Topology Optimization Design Of Quasi-periodic Hierarchical Structures For Additive Manufacturing

Porous hierarchical structure has been widely used in engineering for its high specific strength and stiffness,improved corrosion-resistance and multifunctionality.The design of multi-scale topology optimization for such structures has been a hot topic during the past two decades.With the continuous improvement and development of additive manufacturing technology,the manufacturing of porous structure becomes possible.Therefore,the research on advanced design methods,through the design of porous hierarchical structures and microstructure with the change of space(gradient multi-scale structure design),to improve the performance of hierarchical structure,has become a research hotspot.With the increasing of the complexity of porous structure can not only improve the performance of structure,but also lead to the increase of manufacturing difficulty and cost.Therefore,it is necessary to consider the coordination between the performance improvement and the manufacturing difficulties caused by the complexity of porous structure.Quasi-periodic multi-scale structure can improve the optimization space and control the complexity of the structure through the quasi-periodic change of the multi-scale structure.In this paper,the topology optimization design method of quasi-periodic multi-scale structure for additive manufacturing is studied.The main research contents and results are as follows:(1)Topology optimization design of multi-scale structures with alterable microstructural length-width ratios.In the second chapter,a multi-scale topology optimization method is proposed to obtain quasi-periodic hierarchical structures by simultaneously optimizing macrostructure,microstructure and the microstructural length-width ratios.In this chapter,"quasi-periodic" means the microstructure in different points have the similar topology but different length-width ratios.Microstructural topology optimization design generally based on a prescribed rectangle design domain with a fixed micro-structural lengthwidth ratio.In order to further extend the design space,a special composite structure with microstructures of identical topology but different length-width ratios is considered in this chapter.The asymptotic homogenization method is applied to calculate the effective material elastic matrices of the unit cells with different length-width ratios.Sensitivities of structural compliance with respect to the three types of design variables are derived and a gradient-based optimization method is applied to update the design variables.Two numerical examples are presented to verify the validity of the proposed method.Furthermore,the optimized results in the second example are manufactured by 3D printing and the experimental tests are carried out.Comparison of the stiffness performances further proves the validity of this method.(2)Topology optimization design of multi-scale structures with quasi-periodic microstructures based on erode-dilate operator.In this chapter,a new topology optimization design method of graded structure with quasi-periodic microstructures is proposed.The socalled ‘quasi-periodic’ means the microstructure in different points have the similar topology but different parameters,for example the square microstructures who have inner circles with varied radius.For parametrize the microstructure with arbitrary topology described by element density,an erode-dilate operator is introduced,and then the quasi-periodic microstructures with arbitrary topology can be described by element densities and a parametric.By this way,we can optimize the microstructural topology and the parametric of microstructures,which are varied in macro design domain,simultaneously,for improving the performances of graded structure.Furthermore,the microstructures neighbored are connected in the obtained results which benefits the rapid trial-manufacture by additive manufacturing.Three numerical examples are used to demonstrate the effectiveness of the proposed method.(3)Extended application of erode-dilate operator: Topology optimization design of multi-scale structures with bidirectional erode-dilate operators、Topology optimization design of multi-scale structures with the consideration of singular-cell connection 、 Topology optimization design of multi-scale structures with erode-dilate operator based on MMC method.In this chapter,based on the idea of erode-dilate,a new algorithm of bidirectional erode-dilate operator is proposed to further improve the structure design space.At the same time,a erode-dilate algorithm considering the singular-cell connectivity is proposed to solve the connection problem of microstructures.Considering the difference between MMC method and SIMP method,a topology optimization design of multi-scale structures with erodedilate operator based on MMC method is proposed.In addition,numerical examples are given to verify the validity of the three extended algorithms.(4)A quasi-periodic hierarchical topology optimization design method considering thermoelastic problem.The erode-dilate operator proposed in this paper is used as center ideas to build the multi-physical topology optimization problems.In this chapter,The single and multi-scale structure topology optimization formulation is established,attempting to find maximize surface precision of the precision instruments under thermoelastic loads with the constraints of structural thermoelastic stiffness and material utilization amount.In addition,numerical examples are given to verify the effectiveness of the proposed method.