Study On Topology Optimization Method Of Harmonic Response And Its Application In Forward Design

In traditional design,dynamic stiffness,fatigue strength and other vibration response performance are generally used as the check index in the later stage of design.In fact,after the basic form of the structure is determined,its performance can be improved within a very limited space.Especially when lightweight aluminum alloy parts with lower elastic modulus and yield strength are used for lightweight design,its vibration response performance is generally improved at the cost of increasing the part’s weight in the later design stage,and it does not necessarily have a good improvement effect.Therefore,in the early stage of forward design,besides considering the static performance requirements,it is necessary to consider the vibration response performance requirements for the topology optimization design,which lays a good foundation for the improvement of the vibration response performance and lightweight effect in the later stage.In this paper,the topology optimization of simple harmonic vibration response is studied,focusing on the accuracy,efficiency and unreasonable results of topology optimization under high frequency harmonic excitation.At the same time,the multi-objective topology optimization method is studied,and the topology optimization method of harmonic response is applied to the development of aluminum alloy subframe based on the existing forward design process.(1)Focusing on the accuracy and efficiency of topology optimization method of harmonic response,the efficiency and accuracy of two different harmonic response analysis methods,i.e.modal acceleration method and modal displacement method,are compared.The modal acceleration method is selected to analyze the response of optimization problem.Based on the SIMP material interpolation method and gradient optimization algorithm in Optistruct,topology optimization design of harmonic response of simple structures is carried out,and compared with indirect optimization schemes aiming at maximizing modal frequency or static stiffness,highlighting the advantages of this optimization technology.(2)Focusing on the causes of unreasonable topology optimization results with poor stiffness under high-frequency harmonic excitation,based on existing research,an improved method,which takes volume fraction and amplitude of low frequency vibration displacement response as constraints and minimizing amplitude of high frequency vibration displacement response as objectives,is proposed and used to solve topology optimization problem under harmonic excitation with wide frequency range.It lays a foundation for the forward design considering the higher frequency vibration response performance requirement.(3)Multi-objective topology optimization is carried out based on compromise programming method,and the influence of sub-objective weights on the optimization results is studied.After that,a weighting method composed of analytic hierarchy process and variation coefficient method is used to calculate sub-objective weights instead of empirical weighting method,and converted to an automatic weighting program based on mathematical functions and VBA Programming of Excel.(4)Based on the above research,considering the ultimate load-bearing capacity and local position vibration response performance of the sub-frame,the dynamic stiffness of the body mounting point and static strength under typical working conditions as well as lightweight requirements are taken as the design objectives.Referring to the structure design of a BMW car’s aluminium alloy sub-frame,the process of topological optimization design of the sub-frame is constructed,and the forward design and performance analysis of the aluminium alloy sub-frame are completed.The result shows that the basic performance of the sub-frame designed by the forward design meets the design requirements,and its dynamic stiffness is equivalent to the BMW car’s aluminium alloy sub-frame,while the weight is reduced by 3%.The design provides practical examples for the engineering feasibility of topology optimization method for harmonic response,and also provides design reference for the application of aluminium alloy to realize automobile lightweight.