A Study On Design Optimization Of Structures Subjected To Non-stationary Random Excitation

With the development of computer technology and progress of structural optimization theory,the structural optimization method has been used in more and more engineering fields.As most of random excitations are nonstationary in the practical engineering,the study on design optimization of structures subjected to nonstationary random excitation has attracted increasing attention.Because of the complexity of the non-stationary random vibration analysis,and especially the difficulty in sensitivity analysis,there are still many problems to be solved in the research on optimal design of structures under nonstationary random excitation.In this dissertation,the sensitivity analysis problems of non-stationary random response and dynamic reliability are studied.Then random response and dynamic reliability based design optimization of structures subjected to nonstationary random excitation are further discussed.The main contents are as follows.1.The sensitivity analysis of structural responses under non-stationary random excitations is considered,and an explicit time-domain algorithm based on direct differentiation method(DDM)is proposed.Based on time-domain explicit expressions of dynamic responses,a concise time-domain explicit expression of response sensitivity is derived using DDM.Then a more efficient algorithm for direct calculation of the coefficient matrices in the explicit expression of response sensitivity is derived.Finally,using the two sets of explicit expressions derived for the dynamic response and its sensitivity,an efficient time-domain method is proposed for sensitivity analysis of response variance of a structure under non-stationary random excitations.The numerical results obtained in the study demonstrate the accuracy and efficiency of the presented method.2.The method for sensitivity analysis of structural responses under non-stationary random excitations with a large number of design parameters is studied,and an explicit time-domain algorithm based on adjoint variable method(AVM)is presented.The expressions of the sensitivities of an arbitrary response with respect to different parameters are derived using AVM.Then an efficient algorithm for calculation of the coefficient in the explicit expression is proposed.Finally,an efficient time-domain method is developed for sensitivity analysis of a response variance with respect to different parameters,which dramatically improves the calculation efficiency for sensitivity analysis problem with a large number of structural parameters.3.The consistency problem of AVM for sensitivity analysis of transient dynamic response is studied.The accuracy and convergence rate of the differentiate-then-discretize approach and discretize-then-differentiate approach are investigated.It is found that the consistency problem of the differentiate-then-discretize approach is mainly due to that the transient dynamic solutions do not satisfy the equilibrium equation as assumed in the process of derivation.It is also shown that while this consistency problem may lead to deviation in sensitivity results,the error of time discretization is the primary cause of the derivation,and it has no effect on convergence rate of the method.4.The structural optimization problem considering nonstationary random responses is studied,and an effective algorithm is developed based on the efficient explicit time-domain methods for random responses and their sensitivity analysis.In this study,two optimization models,structural total mass minimization under maximum response variance constraints and maximum response variance minimization under structural mass constraints,are presented to investigate optimization method.The numerical results show the effectiveness and feasibility of proposed method.5.The topology optimization of continuum structure under nonstationary random excitations is studied,and the optimization model of minimizing certain maximum variance response under volume constraint is presented.An effective algorithm is developed based on the SIMP method and the explicit time-domain method for nonstationary random response and its sensitivity analysis.The numerical results show that the topology designs may be different for structure under different nonstationary random excitations.It is also found that the structural stiffness can be improved under given material constraint to control the structural response.6.The structural optimization based on dynamic reliability is studied.An efficient explicit time-domain method of dynamic reliability and its sensitivity analysis is proposed on the basis of the first excursion mechanism and the explicit time-domain method for random response and its sensitivity analysis for structure subject to nonstationary random excitations.Then an effective algorithm is proposed to solve two optimization models,structural total mass minimization under given failure probability constraints and failure probability minimization under structural mass constraints.The numerical results verify the effectiveness of the proposed method.