Topology Optimization Of Continuous Structures Under Non-stationary Random Seismic Excitations

With the rapid development of urbanization,building structures with complex forms and diverse functions have gradually become the trend of development.During the use of building structures,they will be subjected to dynamic loads such as earthquake load and wind load,which are random and non-stationary.Therefore,the topology optimization of structures under non-stationary stochastic dynamics has practical application value.In recent years,the time-domain display method can solve the stochastic dynamic response and its sensitivity of large complex structures quickly and accurately,and the display expressions of response and sensitivity are given,which makes the stochastic dynamic problem simple and efficient.Therefore,the topological optimization of dynamic response is introduced to establish a topological optimization model,and the related problems of topological optimization of continuous structures under non-stationary random seismic loads are studied through reasonable optimization algorithms.The specific research contents are as follows:Firstly,the topological optimization of continuum structures under non-stationary random earthquakes has been studied.Based on the solution idea of time-domain display method,the display expression of structural dynamic response and its variance under random seismic load is derived by combining with the mode acceleration method and Newmark-? method.The display expression of sensitivity under the maximum displacement variance is solved by the time domain display adjoint method.Then two kinds of topology optimization models are established by using PIS material interpolation function.The one is the optimization model which is established with the maximum displacement variance of the degree of freedom as the objective and the volume of the structural material as the constraint.Another is the optimization model which is established with the volume of the structural material as the objective and the maximum displacement variance of the degree of freedom as the constraint.The GCMMA algorithm and numerical filtering technology are used to solve the optimization model.The feasibility and correctness of the optimization method are proved by numerical examples,and the necessity of topological optimization under non-stationary random earthquake is expounded,and the influence of different seismic parameters on topological optimization is given.Secondly,the topological optimization of continuous structures under non-stationary random seismic loads with multi-objective dynamic response has been studied.The optimization models which minimize the weight of the maximum displacement variance and static displacement of the degree of freedom of the structure and the weight and acceleration variance of the maximum displacement variance and acceleration variance of the degree of freedom of the structure are established respectively.Based on the idea of adjoint method,the display expressions of static displacement sensitivity and maximum acceleration variance sensitivity are derived.The feasibility and correctness of the optimization method are proved by an example analysis,and the trend of the topological shape and the optimization objective value of the topological optimization results under different weight coefficients is given.Finally,the topological optimization of three-phase materials under non-stationary random earthquakes has been studied.The three-phase material structure optimization model is established,which takes the maximum displacement variance of the degree of freedom of the structure as the objective function and the volume of the structure material as the constraint.The rules of topology optimization of three-phase material structures under non-stationary random seismic loads are studied by numerical example analysis.The effects of two kinds of solid materials on topology optimization under different volume constraints and the combinations of different materials on the results of topology optimization are compared.