Multi-objective Reliability Optimization Design Of Structures Based On Stochastic Finite Element Method

The randomness of spatial location is widely existed in engineering structures.These uncertainties have great influence on the safety performance and service state of the structure.Therefore,the structural optimization research based on stochastic finite element analysis has attracted the attention of scholars.In this paper,we discuss the discrete-state numerical method of the random field of Galerkin polynomial,and combine the Kirchhoff-Mindlin plate theory to carry out stochastic finite element dynamic analysis around the lightweight structure of automobile door structure,and then carry out the robustness and reliability optimization design.The main contents of research involve the following three aspects.(1)Discretization of the representation of the random fieldFor the random field in two-dimensional space,the variable is discretized by K-L series method,and the integral characteristic equation of the random field is solved by Gakerkin numerical method of high-order polynomial unit.Under the numerical case of the door structure,the Gaussian random field is studied under different covariance function types,and the error of the mean and standard deviation is compared and analyzed.In addition,the numerical method for dealing with two-dimensional non-Gaussian random fields is introduced,and the non-Gaussian random field under the unknown parameter distribution is better realized.(2)Random dynamic finite element analysis of the doorFirstly,the Kirchhoff-Mindlin plane plate theory is introduced.Secondly,based on the uncertainty factor of the random field,the unit matrix expression of the finite element model of the random field model is derived,and the free vibration mode shape and its displacement frequency response are obtained in the dynamic expression equation.Establishing the parametric modeling of the door geometry model and after mapping meshing,then using the unit position and node coordinates to carry out random dynamic finite element analysis of the complex structure of the door,which including modal frequency,mode shape and the harmonic response analysis of forced vibration,as well as the stress distribution and stiffiness under external load conditions.The mean of the random dynamic response under uncertainty are estimated and provide further guide to the optimal design of the structure.(3)Robust optimization design and reliability optimization designSensitivity analysis is carried out on the material thickness of the door parts,and the important thickness of the board is taken as an optimization design variable.In the process of establishing the multi-objective optimization model for door structure optimization,the Latin Hypercube Design of experiments(DOE),Random Field Discrete(K-L),Response Surface Model(RSM),Optimization Algorithm(SQP&GA)and Monte Carlo simulation(MCS)were used.The difference of design parameters such as material thickness,elastic modulus and density in the structure is introduced into the analysis,and the thickness of each component is optimized from the perspective of deterministic optimization and random optimization,thereby improving the reliability of design variables and the robustness of the objective function.