Topological Optimization Of Truss And Continuum Structures Under Non-stationary Random Excitation

The engineering structures are inevitably affected by various random loads during the service period such as wind load,earthquake load and so on,and furthermore,these kind of random loads behave obviously non-stationary.Therefore,it is of great value in engineering application to make the research on topological optimization design of structures under non-stationary random loads.In recent years,the explicit time-domain method has demonstrated high efficiency and high accuracy in the non-stationary random vibration analysis of large complex structures,and showed good practicability in the sensitivity analysis.According to the study above,the main content of this dissertation is to derive the explicit time-domain expressions for sensitivity analysis of non-stationary stochastic responses by combining the mode superposition and the Newmark-? method,which is based on the explicit time-domain method of sensitivity analysis.It is shown that the explicit time-domain expressions above cannot ensure the accuracy and computational efficiency in sensitivity analysis because of the uncertainty of selecting modal number,to overcome this defect,the mode acceleration method is introduced to modify the results of sensitivity analysis.Then it is applied to the topology optimization problem of truss structure and continuum structure by effective optimization algorithm.The main research work is as follows:Firstly,the sensitivity equation is converted into mode space,according to the idea of explicit time-domain method in sensitivity analysis,an explicit time-domain expression for sensitivity analysis based on mode superposition method and Newmark-? method is derived.Then the mode acceleration method is introduced to modify the explicit time-domain expression,which can not only significantly improve the computing efficiency but also enhance the computation accuracy.Illustrative numerical examples are presented to show the effectiveness and comparative advantages of the proposed method.Secondly,an optimization model is established,which takes minimizing the volume of truss structure as the objective and the variance of response as the constraint.According to the physical meaning of the coefficient matrix in the proposed method,the process of response and sensitivity analysis is simplified,and the moving asymptotes method of global convergence is adopted to solve the optimization problem.Then numerical examples are given to illustrate the effectiveness and comparative advantages of the proposed method in the shape and topology optimization of truss structures subjected to non-stationary random earthquake.Thirdly,aiming at the problem that there are a large number of design variables,and the objectives and constraints are relatively few,the explicit expression established by adjoint variable method is used for sensitivity analysis,then according to the idea of above explicit expression,sensitivity analysis of structural velocity and acceleration in explicit expression established by adjoint variable method is derived.At the same time,the mode acceleration method is introduced to solve the adjoint equation and the response coefficient matrix,which can further improve the efficiency of the method.Then numerical examples are given to demonstrate the effectiveness and the comparative advantages of the improved method in the topology optimization of 2D continuum structure and 3D continuum structure subjected to non-stationary random excitation.Finally,the major research work is summarized and giving a prospect of the future study.