Microstructural Design Based On Topology Optimization Method

Microstructures are ubiquitous in nature,they have great potential both in naturally formed and material manufactured.Based on the finite element analysis(FEA)method,the asymptotic homogenization method is widely used in microstructural analysis because of its perfect mathematical theory,and structural topology optimization has played a huge advantage in the optimization design of microstructures.Along with improvement and development of controlled material synthesis,industrial manufacturing technology and practical application requirements,the analysis and design of graded microstructures,as well as hierarchical microstructures,became more and more important especially in advanced engineering fields.Nonetheless,traditional asymptotic homogenization can only analyze the rectangular periodic unit cell filled with microstructures,while traditional topology optimization methods,including level set method,etc.,are difficult to introduce geometric constraints and post-processing is necessary to import the optimized model into CAD/CAE system because of its implicit expressions.In order to address above mentioned challenges and deficiencies,based on the discrete moving morphable components(MMC)framework with explicit geometrical description and asymptotic-analysis-based homogenization(AH)method,we further introduce geometric manufacturing constraints,continued hierarchical structure model and improved asymptotic-analysisbased homogenization(AHTO)method.With the solid theoretical foundation,our research systematically integrate the analysis,design and optimization into a unified framework about graded microstructures and hierarchical microstructures.Then we carry out the research about mechanical equilibrium and thermal stability and finally suggest some designs which are quite suitable for actual manufacturing.Firstly,we develop a topology optimization method for designing structure equipped with graded infill components under the so-called MMC framework.Different to existing works,in the present work,each infill component can be identified intelligently and flexibly resorting to the explicit component description.Furthermore,the proposed approach not only has a small number of design variables but also be simple to be applied.According to the limitation in fabrication,the geometric constraint can be imposed selectively thus as to facilitate engineering manufacturing application.In addition,the analytical representation and sensitivity of the nonintersect constraint is derived,which has huge potential in the engineering application based on MMC.In addition,the optimized result can be extracted and remodeled in CAD/CAE system directly because of the advantage in explicit geometric description.Secondly,a parallel divide-and-conquer scheme is proposed to help accelerate the automatically design of configurations filled with graded microstructures concerning their mechanical behaviour.The algorithm is built on a solid theoretical ground,the asymptotic-analysis-based homogenization(AHTO plus)framework where the representation,response analysis and topology optimisation of porous material filled with graded microstructures are systematically integrated.We have shown that the AHTO plus framework possesses a strong favour for computational parallelism,and this feature is made the best use of in the proposed zoning scheme.The gradient-based sensitivity analysis formulation is also derived,which helps further speed up the procedure of the analysis and design about the multiscale problem.The proposed method gets validated through a comparison with 2D benchmark examples,and the high efficiency brought by the use of parallel computing is demonstrated,especially through 3D examples that have been barely investigated in existing literatures.In the end,we have also discussed another potential use of the proposed scheme in generating manifolds filled with graded microstructures.Finally,based on the discrete MMC framework,a continuous model comprised of hierarchical structure is proposed in order to deal with the problem about heat regulation in micro-andnano-scale hot spot.With the solid ground about material synthesis in physical chemistry,the proposed approach directly uses carbon nanotube(CNT)as optimization component,and adopts a widely accepted hierarchical structure as the design idea,then does optimization design in nanoscale,which satisfies both geometric constraints and manufactural limitations.In addition,the geometric confinement in mathematical form in hierarchical structural design is presented,which can shrink the search space effectively,and the upper bound about the design parameters is derived in this article.The proposed approach overcomes the complexity in the natural inspired artificial design and the difficulties in introducing geometric constraint for traditional topology optimization approaches and so on.The proposed approach shows good potential in the manufacturable heat dissipation structures in micro-and-nano scale.Under the topology optimization framework with explicit geometric description and mathematical asymptotic analysis theory,we carry out the research about the topology optimization using components equipped with graded infill structure,gradient porous material analysis and optimization design and micro-nano scale thermal conduction system design and analysis.Compared to previous work,the proposed method can provide significant reference in the design and analysis of microstructures and will give quite good structural design in manufacturable application in advanced fields.Last but not least,with the improvement of the manufacturing and material synthesis technology,our research shows great prospect in functional gradient material(FGM),microelectromechanical systems(MEMS)and nanoelectromechanical systems(NEMS),as well as in mechanical,thermal,acoustics and optical aspects,especially for the equipment and device with well-designed microstructures.