Study On Dynamic Reliability Of Mechanical Structures Based Upon The Random Field Theory

Research on the life and reliability of mechanical structures and products plays a key role for improving the performance stability and product competitiveness of major equipments.Modern engineering equipments are becoming more and more complicated,there exsits a mass of uncertainties in the mechanical structures and products,especially dynamic or time-dependent uncertainty,such as structures withstanding dynamic loadings which varies with time and the degeneration of material properties versus time.Considering the time-dependent uncertainties for the structural dynamic reliability analysis during the design stage not only to improve the product's reliability and safety but also to effectively promote the defensive design for probable failure rules during the total life cycle.Although the probabilistic engineering design had received wide attention for a long time and static reliability analysis methods have been developed gradually,reliability analysis and reliability based design considering time-dependent uncertainties still existing problems need to be addressed,such as dynamic reliability modeling for complicated problems,high efficient solving methods for dynamic reliability,system reliability computation for dynamic structures,reliability analysis for materials with random field properties.Therefore,the present dissertation will conduct study mainly centering on structural dynamic reliability problem,i.e.the reliability modeling,solution strategy and analysis method,striving for making a series of exploration and attempt on the efficient practical analysis method for dynamic reliability problems in engineering.Research contents are mainly based upon the random field theory and probabilistic reliability,carrying on research of four contents considering time-dependent uncertainties,i.e.probability-interval hybrid dynamic reliability,surrogate modelling-based dynamic reliability,structural system dynamic reliability and dynamic reliability analysis of materials with random field properties.To some extent,this study can solve the dynamic reliability problems of mechanical structures and products,providing guidance and reference significance for reliability based design and security defense of products during total life cycle.In view of this thought,the following studies are carried out in this dissertation:(1)An interval PHI2(I-PHI2)analysis method of dynamic reliability is built.There exists a large number of inherently uncertain parameters in dynamic reliabil ity problem,so the uncertainty modeling and time-dependent reliability analysis have important significance in engineering.When the traditional methods are utilized to evaluate the structural reliability under the stochastic loadings,supposing the distribution parameters of random variables such as strength,stiffness and damping are determined values,however,in most situations the accurate distribution parameters value of random variables and stochastic processes can hardly be known in practical engineering.In this dissertation,an interval PHI2 analysis method for solving the time-dependent reliability is proposed for random uncertain structures with the interval distribution parameters of random variables.Firstly,a dynamic reliability analysis model is built for the uncertain problem,whose distribution parameters of random variable and stochastic processes are consi dered as interval.The Nataf transformation technique is used to standardize the input parameters,i.e.random variables and stochastic processes,in which the correlations between the input variables are also transferred into the standard coordinate space.The distribution parameters of random variables and stochastic processes are determined using the interval analysis method.Secondly,the analytical expression for computing out-crossing rate with interval parameters is derived,and the upper and lower boundaries of out-crossing rate are easily obtained,in this way the influence of computational accuracy of time intervals is avoided.Thirdly,the traditional time-independent reliability analysis tools can be used to solve the dynamic problem,the uppe r and lower boundaries of structural dynamic reliability indices and failure probabilities are obtained.Finally,two numerical examples and one engineering example are presented to verify the effectiveness of the proposed method.(2)A surrogate modelling-based dynamic reliability analysis method is proposed.In the dynamic reliability analysis,due to high computational efficiency of out-crossing rate method,it is always used to evaluate the structural reliability under the time-dependent service conditions.However,when using the out-crossing rate method to compute the crossings,supposing that all the crossing events are independent statistically.The crossings times are assumed to obey Poisson's process or Markov process,thus assumed condition would result in the calculated reliability result to be conservative.Therefore,in order to overcome the problem brought from the assumed conditions of the out-crossing rate method,a surrogate modelling-based dynamic reliability analysis method for the nondeterministic structures is developed in this dissertation,which can solve the dynamic reliability problem with stochastic process avoiding computational process of out-crossing rate.Firstly,a stationary Gaussian stochastic process can be discretized as a serial of random variables through the superior Expansion Optimal Linear Estimation technique.The random variables from the structural parameters as well as the random variables discretized from the stochastic processes are considered as input parameters,the maximum of the uncertain structural responses are considered as output parameters,then a surrogate model can be developed between the input parameters and the output parameters.Secondly,utilizing the Bucher design method to select sample points,and the undetermined coefficients in the response surface model are solved using the linear least squares fitting method.Introducing the gradient projection technique to update the sample points in order to guarantee the accuracy and efficiency of reliability analysis.Thirdly,the dynamic reliability problem with stochastic processes is transferred as static reliability problem,and the first order reliability method or second order reliability method can be used to compute the time-dependent reliabilities and failure prob abilities.Finally,four demonstrative examples are provided for illustrating the accuracy and efficiency of the proposed method in this dissertation.(3)A novel dynamic reliability analysis method for system structures is developed.In practical engineering,there exists many inherent uncertain parameters in system structures,and the traditional structural system reliability analysis methods can only obtain static failure probabilities and reliability indices.However,in general,these system structures have the characteristics of varying with time,thus the traditional method will be difficult to deal with this kind of dynamic problem.Therefore,the present dissertation developed an efficient dynamic reliability analysis method for the system structures with time-dependent uncertain parameters.Firstly,a dynamic system reliability analysis model is proposed for the system structures,which withstanding dynamic loadings conditions and material characteristics decay with time.And event matrices and corresponding probability matrices are generated for the time-dependent system structures,herein the research thought of traditional static matrix based system reliability method is introduced into dynamic system reliability problems.Secondly,perform the initialize processing for the stochastic loadings and degradation model in the input parameters,all the random variables are transferred into standard normal space.An efficient i HL-RF iterative approach is utilized to fast search the most probable failure point(MPP),and linear treatments are performed at the MPP for all the limit state functions at each moment.Thirdly,the PHI2 method is used to solve the limit state function of each component in the dynamic system structures,and the correlation between the system structures is measured through the DS correlation model.Multidimensional integrations for the system structures are calculated based upon the operational rules of the matrices,then the dynamic reliability results of the system structures are obtained.Finally,the dynamic reliability analysis of series system and parallel system are verified using two numerical examples and one engineering application example,which shows eff ectiveness of the proposed method.(4)The material with random field property is studied and corresponding dynamic reliability analysis method is proposed.In the engineering's reliability analysis,most analysis methods address the geometric sizes and material properties of structures as random variables.However,in some situations,material properties obeying the random field distribution exist commonly in practical problems,such as concrete and composite materials are mixed with a variety of m aterials,using random variables to describe the uncertainties would be inappo site.Therefore,in order to solve such problem,more reasonable random field distribution is used to describe them and a dynamic reliability analysis method for random field property is proposed.Firstly,error analysis is performed for the Karhunen-Loève series expansion and expansion optimal linear estimation methods,and the expressions of error variance are obtained.Secondly,these two discretization methods are utilized to simulate the laminated composited plate,and the effects from the discretized numbers and correlation lengths for accuracy are measured.Thirdly,laminated composited plates are manufactured and the hammering method is used to measure their experimental modals,then corresponding finite element models are developed and validated.Finally,a more accurate discretized strategy is chosen to perform the dynamic reliability analysis for laminated composited plate,and the practical of the proposed method is verified.