Stochastic Material Point Method And Reliability Analysis Of Transient Dynamics For Structural System

The study of transient dynamics such as explosion and high-speed impact is an important foundation for military and aerospace science and technology research,which is of great significance to the development of military and aerospace fields.Due to the complexity of the transient dynamics problems such as explosion and high-speed impact,it is difficult to carry out theoretical analysis and experimental research.With the advent of computers and the development of computational mechanics,numerical calculation methods have been highly appreciated by scholars in recent years,becoming an important means to study transient dynamics issues such as explosions and high-speed impacts.However,both the theory and algorithm for the stochastic analysis and reliability analysis of the structure in this field are in the exploration stage.As a result,it is meaningful for both the theoretical research and engineering applications in this domain to propose a kind of numerical method that could efficiently solve the issues of stochastic analysis and reliability analysis in transient dynamics such as explosion and high-speed impact.This paper firstly presents the stochastic material point method(SMPM)based on the original material point method(MPM)in the world,and it is successfully applied to the field of stochastic analysis and reliability analysis of transient dynamics such as explosion and high-speed impact.The specific research content includes the following aspects:(1)Based on the advantages of the material point method for solving physical issues involving large deformation,multi-material coupling and material failure problems,the algorithm implementation process and calculation of material point method in solving transient dynamic problems such as deterministic explosion and high-speed impact are given in detail,and the correctness of the algorithm and program are verified through some specific examples.(2)The stochastic material point method is proposed.The corresponding discrete method of random field in stochastic material point method,the calculation formula of statistical characteristics of response and the solution process are given.At the same time,the influence of grid size on the discrete precision of random field in stochastic material point method under a certain grid size is discussed.(3)Considering the specific parameters as random quantities based on stochastic material point method,the statistical characteristics of the specific response and the explicit expressions of the basic randomness sensitivity are given,forming the algorithm of statistical response for solving the transient problems such as explosion and high-speed impact,and the algorithm of dynamic stochastic response is validated by Monte Carlo numerical simulation.The results show that the stochastic material point method shows good calculation accuracy and calculation efficiency when solving the stochastic response of transient dynamics problems of explosion and impact.(4)The failure criterion of the structure under the action of explosion and high-speed impact load is determined and the performance function of the metal structure under high strain rate is given,building the failure model of the structural system under the action of explosion and high-speed impact load.Eventually,the whole algorithm of stochastic material point method for solving transient dynamic reliability problems is formed and verified by some specific examples.The results show that this method has higher accuracy and efficiency in the reliability analysis of structural systems subjected to explosion and high-speed impact loads.