Static And Dynamic Reliability Of Random Structure Based On Probability Density Evolution Theory

The analysis of the static and dynamic reliability of stochastic structures has always been a hot reseach in the field of engineering structural safety,which has broad prospects for development and important application prospects in the actual projects.As a result of the building structures design reference period is generally 50 years,it is difficult to avoid many severe dynamic loading within the specified design time,such as earthquakes,strong winds,and explosions,the dynamic loads have strong randomness in time,space,and intensity.At the same time,many parameters of the structure itself have a strong randomness.Therefore,the response of the engineering structure under external incentives must have a large fluctuation.At present,the classic structural design and analysis methods can no longer meet the requirements of the development of the engineering structure.In order to further study the dynamic characteristics of engineering structures under the action of disastrous dynamics,it is necessary to comprehensively consider the analysis of response and dynamic reliability of structures with random parameters under random excitation.How to effectively solve this problem will have very important theoretical and practical implications for the safety of the structure.Based on this background,this paper first studies the static and dynamic reliability of stochastic structures under high-dimensional basic random variables,based on the first exceeding the damage criteria and the idea of ??equivalent extremum events,the system reliability of the structure is analyzed,and the system reliability of the structure under different safety margins is given.The content of this study promotes the evolution of probability density theory in engineering applications.The significance of this study provides a reference for the refinement of engineering structural reliability.The main research content is as follows:(1)Firstly,this paper extends the use of probability density evolution method into the reliability analysis of stochastic structure linear response under random static load and the problem of dynamic reliability analysis of nonlinear stochastic structure.A general program of probability density evolution algorithm and classical structure reliability method was compiled under MATLAB platform.Numerical results of several typical explames indicatethat,compared to the classical structural reliability calculation method,this method does not need to consider the complex structure limit state function.And the probability density evolution method can effectively and accurately solve the probability density function and failure probability of random structures under linear and nonlinear responses.It is worth mentioning that,with a certain degree of computational accuracy,the computational time of the probability density evolution method is several decades shorter than that of the Monte Carlo method.(2)The random seismic excitation model of the engineering structure was studied.According to the mathematical decomposition of the random process expression and the random ground motion physical model,a uniform random variable in the random function was used as a basic random variable to represent the original Gaussian process.Generate 328 representative samples set of stationary Gaussian random ground motion processes with probability given by a given power spectral density function,and establish a non-stationary random ground motion model with the time envelope function,and then generate a corresponding MATLAB program to generate randomly oscillates the acceleration time course non-stationary.(3)Under the ANSYS large-scale general-purpose finite element software,Using the APDL language to realize finite element modeling of an 11-story frame-tube structure,and the static analysis and modal analysis of the structure were completed.Gaussian stationary random earthquake processes are generated through trigonal series models.Nonstaionary random earthquake processes can be obtained by multiplying time envelop function with stationary process.A random parameter is used as a random variable to describe the randomness of the seismic excitation,and the randomness of the parameters of the structure itself is also considered.Multiple deterministic analysis of the structure is performed based on the MATLAB program with calling the ANSYS general program.Substituting the structural response into the probability density evolution equation to obtain the evolution of the mean,standard deviation and response probability density of the structural response over time.Finally,Based on the thought equivalent extreme value event,the system reliability of the frame-tube structure under multiple failure mechanisms is considered,and the system reliability values under different safety margins under displacement failure criterion and strength failure criterion are obtained.(4)Finally,the research content of this article is summarized,and some suggestions and directions are given in the future.