Research On Sensitivity Filtering And Post Processing Methods For Structure Topology Optimization Based On Variable Density Method

Structural optimization is to find the optimal solution of design variables in the design domain for a specific model to determine the model structure that satisfies the constraints and the objective function.Among them,structural topology optimization can optimize material distribution while ensuring structural continuity,which has become one of the most challenging research topics in structural optimization.At present,a variety of topology optimization methods have been proposed in this field.Among them,the variable density method is widely used due to the few design variables and simple procedures.When using the variable density method to optimize the continuum structure topology,the optimization goal is to obtain optimization results with clear boundaries and simple structures.However,in the actual optimization process,numerical instability such as checkerboard phenomenon and grid dependence is easy to occur.The problem leads to phenomena such as boundary diffusion and slender rod structure in the optimization results,which increases the complexity of the model structure and makes it less direct manufacturability,which restricts the development of the variable density method in the field of structural topology optimization.For this reason,based on the existing research,this paper takes the continuum structure as the research objective,based on the variable density method for topology optimization sensitivity filtering method,topology optimization boundary smoothing method,and topology optimization post-processing method based on manufacturing process constraints.Were studied.The research work of this paper is carried out from the following aspects:1.The basic theory,mathematical modeling theory and interpolation model of variable density method for topology optimization of continuum structure are studied in detail.The optimization criterion method based on variable density method is discussed.The numerical instability phenomenon in the application of variable density method is analyzed,and the corresponding solutions are proposed.2.In order to solve the boundary diffusion problem in Sigmund sensitivity filtering method,a partition density modified sensitivity filtering method for continuum structure is proposed.In this method,the original filtering region is divided into different regions,and a new composite convolution factor is used to process different regions,and the cell density is preset to modify the weights,so as to ensure the fast convergence and iteration of the near distance cell at the center,reduce the weight value of the cell at the boundary of the peripheral region,and effectively weaken the problem of boundary diffusion.3.In order to solve the problem of zigzag boundary in the topology optimization results of the partition density correction sensitivity filtering method,this paper proposes a topology optimization boundary smoothing method for continuum structure based on corner fitting.This method uses binary processing to the topology optimization results,extracts the model boundary,calculates the target corner set,and uses it as the reference point for curve fitting to obtain the model result of boundary smoothing Structure.This method can effectively avoid the generation of serrated boundary,reduce the difficulty of model reconstruction,and improve the direct manufacturing ability of the model.4.Aiming at the problem that it is difficult to directly manufacture the topology optimization results,a topology optimization model based on manufacturing process constraints is established after analyzing the common manufacturing process constraints.Manufacturing process constraints are introduced into the mathematical model of variable density method to make the topology optimization results more suitable for manufacturing under the constraint of structure volume.Two engineering examples of automobile suspension lower control arm and rb-10-001 industrial robot are used to illustrate the effectiveness of the method in solving the practical structural optimization problems.The 3D printing technology is applied to trial produce the model to further illustrate the feasibility of the method.