Research On Robust Bi-directional Evolutionary Topology Optimization Method

With the rise of additive manufacturing technology,topology optimization has become an important tool for structural optimization.It aims to find the optimal number of holes and their distribution under given load and boundary conditions,so that the structural performance is optimal,its application covers aviation,aerospace,shipbuilding,high-speed train and so on.There are various uncertainties in engineering practice,and these uncertainties can only be minimized but cannot be avoided.Multiple uncertainties coupled together will result in large deviations.This paper combines the techniques of both the topology optimization and uncertainty analysis in structural design,the study of robust topology optimization method for the design of continuum,periodic continuum,isotropic material and multi-level structures are carried out,using the bi-directional evolutionary topology optimization(BETO)method with smooth boundary representation.The main work are summarized as follows:Firstly,this paper proposes an uncertainty analysis method based on orthogonal decomposition and uniform sampling(ODUS),which overcomes several numerical difficulties such as complex derivation,low calculation efficiency and difficult to obtain explicit sensitivity information,when the existing interval quantization method employed to quantificate the load uncertainty.The technique of orthogonal decomposition is used to separate the uncertainty variables into several coefficients unrelated to finite element analysis,which saves the computational cost in the process of uncertainty quantification.Using the technique of uniform sampling,the original uncertainty problem can be transformed into a generalized deterministic problem,then explicit sensitivity information is yielded and easy to solve.In addition,the influence of sample size with respect to the load magnitude and direction on ODUS calculation accuracy is further analyzed.A relative dispersion index including the extremes of structural response is proposed,which can be used to visually compare the deterministic design results with the corresponding robust ones.The effectiveness and efficiency of the proposed method are verified by some typical examples.Secondly,this paper proposes a robust topology optimization method for the design of periodic continuum structure,which overcomes the problem that the periodic unit cell topology is susceptible to load disturbance.All elements of the design domain are subjected to sensitivity averaging according to the specified number of cycles before performing node sensitivity filtering,and then the element sensitivity is converted into the node sensitivity,in this case,periodic designs can be obtained based on the idea of sensitivity consistency,which overcomes the difficulty that structural design domains cannot be equidistantly divided by elemental node numbers.The ODUS method is used to transform the load uncertainty problem into multi-case problem under deterministic conditions.The sensitivities for the robust design of periodic continuum structure are derived,according to three uncertainty situations of load magnitude,direction and mixing of the both,the effectiveness and robustness of the proposed method are verified by 2D and 3D examples.Then,this paper proposes a robust topology optimization method for the design of isotropic material microstructure.The weighting of expectation and variance of the microstructure's extreme performance is taken as the objective function,when taking into account the probability uncertainty of the base material.The material uncertainty is efficiently quantified by introducing a non-intrusive polynomial chaos expansion(PCE)method,and the problem that the relationship between material properties and objective functions cannot be expressed is solved.The macroscopic equivalent properties of material microstructure is evaluated by using the energy-based homogenization method(EBHM),four isotropic material microstructures with extreme properties were obtained,and the effectiveness and superiority of the proposed method were verified.Subsequently,this paper proposes a robust topology optimization method for the design of multi-level structures under multi-source mixed uncertainty.The ODUS method is used to quantify the load interval uncertainty characterized by ‘bounded but unknown';the non-intrusive PCE method is used to solve the problem when material uncertainty subjecting to the probability distribution.The effects of single-load uncertainty,multi-load uncertainty,material uncertainty,periodic constraints on the robust design of multi-level structures under mixed uncertainty are all studied.The proposed method is also applied to the 3D Michell structure,and the topological configurations with excellent performance are obtained.The design results under different conditions are printed out through the additive manufacturing technology,and the effectiveness and practicability of the proposed method are verified.Finally,this paper summarizes the research results and innovations.Furthermore,the prospects for further research work are outlined.