Research On Key Issues In Topology Optimization Of Dynamic Structures

Nowadays,topology optimization of dynamic structures is a challenging research topic.It demonstrates great values in engineering applications covering high-end equipment,aeronautical and aerospace structure designs.However,there exist several key difficulties and obstacles that hinder the development and application of topology optimization in engineering practice of dynamic structure designs.To circumvent these difficulties,the main contributions are as follows.(1)Establishment of topology optimization method for large-scale problems with the objective function related to harmonic responses.Although different topology optimization methods based on the mode displacement method(MDM)were applied to solve the optimization problems related to harmonic responses,structures were mostly limited to a small number of DOFs in the previous work.In this work,it is found that the truncation modes of the MDM as well as the localized modes related to the material interpolation model are intrinsic reasons causing the low accuracy of harmonic responses and the non-convergent results.Therefore,the MDM is replaced with the mode acceleration method(MAM)and full method(FM)of high accuracy in the optimization procedure.It is shown that accuracies of dynamic response analysis and sensitivity analysis are greatly improved with the help of MAM and FM.Theoretical studies and numerical examples reveal that large-scale problems can efficiently be dealt with based on the MAM and FM.Further discussions are also made about the convergence difficulty of topology optimization when the harmonic excitation frequency is larger than the resonance frequency of the initial structure.A solution strategy is proposed to define the objective function over a specific frequency range.(2)Establishment of topology optimization method related to rotating load.Rotating load caused by the centrifugal force of mass unbalance in rotating machinery is a kind of typical dynamic excitation in engineering practice.It widely exists in aircrafts and mechanical equipment.In fact,the rotating load can theoretically be decomposed into two harmonic excitations in two orthogonal directions with phase difference.Due to the presence of phase difference,topology optimization is more complicated than in the common case of harmonic excitations in phase.As the structural response is time-dependent,two topology optimization formulations are thus established to minimize the dynamic compliance and the maximum displacement amplitude of the loaded node over a period,respectively.Validities and effects of the proposed optimization formulations are illustrated and compared through typical numerical tests.It is found that both formulations have the ability to reduce the structure vibration caused by the rotating load.(3)Establishment of structural topology optimization method for large-scale problems with the objective function related to dynamic responses under stationary random force excitation.The commonly used Complete Quadratic Combination method(CQC)is not only computationally expensive but also results in non-convergent design pattern due to the low computing accuracy of random responses for large-scale problems.To circumvent these difficulties,an efficient and accurate optimization procedure integrating the Pseudo Excitation Method(PEM)and MAM is introduced into the topology optimization.In this framework,random responses are calculated using the PEM to ascertain a high efficiency over the CQC.More importantly,the accuracy of random responses is improved indirectly by solving the pseudo harmonic responses involved in the PEM with the help of the MAM.Numerical examples fully demonstrate the validity of the developed optimization procedure for large-scale problems.(4)The integrated optimization design of supporting structure topology and the packed components layout involving the dynamic response.Static performances were usually considered in the previous integrated optimization problems while the dynamic responses are hardly taken into account.Therefore,the integrated optimization models considering harmonic responses and random responses are established to design the supporting structure topology and component location simultaneously.The finite circle method(FCM),density points technique and mesh embedding technique are adopted to model the whole system.The integrated optimization models proposed here can meet the requirements of engineering practice.Their validities and advantages are demonstrated by numerical examples.