECD/NEA,one-dimensional slab benchmark,and the Hoogenboom full-core problem.The comparison results showed that the FP method was able to achieve efficient FSCA.展开更多
One of the most critical and complicated steps in mine design is a selection of suitable mining method based upon geological,geotechnical,geographical,safety and economical parameters.The aim of this study is developi...One of the most critical and complicated steps in mine design is a selection of suitable mining method based upon geological,geotechnical,geographical,safety and economical parameters.The aim of this study is developing a Monte Carlo simulation to selection the optimum mining method by using effective and major criteria and at the same time,taking subjective judgments of decision makers into consideration.Proposed approach is based on the combination of Monte Carlo simulation with conventional Analytic Hierarchy Process(AHP).Monte Carlo simulation is used to determine the confdence level of each alternative’s score,is calculated by AHP,with the respect to the variance of decision makers’opinion.The proposed method is applied for Jajarm Bauxite Mine in Iran and eventually the most appropriate mining methods for this mine are ranked.展开更多
This paper presents a novel framework for stochastic analysis of linear elastic fracture problems.Monte Carlo simulation(MCs)is adopted to address the multi-dimensional uncertainties,whose computation cost is reduced ...This paper presents a novel framework for stochastic analysis of linear elastic fracture problems.Monte Carlo simulation(MCs)is adopted to address the multi-dimensional uncertainties,whose computation cost is reduced by combination of Proper Orthogonal Decomposition(POD)and the Radial Basis Function(RBF).In order to avoid re-meshing and retain the geometric exactness,isogeometric boundary element method(IGABEM)is employed for simulation,in which the Non-Uniform Rational B-splines(NURBS)are employed for representing the crack surfaces and discretizing dual boundary integral equations.The stress intensity factors(SIFs)are extracted by M integral method.The numerical examples simulate several cracked structures with various uncertain parameters such as load effects,materials,geometric dimensions,and the results are verified by comparison with the analytical solutions.展开更多
文摘The aim of this study is to evaluate the uncertainty of 2πα and 2πβ surface emission rates using the windowless multiwire proportional counter method.This study used the Monte Carlo method (MCM) to validate the conventional Guide to the Expression of Uncertainty in Measurement (GUM) method.A dead time measurement model for the two-source method was established based on the characteristics of a single-channel measurement system,and the voltage threshold correction factor measurement function was indirectly obtained by fitting the threshold correction curve.The uncertainty in the surface emission rate was calculated using the GUM method and the law of propagation of uncertainty.The MCM provided clear definitions for each input quantity and its uncertainty distribution,and the simulation training was realized with a complete and complex mathematical model.The results of the surface emission rate uncertainty evaluation for four radioactive plane sources using both methods showed the uncertainty’s consistency E_(n)<0.070 for the comparison of each source,and the uncertainty results of the GUM were all lower than those of the MCM.However,the MCM has a more objective evaluation process and can serve as a validation tool for GUM results.
基金Project supported by the Hefei National Research Center for Physical Sciences at the Microscale (Grant No.KF2021002)the Natural Science Foundation of Shanxi Province,China (Grant Nos.202303021221029 and 202103021224051)+2 种基金the National Natural Science Foundation of China (Grant Nos.11975024,12047503,and 12275263)the Anhui Provincial Supporting Program for Excellent Young Talents in Colleges and Universities (Grant No.gxyq ZD2019023)the National Key Research and Development Program of China (Grant No.2018YFA0306501)。
文摘The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy.At low temperatures,theoretical predictions[Phys.Rev.A 72053604(2005)]and[arXiv:0706.1609]indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering.However,due to ergodic difficulties faced by Monte Carlo methods at low temperatures,this topological phase has not been numerically explored.We propose a linear cluster updating Monte Carlo method,which flips spins without rejection in the anisotropy limit but does not change the energy.Using this scheme and conventional Monte Carlo methods,we succeed in revealing the nature of topological phases with half-vortices and domain walls.In the constructed global phase diagram,Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier.We also propose and explore a wide range of quantities,including magnetism,superfluidity,specific heat,susceptibility,and even percolation susceptibility,and obtain consistent and reliable results.Furthermore,we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes,as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections.The critical exponents of different types of phase transitions are reasonably fitted.The results are useful to help cold atom experiments explore the half-vortex topological phase.
基金Supported by the European Union-NextGenerationEU,through the National Recovery and Resilience Plan of the Republic of Bulgaria,No.BG-RRP-2.004-0008.
文摘In public health,simulation modeling stands as an invaluable asset,enabling the evaluation of new systems without their physical implementation,experimentation with existing systems without operational adjustments,and testing system limits without real-world repercussions.In simulation modeling,the Monte Carlo method emerges as a powerful yet underutilized tool.Although the Monte Carlo method has not yet gained widespread prominence in healthcare,its technological capabilities hold promise for substantial cost reduction and risk mitigation.In this review article,we aimed to explore the transformative potential of the Monte Carlo method in healthcare contexts.We underscore the significance of experiential insights derived from simulated experimentation,especially in resource-constrained scenarios where time,financial constraints,and limited resources necessitate innovative and efficient approaches.As public health faces increasing challenges,incorporating the Monte Carlo method presents an opportunity for enhanced system construction,analysis,and evaluation.
文摘An approach for generating test problems by a computer using the Monte Carlo method based upon user-given characterizations is described.A single point X~* is prespocified by the user to be a solution of the test problems.The approach is flex- ible enough to specify function values,gradients,Hesse,degeneracy degree and ill- conditioned degree at the point X~*.Other numerical features such as indefiniteness, convexity are also under user's control.
文摘After the trajectory simulation model of rudder control rocket with six degrees of freedom is established by Matlab/ Simulink, the simulated targeting of rudder control rocket with rudder angle error and starting control moment error is carried out respectively by means of Monte Carlo method and the distribution of impact points of rudder control rocket is counted from all the successful subsamples. In the case of adding interference errors associated with rudder angle error and starting time error, the simulation analysis of impact point dispersion is done and its lateral and longitudinal correction abilities at different targeting angles are simulated to identify the effects of these factors on characteristics and control precision of the rudder control rocket, which provides the relevant reference for high-precision design of rudder control system.
基金Supported by National Natural Science Foundation of China(Grant No.51375013)Anhui Provincial Natural Science Foundation of China(Grant No.1208085ME64)
文摘Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.
文摘The conduct mechanism of the doped polymer is considered. In an asymmetrysystem composed of high polymer and doping conductive matte, chain or congeries framework will beformed between the conductive particles to improve the conductance characteristic. In thisprocession, the conductive particles interact to each other. In this paper, we describe theconductance of the doped polymer by Monte Carlo method. The results accord with the experimentsquite well. It can be concluded that there is an evident change of doped polymer from nonconductorto metal.
基金supported by National Natural Science Foundation of China (Grant No. 51075198)Jiangsu Provincial Natural Science Foundation of China (Grant No. BK2010479)+2 种基金Innovation Research of Nanjing Institute of Technology, China (Grant No. CKJ20100008)Jiangsu Provincial Foundation of 333 Talents Engineering of ChinaJiangsu Provincial Foundation of Six Talented Peak of China
文摘Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on ＂The Guide to the Expression of Uncertainty in Measurement（GUM）＂. In order to compute spatial straightness error（SSE） accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization（QPSO） is proposed to solve the minimum zone SSE and Monte Carlo Method（MCM） is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function（PDF） for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine（CMM） is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.
基金Project supported by the Special Foundation for State Major Basic Research Program of China （Grant No G2000035602） and the National Natural Science Foundation of China （Grant No 90307006）.
文摘A two-dimensional （2D） full band self-consistent ensemble Monte Carlo （MC） method for solving the quantum Boltzmann equation, including collision broadening and quantum potential corrections, is developed to extend the MC method to the study of nano-scale semiconductor devices with obvious quantum mechanical （QM） effects. The quantum effects both in real space and momentum space in nano-scale semiconductor devices can be simulated. The effective mobility in the inversion layer of n and p channel MOSFET is simulated and compared with experimental data to verify this method. With this method 50nm ultra thin body silicon on insulator MOSFET are simulated. Results indicate that this method can be used to simulate the 2D QM effects in semiconductor devices including tunnelling effect.
基金supported by the National Special Project for Magnetic Confined Nuclear Fusion Energy(Nos.2013GB108004 and2015GB108002)the Chinese National Natural Science Foundation(No.11175207)
文摘It can be difficult to calculate some under-sampled regions in global Monte Carlo radiation transport calculations. The global variance reduction(GVR) method is a useful solution to the problem of variance reduction everywhere in a phase space. In this research, a GVR procedure was developed and applied to the Chinese Fusion Engineering Testing Reactor(CFETR). A cylindrical CFETR model was utilized for comparing various implementations of the GVR method to find the optimum.It was found that the flux-based GVR method could ensure more reliable statistical results, achieving an efficiency being 7.43 times that of the analog case. A mesh tally of the scalar neutron flux was chosen for the GVR method to simulate global neutron transport in the CFETR model.Particles distributed uniformly in the system were sampled adequately through ten iterations of GVR weight window.All voxels were scored, and the average relative error was 2.4% in the ultimate step of the GVR iteration.
基金supported by the National Natural Science Foundation of China(Nos.11775126,11545013,11605101)the Young Elite Scientists Sponsorship Program by CAST(No.2016QNRC001)+1 种基金Science Challenge Project by MIIT of China(No.TZ2018001)Tsinghua University,Initiative Scientific Research Program。
文摘In loosely coupled or large-scale problems with high dominance ratios,slow fission source convergence can take extremely long time,reducing Monte Carlo(MC)criticality calculation efficiency.Although various acceleration methods have been developed,some methods cannot reduce convergence times,whereas others have been limited to specific problem geometries.In this study,a new fission source convergence acceleration(FSCA)method,the forced propagation(FP)method,has been proposed,which forces the fission source to propagate and accelerate fission source convergence.Additionally,some stabilization techniques have been designed to render the method more practical.The resulting stabilized method was then successfully implemented in the MC transport code,and its feasibility and effectiveness were tested using the modified OECD/NEA,one-dimensional slab benchmark,and the Hoogenboom full-core problem.The comparison results showed that the FP method was able to achieve efficient FSCA.
文摘One of the most critical and complicated steps in mine design is a selection of suitable mining method based upon geological,geotechnical,geographical,safety and economical parameters.The aim of this study is developing a Monte Carlo simulation to selection the optimum mining method by using effective and major criteria and at the same time,taking subjective judgments of decision makers into consideration.Proposed approach is based on the combination of Monte Carlo simulation with conventional Analytic Hierarchy Process(AHP).Monte Carlo simulation is used to determine the confdence level of each alternative’s score,is calculated by AHP,with the respect to the variance of decision makers’opinion.The proposed method is applied for Jajarm Bauxite Mine in Iran and eventually the most appropriate mining methods for this mine are ranked.
基金The authors thank the financial support of National Natural Science Foundation of China(NSFC)under Grant(Nos.51904202,11902212,11901578).
文摘This paper presents a novel framework for stochastic analysis of linear elastic fracture problems.Monte Carlo simulation(MCs)is adopted to address the multi-dimensional uncertainties,whose computation cost is reduced by combination of Proper Orthogonal Decomposition(POD)and the Radial Basis Function(RBF).In order to avoid re-meshing and retain the geometric exactness,isogeometric boundary element method(IGABEM)is employed for simulation,in which the Non-Uniform Rational B-splines(NURBS)are employed for representing the crack surfaces and discretizing dual boundary integral equations.The stress intensity factors(SIFs)are extracted by M integral method.The numerical examples simulate several cracked structures with various uncertain parameters such as load effects,materials,geometric dimensions,and the results are verified by comparison with the analytical solutions.
