Structural Stochastic Analysis Based On Monophyletic Random Vector

Stochastic structural models are more reasonable than determinate structural models.Studying the influence of stochastic factors can make designers and builders better grasp the key points in design and construction.However,there are so many stochastic factors in engineering.With the increase of random variables in the model,the difficulty of structural modeling and calculating analysis will increase significantly.some scholars solve the problem of hundreds of stochastic factors by the way of orthogonal expansion,which only needs 10-20 variables.In this paper,we continue to optimize this problem,that is,to express multiple random variables with one random variable.Monophyletic random vector is characterized by easy design and convenient application.It is of great significance to reduce the difficulty of stochastic analysis by using the monophyletic random vector which only need one basic random variables to simulate stochastic system.By using the monophyletic random vector to simulate system,the influence of parameter variation on the system performance can be understood intuitively,which is convenient for sensitivity analysis and optimization design.For the stochastic system based on correlation theory,such as stochastic structure,random field,stochastic process and composite stochastic problems,this method has potential application value.Three orthogonal expansion of stochastic processes based on the monophyletic random vector,the stochastic process of non stationary earthquake is simulated,and the power spectrum is compared.Based on the monophyletic random vector,the stochastic structure is expressed.The finite element method based on the monophyletic random vector is proposed,and the numerical example is analyzed and compared with the Monte-Carlo method.Based on the monophyletic random vector,the static elastic analysis of the structure is carried out,the static equilibrium equation is established,and the equilibrium equation of the random finite element of the multi order expansion is derived,and the expansion and iterative solution of the static equation is proposed.The reliability of the method is demonstrated by the comparison of the example.Based on the monophyletic random vector and considering the earthquake uncertainty and the randomness of structure,start from the perspective of the total probability,an anti-collapse performance evaluation method for RC frame structures is proposed.In the paper,a structure example is subjected to an incremental dynamic analysis by using MSC.Marc,based on MATLAB introduces parallel computing to improve efficiency,using lognormal fitting fragility curves of structure,obtains the indicators of structural performance.