| Moving load is a usual kind of loading type who is acting on structures in the engineering industry.However,the dynamic response topology optimization problem of such structure has not been studied completely.It is worth noting that the main characteristics of moving load are the loading position is variable with time and the structural response excited by the load is transient.Therefore,there are some challenges when dealing with the above optimization problem.For instance,the loading position needs to be "sit in the right seat".Meanwhile,the computational cost for dynamic response and sensitivity analysis is high.Furthermore,there are localized-mode or other numerical problems.Especially,the Finite Element(FE)mesh will be denser if the moving load moves fast,for the fact that the moving load needs to be applied element by element,besides,the structural transient response is composed of high-frequency part.Consequently,the number of design variables will be increasingly large when the traditional topology optimization models are employed.To overcome above challenges,the Moving Morphable Component(MMC)method is utilized in the present work.There are some advantages to solving the optimization problem based on MMC.Such as the FE analysis model and the optimization model are completely decoupled,which makes that there are a few design variables and high-efficiency.Besides,structural boundary described in an explicit way eliminates the gray-scaled element and localized-mode issues who are common in traditional methods.Specific research contents are as follows:Firstly,an explicit solution framework for structural dynamic response topology optimization problem excited by moving load is proposed.It is assumed that the structure is constructed with a series of movable,morphable,crossable or overlapped components.Meanwhile,the design variables are those parameters characterizing the positions and geometries of the components.Considering there are a large number of freedoms in FE model,the mode reduction technique is introduced to reduce the complexity of the problem.On the basis of that,the problem formulations whose objective function is the time-domain maximum dynamic compliance of structure or the time-domain maximum displacement response of specific points are proposed.Moreover,the corresponding sensitivity analysis is carried out.Secondly,the optimal designs of structures under moving force are obtained.The moving force is applied to FE model by " sit in the right seat ".Subsequently,the dynamic response,objective function and the corresponding sensitivity are calculated successively.Based on this,the optimal designs of structures are realized.At the same time,the influence of structural optimal design caused by parameters of moving force has been discussed,such as velocity,the frequency of a convex sinusoidal half wave force or others.Numerical examples demonstrate that the proposed method performs well in convergence and stability.Due to the FE model and optimization model are completely decoupled in the MMC method,the surge of design variables could be avoided effectively while the moving force moves fast.Besides,the explicit description of structural geometric boundary can not only eliminate the gray-scale element problem and localized-mode problem,but avoid changing structural dynamic characteristics if the secondary design of structure is executed.Thirdly,the optimal designs of the structures under moving mass are obtained.Compared with the moving force,the inertia of moving mass has significantly effect on structural dynamic characteristic.At the same time,the moving mass and structure consist a time-varying coupling system.Therefore,a reanalysis method is utilized to reduce computational cost for FE and sensitivity analysis when solving structural dynamic response at each time step.In addition,some parameters,such as the coupling type,velocity,value of moving mass as well as the irregularity of coupling interface are discussed to observe their influence on structural optimal design. |
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