Long-term responses of floating structures pose a great concern in their design phase. Existing approaches for addressing long-term extreme responses are extremely cumbersome for adoption. This work aims to develop an...Long-term responses of floating structures pose a great concern in their design phase. Existing approaches for addressing long-term extreme responses are extremely cumbersome for adoption. This work aims to develop an approach for the long-term extreme-response analysis of floating structures. A modified gradient-based retrieval algorithm in conjunction with the inverse first-order reliability method(IFORM) is proposed to enable the use of convolution models in long-term extreme analysis of structures with an analytical formula of response amplitude operator(RAO). The proposed algorithm ensures convergence stability and iteration accuracy and exhibits a higher computational efficiency than the traditional backtracking method. However, when the RAO of general offshore structures cannot be analytically expressed, the convolutional integration method fails to function properly. A numerical discretization approach is further proposed for offshore structures in the case when the analytical expression of the RAO is not feasible. Through iterative discretization of environmental contours(ECs) and RAOs, a detailed procedure is proposed to calculate the long-term response extremes of offshore structures. The validity and accuracy of the proposed approach are tested using a floating offshore wind turbine as a numerical example. The long-term extreme heave responses of various return periods are calculated via the IFORM in conjunction with a numerical discretization approach. The environmental data corresponding to N-year structural responses are located inside the ECs, which indicates that the selection of design points directly along the ECs yields conservative design results.展开更多
This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are...This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.展开更多
In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering ...In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method （SFEM） based on the harmonious finite element （HFE） technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.展开更多
To meet the high demand for reliability based design of slopes, we present in this paper a simplified HLRF(Hasofere Linde Rackwitze Fiessler) iterative algorithm for first-order reliability method(FORM). It is simply ...To meet the high demand for reliability based design of slopes, we present in this paper a simplified HLRF(Hasofere Linde Rackwitze Fiessler) iterative algorithm for first-order reliability method(FORM). It is simply formulated in x-space and requires neither transformation of correlated random variables nor optimization tools. The solution can be easily improved by iteratively adjusting the step length. The algorithm is particularly useful to practicing engineers for geotechnical reliability analysis where standalone(deterministic) numerical packages are used. Based on the proposed algorithm and through direct perturbation analysis of random variables, we conducted a case study of earth slope reliability with complete consideration of soil uncertainty and spatial variability.展开更多
The forming limit curve （FLC） can be obtained by means of curve fitting the limit strain points of different strain paths. The theory of percent regression analysis is applied to the curve fitting of forming limit e...The forming limit curve （FLC） can be obtained by means of curve fitting the limit strain points of different strain paths. The theory of percent regression analysis is applied to the curve fitting of forming limit experimental data.Forecast intervals of FLC percentiles can be calculated. Thus reliability and confidence level can be considered. The theoretical method to get the limits of limit strain points distributing region is presented, and the FLC position can be adjusted according to practical requirement. Method for establishing FLC with high reliability using small samples is presented at the same time. This method can make full use of the current experimental data and the previous data.Compared with the traditional method that can only use current experimental data, fewer specimens are required in the present method to obtain the same precision and the result is more accurate with the same number of specimens.展开更多
The first order reliability method (FORM) is widely adopted for structural reliability evaluation due to its numerical efficiency. Concerning the issue of FORM often failing to converge when the limit state function (...The first order reliability method (FORM) is widely adopted for structural reliability evaluation due to its numerical efficiency. Concerning the issue of FORM often failing to converge when the limit state function (LSF) behaves high nonlinearity, a new iteration scheme called "rotated gradient algorithm (RGA)" is proposed and combined with Kriging model to evaluate the reliability of implicit performance function. In this paper, the Kriging model is applied to approximate the real LSF first. Then the scheme of RGA, constructed in terms of gradient information of two adjacent design points obtained during the process of calculation, is used to calculate the reliability index. Numerical examples show the validity in convergence and accuracy of the proposed methodfor arbitrary nonlinear performance function.展开更多
This study presents a new tool for solving stochastic boundary-value problems. This tool is created by modify the previous spectral stochastic meshless local Petrov-Galerkin method using the MLPG5 scheme. This modifie...This study presents a new tool for solving stochastic boundary-value problems. This tool is created by modify the previous spectral stochastic meshless local Petrov-Galerkin method using the MLPG5 scheme. This modified spectral stochastic meshless local Petrov-Galerkin method is selectively applied to predict the structural failure probability with the uncertainty in the spatial variability of mechanical properties. Except for the MLPG5 scheme, deriving the proposed spectral stochastic meshless local Petrov-Galerkin formulation adopts generalized polynomial chaos expansions of random mechanical properties. Predicting the structural failure probability is based on the first-order reliability method. Further comparing the spectral stochastic finite element-based and meshless local Petrov-Galerkin-based predicted structural failure probabilities indicates that the proposed spectral stochastic meshless local Petrov-Galerkin method predicts the more accurate structural failure probability than the spectral stochastic finite element method does. In addition, generating spectral stochastic meshless local Petrov-Galerkin results are considerably time-saving than generating Monte-Carlo simulation results does. In conclusion, the spectral stochastic meshless local Petrov-Galerkin method serves as a time-saving tool for solving stochastic boundary-value problems sufficiently accurately.展开更多
A probabilistic progressive failure analyzing method is applied to estimating the reliability of a simply supported laminated composite plate with an initial imperfection under bi-axial compression load. The initial i...A probabilistic progressive failure analyzing method is applied to estimating the reliability of a simply supported laminated composite plate with an initial imperfection under bi-axial compression load. The initial imperfection and the strength parameters are considered as random variables. Ply-level failure probability is evaluated by the first order reliability method (FORM) together with the Tsai-Wu strength criterion and Tan criterion. Current stresses in the laminated structure are calculated by the classical lamination theory with the stiffness modified based on the last step ply failure. Probabilistically dominant ply-level failure sequences leading to overall system failure are identified, based on which the system failure probability is estimated. A numerical example is presented to demonstrate the methodology proposed. Through parameter studies it is shown that the deviation of the initial imperfection and some of the strength parameters largely influence the system reliability.展开更多
Reliability and optimization are two key elements for structural design. The reliability~ based topology optimization （RBTO） is a powerful and promising methodology for finding the optimum topologies with the uncert...Reliability and optimization are two key elements for structural design. The reliability~ based topology optimization （RBTO） is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topol- ogy optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach （the performance measure approach, PMA） and the decoupled approaches （the so-called Hybrid method and the sequential optimization and reliability assessment, SORA）. For reliability analysis, the stochastic response surface method （SRSM） was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique. The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the de- terministic, RBTOs were compared with one another; and useful conclusions regarding validity, accuracy and efficiency were drawn.展开更多
Buckling-restrained braces （BRBs） have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression b...Buckling-restrained braces （BRBs） have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Although design guidelines for BRB applications have been developed, systematic procedures for assessing performance and quantifying reliability are still needed. This paper presents an analytical framework for assessing buckling-restrained braced frame （BRBF） reliability when subjected to seismic loads. This framework efficiently quantifies the risk of BRB failure due to low-cycle fatigue fracture of the BRB core. The procedure includes a series of components that： （1） quantify BRB demand in terms of BRB core deformation histories generated through stochastic dynamic analyses; （2） quantify the limit-state of a BRB in terms of its remaining cumulative plastic ductility capacity based on an experimental database; and （3） evaluate the probability of BRB failure, given the quantified demand and capacity, through structural reliability analyses. Parametric studies were conducted to investigate the effects of the seismic load, and characteristics of the BRB and BRBF on the probability of brace failure. In addition, fragility curves （i.e., conditional probabilities of brace failure given ground shaking intensity parameters） were created by the proposed framework. While the framework presented in this paper is applied to the assessment of BRBFs, the modular nature of the framework components allows for application to other structural components and systems.展开更多
Caisson breakwaters are mainly constructed in deep waters to protect an area against waves.These breakwaters are con-ventionally designed based on the concept of the safety factor.However,the wave loads and resistance...Caisson breakwaters are mainly constructed in deep waters to protect an area against waves.These breakwaters are con-ventionally designed based on the concept of the safety factor.However,the wave loads and resistance of structures have epistemic or aleatory uncertainties.Furthermore,sliding failure is one of the most important failure modes of caisson breakwaters.In most previous studies,for assessment purposes,uncertainties,such as wave and wave period variation,were ignored.Therefore,in this study,Bayesian reliability analysis is implemented to assess the failure probability of the sliding of Tombak port breakwater in the Persian Gulf.The mean and standard deviations were taken as random variables to consider dismissed uncertainties.For this purpose,the frst-order reliability method(FORM)and the frst principal curvature cor-rection in FORM are used to calculate the reliability index.The performances of these methods are verifed by importance sampling through Monte Carlo simulation(MCS).In addition,the reliability index sensitivities of each random variable are calculated to evaluate the importance of diferent random variables while calculating the caisson sliding.The results show that the reliability index is most sensitive to the coefcients of friction,wave height,and caisson weight(or concrete density).The sensitivity of the failure probability of each of the random variables and their uncertainties are calculated by the derivative method.Finally,the Bayesian regression is implemented to predict the statistical properties of breakwater sliding with non-informative priors,which are compared to Goda’s formulation,used in breakwater design standards.The analysis shows that the model posterior for the sliding of a caisson breakwater has a mean and standard deviation of 0.039 and 0.022,respectively.A normal quantile analysis and residual analysis are also performed to evaluate the correctness of the model responses.展开更多
This paper investigates the reliability of composite laminates with various lay-ups under fatigue loading.The prediction of failure probability of composite laminates subjected to different loads involves many uncerta...This paper investigates the reliability of composite laminates with various lay-ups under fatigue loading.The prediction of failure probability of composite laminates subjected to different loads involves many uncertainties associated with mechanical properties,loading,and boundary conditions.Failure in the composite material is truly hard to trace because there are individual faults in each ply,and we face a stochastic process due to the scatter in the mechanical properties.The continuum damage mechanics(CDM),as a powerful approach,is applied to model the damage of fiber,matrix,and fiber/matrix debonding.This method defines criteria for damage detection and determines safe zones.The material constitutive equations are executed using a subroutine inAbaqus.The first-order reliability method and second-order reliability method have been applied to examine the reliability of laminated composites.The results are compared with those of the Monte Carlo simulation.Different composite laminates under different stress levels are considered for the failure probability investigation.The limit state functions and random variables have been determined based on the CDM model.Finally,the effects of the number of cycles,applied stress,and stacking sequence of the laminate on the reliability and fatigue life in fiber-reinforced laminated composites are assessed.展开更多
Parametric uncertainties should always be considered when setting design criteria in order to ensure safe and cost effective design of engineered structures. This paper presents the results of the reliability assessme...Parametric uncertainties should always be considered when setting design criteria in order to ensure safe and cost effective design of engineered structures. This paper presents the results of the reliability assessment of a fully laterally restrained steel floor I-beam to Eurocode 3 design rules. The failure modes considered are bending, shear and deflection. These were solved to obtain reliability indices using first order reliability method coded in MATLAB environment. Parametric sensitivity analyses were carried out at varying values of the design parameters to show their relative contributions to the safety of the beam. It was seen that reliability indices generally decreased with an increase in load ratio, imposed load, beam span in bending, shear stress and deflection respectively. In addition, increasing the beam span beyond 10 m, load ratio above 1.4 and imposed load beyond 30 kN/m made the beam fail as these parameters gave negative reliability indices. For failure in deflection, reliability index rose with an increase in the radius of gyration and overall depth of the beam section accordingly. Furthermore, the reliability index surged as the thickness of the web increased when taking into account, shear failure. The results of the analysis showed that the steel beam is very safe in shear and at some load ratios and imposed loads for failure in bending and deflection respectively. The average values of reliability indices obtained for load ratios ranging from 1.0 to 1.4 fell from 3.017 to 3.457 for all failure mode studied. These values are within the recommended reliability indices by the Joint Committee on Structural Safety for structure with moderate failure consequences and beams in flexure.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos.52088102 and 51879287)National Key Research and Development Program of China (Grant No.2022YFB2602301)。
文摘Long-term responses of floating structures pose a great concern in their design phase. Existing approaches for addressing long-term extreme responses are extremely cumbersome for adoption. This work aims to develop an approach for the long-term extreme-response analysis of floating structures. A modified gradient-based retrieval algorithm in conjunction with the inverse first-order reliability method(IFORM) is proposed to enable the use of convolution models in long-term extreme analysis of structures with an analytical formula of response amplitude operator(RAO). The proposed algorithm ensures convergence stability and iteration accuracy and exhibits a higher computational efficiency than the traditional backtracking method. However, when the RAO of general offshore structures cannot be analytically expressed, the convolutional integration method fails to function properly. A numerical discretization approach is further proposed for offshore structures in the case when the analytical expression of the RAO is not feasible. Through iterative discretization of environmental contours(ECs) and RAOs, a detailed procedure is proposed to calculate the long-term response extremes of offshore structures. The validity and accuracy of the proposed approach are tested using a floating offshore wind turbine as a numerical example. The long-term extreme heave responses of various return periods are calculated via the IFORM in conjunction with a numerical discretization approach. The environmental data corresponding to N-year structural responses are located inside the ECs, which indicates that the selection of design points directly along the ECs yields conservative design results.
基金supported by the National Natural Science Foundation of China(Grant Nos.52109144,52025094 and 52222905).
文摘This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.
基金supported by the National Natural Science Foundation of China(Grant No.50379046)the Doctoral Fund of the Ministry of Education of China(Grant No.A50221)
文摘In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method （SFEM） based on the harmonious finite element （HFE） technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.
基金Financial supports from National Science Foundation of China(Grant Nos.51609072,51879091,51479050 and 41630638)the National Key Basic Research Program of China("973" Program)(Grant No.2015CB057901)the Public Service Sector R&D Project of Ministry of Water Resource of China(Grant No.201501035-03)
文摘To meet the high demand for reliability based design of slopes, we present in this paper a simplified HLRF(Hasofere Linde Rackwitze Fiessler) iterative algorithm for first-order reliability method(FORM). It is simply formulated in x-space and requires neither transformation of correlated random variables nor optimization tools. The solution can be easily improved by iteratively adjusting the step length. The algorithm is particularly useful to practicing engineers for geotechnical reliability analysis where standalone(deterministic) numerical packages are used. Based on the proposed algorithm and through direct perturbation analysis of random variables, we conducted a case study of earth slope reliability with complete consideration of soil uncertainty and spatial variability.
文摘The forming limit curve （FLC） can be obtained by means of curve fitting the limit strain points of different strain paths. The theory of percent regression analysis is applied to the curve fitting of forming limit experimental data.Forecast intervals of FLC percentiles can be calculated. Thus reliability and confidence level can be considered. The theoretical method to get the limits of limit strain points distributing region is presented, and the FLC position can be adjusted according to practical requirement. Method for establishing FLC with high reliability using small samples is presented at the same time. This method can make full use of the current experimental data and the previous data.Compared with the traditional method that can only use current experimental data, fewer specimens are required in the present method to obtain the same precision and the result is more accurate with the same number of specimens.
文摘The first order reliability method (FORM) is widely adopted for structural reliability evaluation due to its numerical efficiency. Concerning the issue of FORM often failing to converge when the limit state function (LSF) behaves high nonlinearity, a new iteration scheme called "rotated gradient algorithm (RGA)" is proposed and combined with Kriging model to evaluate the reliability of implicit performance function. In this paper, the Kriging model is applied to approximate the real LSF first. Then the scheme of RGA, constructed in terms of gradient information of two adjacent design points obtained during the process of calculation, is used to calculate the reliability index. Numerical examples show the validity in convergence and accuracy of the proposed methodfor arbitrary nonlinear performance function.
文摘This study presents a new tool for solving stochastic boundary-value problems. This tool is created by modify the previous spectral stochastic meshless local Petrov-Galerkin method using the MLPG5 scheme. This modified spectral stochastic meshless local Petrov-Galerkin method is selectively applied to predict the structural failure probability with the uncertainty in the spatial variability of mechanical properties. Except for the MLPG5 scheme, deriving the proposed spectral stochastic meshless local Petrov-Galerkin formulation adopts generalized polynomial chaos expansions of random mechanical properties. Predicting the structural failure probability is based on the first-order reliability method. Further comparing the spectral stochastic finite element-based and meshless local Petrov-Galerkin-based predicted structural failure probabilities indicates that the proposed spectral stochastic meshless local Petrov-Galerkin method predicts the more accurate structural failure probability than the spectral stochastic finite element method does. In addition, generating spectral stochastic meshless local Petrov-Galerkin results are considerably time-saving than generating Monte-Carlo simulation results does. In conclusion, the spectral stochastic meshless local Petrov-Galerkin method serves as a time-saving tool for solving stochastic boundary-value problems sufficiently accurately.
基金the Scientific Research Foundation for Returned Overseas Chinese Scholars,State Education Ministrythe Research Foundation of Huazhong University of Science and Technology
文摘A probabilistic progressive failure analyzing method is applied to estimating the reliability of a simply supported laminated composite plate with an initial imperfection under bi-axial compression load. The initial imperfection and the strength parameters are considered as random variables. Ply-level failure probability is evaluated by the first order reliability method (FORM) together with the Tsai-Wu strength criterion and Tan criterion. Current stresses in the laminated structure are calculated by the classical lamination theory with the stiffness modified based on the last step ply failure. Probabilistically dominant ply-level failure sequences leading to overall system failure are identified, based on which the system failure probability is estimated. A numerical example is presented to demonstrate the methodology proposed. Through parameter studies it is shown that the deviation of the initial imperfection and some of the strength parameters largely influence the system reliability.
基金Project supported by the National Natural Science Foundation of China(Nos.51275040 and 50905017)the Programme of Introducing Talents of Discipline to Universities(No.B12022)
文摘Reliability and optimization are two key elements for structural design. The reliability~ based topology optimization （RBTO） is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topol- ogy optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach （the performance measure approach, PMA） and the decoupled approaches （the so-called Hybrid method and the sequential optimization and reliability assessment, SORA）. For reliability analysis, the stochastic response surface method （SRSM） was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique. The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the de- terministic, RBTOs were compared with one another; and useful conclusions regarding validity, accuracy and efficiency were drawn.
基金Federal Highway Administration Under Grant No. DDEGRD-06-X-00408
文摘Buckling-restrained braces （BRBs） have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Although design guidelines for BRB applications have been developed, systematic procedures for assessing performance and quantifying reliability are still needed. This paper presents an analytical framework for assessing buckling-restrained braced frame （BRBF） reliability when subjected to seismic loads. This framework efficiently quantifies the risk of BRB failure due to low-cycle fatigue fracture of the BRB core. The procedure includes a series of components that： （1） quantify BRB demand in terms of BRB core deformation histories generated through stochastic dynamic analyses; （2） quantify the limit-state of a BRB in terms of its remaining cumulative plastic ductility capacity based on an experimental database; and （3） evaluate the probability of BRB failure, given the quantified demand and capacity, through structural reliability analyses. Parametric studies were conducted to investigate the effects of the seismic load, and characteristics of the BRB and BRBF on the probability of brace failure. In addition, fragility curves （i.e., conditional probabilities of brace failure given ground shaking intensity parameters） were created by the proposed framework. While the framework presented in this paper is applied to the assessment of BRBFs, the modular nature of the framework components allows for application to other structural components and systems.
文摘Caisson breakwaters are mainly constructed in deep waters to protect an area against waves.These breakwaters are con-ventionally designed based on the concept of the safety factor.However,the wave loads and resistance of structures have epistemic or aleatory uncertainties.Furthermore,sliding failure is one of the most important failure modes of caisson breakwaters.In most previous studies,for assessment purposes,uncertainties,such as wave and wave period variation,were ignored.Therefore,in this study,Bayesian reliability analysis is implemented to assess the failure probability of the sliding of Tombak port breakwater in the Persian Gulf.The mean and standard deviations were taken as random variables to consider dismissed uncertainties.For this purpose,the frst-order reliability method(FORM)and the frst principal curvature cor-rection in FORM are used to calculate the reliability index.The performances of these methods are verifed by importance sampling through Monte Carlo simulation(MCS).In addition,the reliability index sensitivities of each random variable are calculated to evaluate the importance of diferent random variables while calculating the caisson sliding.The results show that the reliability index is most sensitive to the coefcients of friction,wave height,and caisson weight(or concrete density).The sensitivity of the failure probability of each of the random variables and their uncertainties are calculated by the derivative method.Finally,the Bayesian regression is implemented to predict the statistical properties of breakwater sliding with non-informative priors,which are compared to Goda’s formulation,used in breakwater design standards.The analysis shows that the model posterior for the sliding of a caisson breakwater has a mean and standard deviation of 0.039 and 0.022,respectively.A normal quantile analysis and residual analysis are also performed to evaluate the correctness of the model responses.
文摘This paper investigates the reliability of composite laminates with various lay-ups under fatigue loading.The prediction of failure probability of composite laminates subjected to different loads involves many uncertainties associated with mechanical properties,loading,and boundary conditions.Failure in the composite material is truly hard to trace because there are individual faults in each ply,and we face a stochastic process due to the scatter in the mechanical properties.The continuum damage mechanics(CDM),as a powerful approach,is applied to model the damage of fiber,matrix,and fiber/matrix debonding.This method defines criteria for damage detection and determines safe zones.The material constitutive equations are executed using a subroutine inAbaqus.The first-order reliability method and second-order reliability method have been applied to examine the reliability of laminated composites.The results are compared with those of the Monte Carlo simulation.Different composite laminates under different stress levels are considered for the failure probability investigation.The limit state functions and random variables have been determined based on the CDM model.Finally,the effects of the number of cycles,applied stress,and stacking sequence of the laminate on the reliability and fatigue life in fiber-reinforced laminated composites are assessed.
文摘Parametric uncertainties should always be considered when setting design criteria in order to ensure safe and cost effective design of engineered structures. This paper presents the results of the reliability assessment of a fully laterally restrained steel floor I-beam to Eurocode 3 design rules. The failure modes considered are bending, shear and deflection. These were solved to obtain reliability indices using first order reliability method coded in MATLAB environment. Parametric sensitivity analyses were carried out at varying values of the design parameters to show their relative contributions to the safety of the beam. It was seen that reliability indices generally decreased with an increase in load ratio, imposed load, beam span in bending, shear stress and deflection respectively. In addition, increasing the beam span beyond 10 m, load ratio above 1.4 and imposed load beyond 30 kN/m made the beam fail as these parameters gave negative reliability indices. For failure in deflection, reliability index rose with an increase in the radius of gyration and overall depth of the beam section accordingly. Furthermore, the reliability index surged as the thickness of the web increased when taking into account, shear failure. The results of the analysis showed that the steel beam is very safe in shear and at some load ratios and imposed loads for failure in bending and deflection respectively. The average values of reliability indices obtained for load ratios ranging from 1.0 to 1.4 fell from 3.017 to 3.457 for all failure mode studied. These values are within the recommended reliability indices by the Joint Committee on Structural Safety for structure with moderate failure consequences and beams in flexure.
