Research On Multiscale Topology Optimization Design Method For Thermal Metamaterials

Metamaterial,a kind of artificial composite material with special properties that do not exist in nature,is usually obtained by the artificial design of structures.It has attracted much attention because of its extraordinary properties that natural materials do not have.As a member of the metamaterials,thermal metamaterials can manipulate the heat flow to form a series of extraordinary thermal functionalities,such as thermal cloaking,thermal concentrating,and thermal rotating,which have significant application value in aeronautic and astronautic,energy,electronics,and other fields.In this thesis,by taking thermal metamaterials as the research objects and adopting the multiscale topology optimization design idea in the field of structural optimization,the multiscale topology optimization design method of thermal metamaterials is studied.Various types of thermal metadevices are fabricated,and their thermal functionalities are simulated and experimentally verified.The main work of this thesis is as follows:Firstly,the topology optimization design of a microstructure with a specific thermal conductivity tensor is studied.In order to solve the problems of relying on experience and low efficiency in traditional design methods,an inverse homogenization design method based on topology optimization is developed to design microstructures with specific thermal conductivity tensors.Based on the numerical homogenization method,the mapping relationship between the topology of microstructure and its macroscopically effective thermal conductivity tensor is established;On this basis,the topology optimization design model of microstructure with specific thermal conductivity tensor is constructed.The influences of different objective and constraint functions on the optimized results are analyzed,and the design of microstructures with specific thermal conductivity tensors is effectively achieved.Next,the topology optimization design of microstructures of ergodic thermal conductivity tensor space is studied.In order to describe the set of effective thermal conductivity tensors of mixed structures composed of natural material,the thermal conductivity tensor space is defined.Taking the mixed structure of two-phase materials as an example,the size and shape of them thermal conductivity tensor space are determined,and the topology optimization is used to design the microstructure for achieving an ergodic space.On this basis,the numerical simulations and thermal experiments were carried out for several typical microstructures,and the results show that the optimized microstructures have similar thermal conduction behavior compared with the continuous medium possessed the specific thermal conductivity tensor.Thirdly,a domain-by-domain multiscale topology optimization design based on regionalized scattering cancellation is studied for thermal metamaterial with regular shape.At the macroscale,combined with the shape and target function of the thermal metamaterial,the regionalized scattering cancellation method is proposed to obtain the thermal conductivity tensor distribution of each subarea by solving the thermal conduction equation with specific boundary constraints between the subareas;At the microscale,combined with the ergodic thermal conductivity tensor space,the microstructure configuration with the target thermal conductivity tensor is domain-by-domainly optimized to achieve the design of thermal concentrating,cloaking,connecting,and reflecting metamaterials,which improves the flexibility and efficiency of design;The above four types of thermal metadevices are fabricated by 3D printing,and their extraordinary thermal functionalities are tested by numerical simulations and thermal experiments,which verified the effectiveness of the proposed method.Fourthly,a point-by-point multiscale topology optimization design based on transformation thermotics is studied for thermal metamaterial with complex shape.At the macroscale,combined with the shape and target function of the thermal metamaterial,the thermal conductivity tensor distributions within the metamaterial are calculated by transformation thermotics;At the microscale,combined with the ergodic thermal conductivity tensor space,the microstructure configuration with the target thermal conduction tensor is point-by-pointly designed by topology optimization,which solves the difficulty of designing thermal metamaterials with complex shapes and omnidirectional functionalities;On this basis,thermal concentrating,cloaking,and rotating metamaterials are designed;The above three kinds of thermal metadevices are fabricated by 3D printing,and the numerical simulations and thermal experiments are carried out to verify the omnidirectional functionalities of thermal metamaterials.Fifthly,a point-by-point multiscale topology optimization design of the thermal cloaked sensors is studied.To solve the problems of single shape and local temperature distortion in the design of thermal cloaked sensor,a design method of thermal cloaked sensor based on scattering cancellation and transformation thermotics is proposed at the macroscale.Through continuous medium theory simulation,it is verified that the proposed method can design thermal metamaterials with complex shapes for omnidirectionally cloaking sensors;At the microlevel,combined with the ergodic thermal conductivity tensor space,the microstructure configuration with the target thermal conductivity tensor is pointby-pointly designed,and the structure of thermal cloaked sensors with complex shapes is realized;The thermal metadevice is fabricated by 3D printing,and the omnidirectional functionality of the thermal cloaked sensor is tested by numerical simulations and thermal experiments.The results show that the sensor can measure normally while achieving thermal cloaking functionality.Finally,the main work and innovations of this thesis are summarized,and the future research work is further prospected.