Research On The Theory And Method Of Optimization Design Of Novel Structures And Structured Materials

Lattice/porous structures with well-designed periodic/quasi-periodic microstructures possess lightweight,high strength and high specific stiffness advantages and usually have excellent mechanical,thermal,optical and acoustic properties.In the emerging fields of ultralight material,acoustic/photics nonreciprocal transmission equipments,acoustic/photics invisibility cloaks and acoustic/thermotics/photics energy absorbing device design,such lattice/porous structures have broad application prospects.Nowadays,these lattice/porous materials/structures with some supernormal properties are collectively referred to as metamaterials.For the design of metamaterials,empirical design is generally adopted in engineering applications.The design process is long and without theoretical guidance.Therefore.it is necessary to study more advanced metamaterials design methods.In addition,with the rapid development of modern manufacturing technology(for example,additive manufacturing),it is no longer difficult to fabricate lattice/porous structures with complicated microstructures.At the same time?new manufacturing constraints such as minimum print size are also proposed.To control the cost associated with material usage and printing time,engineering practices in additive manufacturing favour lattice/porous structures,which makes the additive manufacturing-oriented lattice/porous structures design becomes a research hotspot.In order to make the utmost of the given material and to meet the manufacturing constraints,different forms of microstructure design with real dimensions are required for different parts of the structure,which is in contradiction with the traditional homogenization-based lattice/porous design methods based on strict scale separation hypothesis and global periodic hypothesis.New manufacturing technology presents new design requirements,in order to meet the design requirements of new structures/materials,new design methods must be developed.Therefore,this paper focuses on a new type of special-function acoustic structure/equipment based on acoustic metamaterials and new structural topology optimization algorithms considering manufacturability requirements.The specific research content is as follows:1.A theoretical model of novel acoustic/elastic wave transmission equipment with non-reciprocal transmission characteristics is proposed.By analyzing the advantages and disadvantages of the previous acoustic diode model,the necessary conditions for achieving acoustic non-reciprocal transmission are conceived.The amplitude-dependent band gap characteristics of weakly nonlinear phononic crystals are theoretically proved.Then a new acoustic diode model based on weak nonlinear phononic crystals and asymmetric linear structures is proposed.The validity of the model is verified by numerical examples.It is proved that the new acoustic diode has the advantages of strict non-reciprocity,high positive energy passing rate,no change of incident wave frequency.At last,possible experimental schemes are also discussed.(Chapter Two)2.An efficient progressive homogenization based printable microstructure design method is developed.By introducing a partitioning strategy,the design domain is divided into a number of sub-regions containing periodic microstructures and transition regions between sub-regions.The approximate equivalent material properties are obtained by using the progressive homogenization technique in each sub-region.and then the finite elements in these regions are divided and connected to the elements of transition region by the quadtree mesh.The element densities of the transition region and the unit cell in each homogenization-region are taken as design variables.the optimal column is given under the SIMP framework.Then,the validity and accuracy of the proposed method are verified by numerical examples.Compared with the traditional strict scale-separation-based homogenization method,this method can obtain smooth connected micro-structures with real sizes.In addition,the proposed method is extremely efficient compared to the full-structure overall solution algorithm based on variable connection technology.(Chapter Three)3.A spatial gradient lattice filling structure optimization design method based on explicit topology optimization method is constructed.The formation law of spatial gradual structure is revealed.Based on the Moving Morphable Components/Voids(MMC/MMV)topology optimization method and the space coordinate perturbation technology,only by introducing a few parameters,the transition from spatial periodic structure to spatial gradient structure can be realized.The corresponding optimized column and sensitivity are given.Numerical examples show that,only use a few design variables,spatially continuous changed filling structure with excellent mechanical properties can be obtained by the proposed method.(Chapter Four)4.A high-efficiency explicit topology optimization method based on multi-resolution technology is established.By taking the advantages of the complete decoupling of the analytical model and the optimized model in the Moving Morphable Components(MMC)Method,an efficient algorithm for solving high-resolution large-scale topology optimization problems is developed to adapt to the optimization design for additive manufacturing structures.Compared with the traditional algorithm,the degree of freedom of analysis and the number of design variables of this method are reduced by an order of magnitude,and the computational efficiency is greatly improved.An effective localized sparse storage technology has been developed.which realizes the localized solution and sparse storage of component topology description function and structure sensitivity information,which greatly reduces the computation time of the discretized topology description function.A design domain partitioning technology based on MMC method is proposed,which can flexibly control the topology complexity of the optimized structure,and numerical experiments show that the traditional SIMP method is a special case of the proposed method.(Chapter Five)5.A new approach for designing additive manufacturing-oriented coated structures with graded lattice infill simultaneously is developed based on the Moving Morphable Components/Voids(MMCs/MMVs)topology optimization framework.To this end,a set of morphable voids are adopted to describe the boundary of the exterior coated solid shell,while a set of morphable components combing with a coordinate perturbation technique are introduced to represent the graded infill material distribution.Under such treatment,both the crisp boundary of the exterior coating shell and the configuration of continuously distributed graded infill can be optimized simultaneously,without any post-processing,only using a very small number of design variables.Numerical examples demonstrate the effectiveness of the proposed approach.