| Considering the influence of factors such as the environment,manufacturing errors,and the correlation between some parameters of mechanical structures,there will be certain uncertainties and correlations between important parameters such as material parameters and geometric parameters.In recent years,the research on the uncertainty,reliability and correlation of mechanical structures has become more and more common,and many effective random,reliability and correlation methods have appeared.However,it is not enough in terms of the method itself and the issue of comparative certainty.The combination of existing new finite element algorithms and stochastic methods,which can be applied and improved in some problems,and research on new uncertain methods need to be further studied,which is also of great significance.Therefore,this paper combines the corresponding finite element numerical algorithm and uncertainty algorithm to further investigate the problems of uncertainty,reliability and correlation commonly encountered in practical engineering applications.The specific research work is summarized as follows:(1)A stochastic stable node integration method is proposed to solve the uncertain thermo-mechanical problem.By combining stable node-based smoothed finite element method(SNS-FEM)and fourth-order moment method,a random analysis is performed on the response temperature of the uncertain steady-state heat transfer process and the resulting thermal displacement and thermal stress.This method can be used to deal with more complicated three-dimensional problems.Compared with the traditional stochastic analysis method,the proposed method has high efficiency,high precision and better stability.At the same time,the random statistical characteristics of the observed response values are more complete.(2)The Aiming at the observed value of thermal stress,several mathematical models are proposed,and a more detailed reliability analysis of thermal stress is carried out based on the model and the principle of probability statistics.Different from the general reliability analysis,the reliability analysis based on the proposed mathematical model considers the influence of different materials(plasticity and brittleness),the model’s own error,the positive and negative thermal stress values,and application fields of each model are explained.In addition,taking the thermo-mechanical problem as the research object,comparing with Monte Carlo simulation(MCS)method,the accuracy of each model in the specific problem and the influence of different random parameters on the reliability analysis results are discussed.(3)A stochastic analysis method for quickly solving correlation problems is developed.This method combines Copula function,perturbation technology and MCS method,and has the characteristics of high efficiency and high precision compared with the existing correlation research.In addition,when obtaining the probability density function(PDF)of the output,the method does not involve statistical analysis of probability,and it is simpler and easier for more complex correlation problems.In this paper,the correlation analysis of the fiber-reinforced composite plate problem which can obtain the output target expression is performed,and the effectiveness of the method is proved.When the target expression of the output cannot be obtained,the intermediate expression as close as possible to the target expression is adopted here.By performing free vibration random analysis on the isotropic single-layer plate and the transverse isotropic composite plate,it is confirmed this method has the characteristics of high efficiency,high precision,and also suitable for random problems without considering correlation. |
