Geometric Nonlinear Analysis Of Stochastic Truss Structure Based On Hybrid Perturbation-Galerkin Method

In actual engineering,randomness exists in structure,such as material characteristics,element size,structure boundary,load,etc.,which will have more or less influence on geometric nonlinear static response analysis.Domestic and foreign scholars have studied the geometric nonlinear static response of parametric uncertain structures,and proposed a variety of stochastic finite element methods,such as Perturbation stochastic finite element method,Spectral stochastic finite element method,Stochastic reduced basis finite element method,The element free Galerkin method,etc.The random finite element method based on perturbation is an important method to solve the geometric nonlinearity of random structures.However,when the variability of random parameters of structures increases,the computational accuracy of random responses obtained by low-order perturbation or even higher-order perturbation will decrease.In order to improve the convergence range and precision of the perturbation method,the hybrid perturbation galerkin method is extended to solve the static response of geometrically nonlinear random structures.The details are as follows:1.Introduced the recursive perturbation finite element method.Assuming that the elastic modulus of the structure is assumed to be a random field,it is discretized using a non-orthogonal polynomial chaotic expansion.The displacement response of the nonlinear random structure and the nonlinear part of the Green strain associated with the displacement are all expanded by a power polynomial with undetermined coefficients,and the static equilibrium equation with random variables is derived.According to the stochastic static equilibrium equation,the coefficient of the same order term on both sides should be zero,and a series of recursive equations are established to solve the undetermined coefficients.The explicit expression of the nonlinear stochastic structure is obtained.Comparing the results of the first four orders of the recursive perturbation method with the Monte Carlo method,the accuracy and effectiveness of the recursive perturbation method are illustrated.2.The hybrid perturbation-Galley gold method is introduced.Based on the perturbation method to solve the power polynomial of the random structure displacement response,the Galerkin test function is constructed.Through the Galerkin projection technique,the trial function coefficients are solved to obtain an explicit expression of the random structure displacement response.3.The hybrid perturbation-Galley method is applied to solve the response of geometric nonlinear stochastic bar structure.The secant elastic modulus and the random response of the displacement term are expressed as power polynomial expansion,and the coefficients of the power polynomial expansion of the geometric nonlinear response of the random structure are determined by the recursive perturbation method.The perturbation terms of the random response are assumed to be Galerkin test functions,and the Galerkin projection is used to solve the trial function coefficients,so as to obtain the explicit expression of the geometric nonlinear response of the random bar structure.The numerical results show that the statistical moments of the structural response calculated by the hybrid perturbation-Galley gold method are closer to those obtained by the high-order perturbation method in the process of increasing the coefficient of variation of random variables.Monte Carlo simulation results.