Research Of Structural Dynamic Topology Optimization Based On The BESO

Because topology optimization is the initial stage of structural design,the correct choice of the topological structure has a strong impact on the performance of the structure.As a result,topology optimization has higher economic benefit than size and shape optimization.It is important to study structural topology optimization and extend its range of application,especially in the field of engineering.At present,however,there are many problems in dynamics topology optimization,such as low computational efficiency,mass sensitivity calculation,long progress of iteration and unstable iteration progress.Aiming at the previous problems,this paper analyzes and studies the dynamics topology optimization problem intensively based on bi-directional evolutionary structural optimization(BESO),and extends the applying scope of bi-directional evolutionary structural optimization in dynamic optimization design.Firstly,the basic theory of BESO is studied,and the numerical instability of the BESO method is analyzed and the solution is given,this paper summarizes basic procedure of the optimization algorithm and program with MATLAB to test BESO by calculating numerical examples.On the basis of previous work,this paper researches a modified BESO.Initial design domain of the algorithm starts from a small area and a simple file technology is used to eliminate the numerical instability problem,which illustrates that the modified BESO can improve computational efficiency of static and dynamic optimization.Secondly,for the dyscalculia of sensitivity and inefficiency of dynamic optimization computation,this paper explores the solution of dynamic optimization problem in the case of equivalent static load based on BESO and describes the basic principle of equivalent static load in detail.Finally,the dynamic optimization problem was transformed into static optimization problem of multi-load condition.A numerical example shows that using the equivalent load can solve the problem of structural dynamic stiffness optimization.Thirdly,this paper researches multi-objective dynamic optimization problem by using the method of solving multi-objective problem and equivalent static load.With building multi-object optimization mathematical model of stiffness and frequency and derive the formula of sensitivity,this paper proposes the complete optimization iteration procedure and illustrates the feasibility of using the equivalent static load to solve the multi objective dynamic topology optimization by calculating numerical examples.On the basis of that,in order to ensure that vibration mode is consistent during dynamic optimization,modal tracing technique is introduced into dynamic multi-object problem.The numerical examples demonstrate that modal tracing technique can trace the wanted modal in the process of optimization.Finally,the traditional BESO easily causes the mistaken delete of unit and instability of iterative process in static and dynamic optimization.To solve above problem,this paper investigates applying smooth processing technique to topology optimization of static and dynamic.The basic principle of smooth processing technology is described in detail and a weight function is used to smooth the whole optimization process.The numerical examples testify that the smoothing technique can achieve the smoothness of static and dynamic optimization process.