Stochastic Analysis Of Semi-rigid Connection Steel Frame Based On Parametric Variational Principle

Considering the nonlinearity of the semi-rigid connection of beams and columns,a new method for static deterministic analysis of steel frames is established based on the parametric variational principle,and the statistical analysis of the uncertainty of the frame system is carried out by using modified stochastic perturbation method.The main contents of this paper are as follows:(1)In order to accurately analyze the influence of nonlinearity of the semi-rigid connection of beam-column joints on the mechanical properties of steel frames.Introduce a parameter that does not participate in the variation and can describe the elastoplastic state of the connection at each semi-rigid node connection;Construct a double fold line reinforced constitutive model in the form of semi-rigid joint parameters;Combine the principle of finite element discrete and minimum potential energy,using the optimization idea in control theory,the nonlinear equations are transformed into standard quadratic programming form,and solved by Lemke algorithm;Establish a new method for deterministic analysis of planar semi-rigid steel frames.(2)Considering the randomness of initial stiffness,load,material,geometric and other parameters of semi-rigid connection,using the sampling and result statistics method of modified stochastic perturbation method,and combined with the calculation method of deterministic problem based on the parametric variational principle,a stochastic statistical algorithm based on modified stochastic perturbation method for planar semi-rigid steel frames is established.(3)The MATLAB program of the algorithm in this paper is written,and the results are as follows:(a)The deterministic algorithm in this paper avoids the hierarchical loading,iterative error and updating the structure of the total rigid matrix when solving the nonlinear problem by the traditional incremental method,and provides an accurate solution for the polyline constitutive problem,which greatly improves the calculation accuracy and efficiency.(b)The modified stochastic perturbation method for uncertainties in this paper avoids the derivation of the stiffness matrix for random variables by traditional stochastic perturbation method,and a small number of samples can guarantee the accuracy of the calculation,and it is suitable for the case of small coefficient of variation,which is more accurate than traditional stochastic perturbation method and Monte Carlo method,and the calculation efficiency is several hundred times that of traditional Monte Carlo method.