The optimization of civil engineering structures is critical for enhancing structural performance and material efficiency in engineering applications.Structural optimization approaches seek to determine the optimal de...The optimization of civil engineering structures is critical for enhancing structural performance and material efficiency in engineering applications.Structural optimization approaches seek to determine the optimal design,by considering material performance,cost,and structural safety.The design approaches aim to reduce the built environment’s energy use and carbon emissions.This comprehensive review examines optimization techniques,including size,shape,topology,and multi-objective approaches,by integrating these methodologies.The trends and advancements that contribute to developing more efficient,cost-effective,and reliable structural designs were identified.The review also discusses emerging technologies,such as machine learning applications with different optimization techniques.Optimization of truss,frame,tensegrity,reinforced concrete,origami,pantographic,and adaptive structures are covered and discussed.Optimization techniques are explained,including metaheuristics,genetic algorithm,particle swarm,ant-colony,harmony search algorithm,and their applications with mentioned structure types.Linear and non-linear structures,including geometric and material nonlinearity,are distinguished.The role of optimization in active structures,structural design,seismic design,form-finding,and structural control is taken into account,and the most recent techniques and advancements are mentioned.展开更多
Due to the high-order B-spline basis functions utilized in isogeometric analysis(IGA)and the repeatedly updating global stiffness matrix of topology optimization,Isogeometric topology optimization(ITO)intrinsically su...Due to the high-order B-spline basis functions utilized in isogeometric analysis(IGA)and the repeatedly updating global stiffness matrix of topology optimization,Isogeometric topology optimization(ITO)intrinsically suffers from the computationally demanding process.In this work,we address the efficiency problem existing in the assembling stiffness matrix and sensitivity analysis using B˙ezier element stiffness mapping.The Element-wise and Interaction-wise parallel computing frameworks for updating the global stiffness matrix are proposed for ITO with B˙ezier element stiffness mapping,which differs from these ones with the traditional Gaussian integrals utilized.Since the explicit stiffness computation formula derived from B˙ezier element stiffness mapping possesses a typical parallel structure,the presented GPU-enabled ITO method can greatly accelerate the computation speed while maintaining its high memory efficiency unaltered.Numerical examples demonstrate threefold speedup:1)the assembling stiffness matrix is accelerated by 10×maximumly with the proposed GPU strategy;2)the solution efficiency of a sparse linear system is enhanced by up to 30×with Eigen replaced by AMGCL;3)the efficiency of sensitivity analysis is promoted by 100×with GPU applied.Therefore,the proposed method is a promising way to enhance the numerical efficiency of ITO for both single-patch and multiple-patch design problems.展开更多
Topology optimization of thermal-fluid coupling problems has received widespread attention.This article proposes a novel topology optimization method for laminar two-fluid heat exchanger design.The proposed method uti...Topology optimization of thermal-fluid coupling problems has received widespread attention.This article proposes a novel topology optimization method for laminar two-fluid heat exchanger design.The proposed method utilizes an artificial density field to create two permeability interpolation functions that exhibit opposing trends,ensuring separation between the two fluid domains.Additionally,a Gaussian function is employed to construct an interpolation function for the thermal conductivity coefficient.Furthermore,a computational program has been developed on the OpenFOAM platform for the topology optimization of two-fluid heat exchangers.This program leverages parallel computing,significantly reducing the time required for the topology optimization process.To enhance computational speed and reduce the number of constraint conditions,we replaced the conventional pressure drop constraint condition in the optimization problem with a pressure inlet/outlet boundary condition.The 3D optimization results demonstrate the characteristic features of a surface structure,providing valuable guidance for designing heat exchangers that achieve high heat exchange efficiency while minimizing excessive pressure loss.At the same time,a new structure appears in large-scale topology optimization,which proves the effectiveness and stability of the topology optimization program written in this paper in large-scale calculation.展开更多
This paper aims to propose a topology optimization method on generating porous structures comprising multiple materials.The mathematical optimization formulation is established under the constraints of individual volu...This paper aims to propose a topology optimization method on generating porous structures comprising multiple materials.The mathematical optimization formulation is established under the constraints of individual volume fraction of constituent phase or total mass,as well as the local volume fraction of all phases.The original optimization problem with numerous constraints is converted into a box-constrained optimization problem by incorporating all constraints to the augmented Lagrangian function,avoiding the parameter dependence in the conventional aggregation process.Furthermore,the local volume percentage can be precisely satisfied.The effects including the globalmass bound,the influence radius and local volume percentage on final designs are exploited through numerical examples.The numerical results also reveal that porous structures keep a balance between the bulk design and periodic design in terms of the resulting compliance.All results,including those for irregular structures andmultiple volume fraction constraints,demonstrate that the proposedmethod can provide an efficient solution for multiple material infill structures.展开更多
Large cavity structures are widely employed in aerospace engineering, such as thin-walled cylinders, blades andwings. Enhancing performance of aerial vehicles while reducing manufacturing costs and fuel consumptionhas...Large cavity structures are widely employed in aerospace engineering, such as thin-walled cylinders, blades andwings. Enhancing performance of aerial vehicles while reducing manufacturing costs and fuel consumptionhas become a focal point for contemporary researchers. Therefore, this paper aims to investigate the topologyoptimization of large cavity structures as a means to enhance their performance, safety, and efficiency. By usingthe variable density method, lightweight design is achieved without compromising structural strength. Theoptimization model considers both concentrated and distributed loads, and utilizes techniques like sensitivityfiltering and projection to obtain a robust optimized configuration. The mechanical properties are checked bycomparing the stress distribution and displacement of the unoptimized and optimized structures under the sameload. The results confirm that the optimized structures exhibit improved mechanical properties, thus offering keyinsights for engineering lightweight, high-strength large cavity structures.展开更多
Background With the development of the Internet,the topology optimization of wireless sensor networks has received increasing attention.However,traditional optimization methods often overlook the energy imbalance caus...Background With the development of the Internet,the topology optimization of wireless sensor networks has received increasing attention.However,traditional optimization methods often overlook the energy imbalance caused by node loads,which affects network performance.Methods To improve the overall performance and efficiency of wireless sensor networks,a new method for optimizing the wireless sensor network topology based on K-means clustering and firefly algorithms is proposed.The K-means clustering algorithm partitions nodes by minimizing the within-cluster variance,while the firefly algorithm is an optimization algorithm based on swarm intelligence that simulates the flashing interaction between fireflies to guide the search process.The proposed method first introduces the K-means clustering algorithm to cluster nodes and then introduces a firefly algorithm to dynamically adjust the nodes.Results The results showed that the average clustering accuracies in the Wine and Iris data sets were 86.59%and 94.55%,respectively,demonstrating good clustering performance.When calculating the node mortality rate and network load balancing standard deviation,the proposed algorithm showed dead nodes at approximately 50 iterations,with an average load balancing standard deviation of 1.7×10^(4),proving its contribution to extending the network lifespan.Conclusions This demonstrates the superiority of the proposed algorithm in significantly improving the energy efficiency and load balancing of wireless sensor networks to extend the network lifespan.The research results indicate that wireless sensor networks have theoretical and practical significance in fields such as monitoring,healthcare,and agriculture.展开更多
A broadband polarization-independent terahertz multifunctional coding metasurface based on topological optimization using liquid crystal(LC)is proposed.The metasurface can achieve reconfigurability for beam steering a...A broadband polarization-independent terahertz multifunctional coding metasurface based on topological optimization using liquid crystal(LC)is proposed.The metasurface can achieve reconfigurability for beam steering and vortex beam generation within a frequency range of 0.68 THz–0.72 THz.Firstly,the metasurface unit is topologically optimized using the non-dominant sequencing genetic algorithms(NSGA-II)multi-objective optimization algorithm.By applying the LC’s electrically tunable refractive index properties,the metasurface unit enables polarization-independent 2-bit coding within a frequency range of 0.68 THz–0.72 THz.Then,based on the designed metasurface unit,the array arrangement of the metasurface is reverse-designed to achieve beam steering and vortex beam generation.The results show that,for beam steering,not only can polarization-independent steering of both single-and multi-beam be achieved within the 35°elevation angle range,but also independent control of the target angle of each beam in the multi-beam steering.For vortex beam generation,the metasurfaces can achieve the generation of single-and multi-vortex beams with topological charges l=±1,±2 within the 35elevation angle range,and the generation angles of each vortex beam in the multi-vortex beam can be independently controlled.This provides flexibility and diversity in the generation of vortex beams.Therefore,the proposed terahertz LC metasurface can realize flexible control of reconfigurable functions and has certain application prospects in terahertz communication,phased array radar,and vortex radar.展开更多
The current research of sandwich structures under dynamic loading mainly focus on the response characteristic of structure.The micro-topology of core layers would sufficiently influence the property of sandwich struct...The current research of sandwich structures under dynamic loading mainly focus on the response characteristic of structure.The micro-topology of core layers would sufficiently influence the property of sandwich structure.However,the micro deformation and topology mechanism of structural deformation and energy absorption are unclear.In this paper,based on the bi-directional evolutionary structural optimization method and periodic base cell(PBC)technology,a topology optimization frame work is proposed to optimize the core layer of sandwich beams.The objective of the present optimization problem is to maximize shear stiffness of PBC with a volume constraint.The effects of the volume fraction,filter radius,and initial PBC aspect ratio on the micro-topology of the core were discussed.The dynamic response process,core compression,and energy absorption capacity of the sandwich beams under blast impact loading were analyzed by the finite element method.The results demonstrated that the overpressure action stage was coupled with the core compression stage.Under the same loading and mass per unit area,the sandwich beam with a 20%volume fraction core layer had the best blast resistance.The filter radius has a slight effect on the shear stiffness and blast resistances of the sandwich beams.But increasing the filter radius could slightly improve the bending stiffness.Upon changing the initial PBC aspect ratio,there are three ways for PBC evolution:The first is to change the angle between the adjacent bars,the second is to further form holes in the bars,and the third is to combine the first two ways.However,not all three ways can improve the energy absorption capacity of the structure.Changing the aspect ratio of the PBC arbitrarily may lead to worse results.More studies are necessary for further detailed optimization.This research proposes a new topology sandwich beam structure by micro-topology optimization,which has sufficient shear stiffness.The micro mechanism of structural energy absorption is clarified,it is significant for structural energy absorption design.展开更多
This paper presents a topology optimization approach for the surface flows on variable design domains.Via this approach,the matching between the pattern of a surface flow and the 2-manifold used to define the pattern ...This paper presents a topology optimization approach for the surface flows on variable design domains.Via this approach,the matching between the pattern of a surface flow and the 2-manifold used to define the pattern can be optimized,where the 2-manifold is implicitly defined on another fixed 2-manifold named as the base manifold.The fiber bundle topology optimization approach is developed based on the description of the topological structure of the surface flow by using the differential geometry concept of the fiber bundle.The material distribution method is used to achieve the evolution of the pattern of the surface flow.The evolution of the implicit 2-manifold is realized via a homeomorphous map.The design variable of the pattern of the surface flow and that of the implicit 2-manifold are regularized by two sequentially implemented surface-PDE filters.The two surface-PDE filters are coupled,because they are defined on the implicit 2-manifold and base manifold,respectively.The surface Navier-Stokes equations,defined on the implicit 2-manifold,are used to describe the surface flow.The fiber bundle topology optimization problem is analyzed using the continuous adjoint method implemented on the first-order Sobolev space.Several numerical examples have been provided to demonstrate this approach,where the combination of the viscous dissipation and pressure drop is used as the design objective.展开更多
A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linea...A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific problem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analysis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples.展开更多
Chiral metamaterials have been proven to possess many appealing mechanical phenomena,such as negative Poisson's ratio,high-impact resistance,and energy absorption.This work extends the applications of chiral metam...Chiral metamaterials have been proven to possess many appealing mechanical phenomena,such as negative Poisson's ratio,high-impact resistance,and energy absorption.This work extends the applications of chiral metamaterials to underwater sound insulation.Various chiral metamaterials with low acoustic impedance and proper stiffness are inversely designed using the topology optimization scheme.Low acoustic impedance enables the metamaterials to have a high and broadband sound transmission loss(STL),while proper stiffness guarantees its robust acoustic performance under a hydrostatic pressure.As proof-of-concept demonstrations,two specimens are fabricated and tested in a water-filled impedance tube.Experimental results show that,on average,over 95%incident sound energy can be isolated by the specimens in a broad frequency range from 1 k Hz to 5 k Hz,while the sound insulation performance keeps stable under a certain hydrostatic pressure.This work may provide new insights for chiral metamaterials into the underwater applications with sound insulation.展开更多
By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M...By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.展开更多
This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of m...This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design.The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads.The topology optimization formula is combined with the ordered solid isotropic material with penalization(ordered-SIMP)multi-material interpolation model.The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function.Furthermore,the sequential optimization and reliability assessment(SORA)is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization(DTO)problem.Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point(MPP).In each cycle,the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle.The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method(MMA)is used to update design variables.Finally,the validity and feasibility of the method are verified by the numerical example of L-shape beam design,T-shape structure design,steering knuckle,and 3D T-shaped beam.展开更多
In recent years,there has been significant research on the application of deep learning(DL)in topology optimization(TO)to accelerate structural design.However,these methods have primarily focused on solving binary TO ...In recent years,there has been significant research on the application of deep learning(DL)in topology optimization(TO)to accelerate structural design.However,these methods have primarily focused on solving binary TO problems,and effective solutions for multi-material topology optimization(MMTO)which requires a lot of computing resources are still lacking.Therefore,this paper proposes the framework of multiphase topology optimization using deep learning to accelerate MMTO design.The framework employs convolutional neural network(CNN)to construct a surrogate model for solving MMTO,and the obtained surrogate model can rapidly generate multi-material structure topologies in negligible time without any iterations.The performance evaluation results show that the proposed method not only outputs multi-material topologies with clear material boundary but also reduces the calculation cost with high prediction accuracy.Additionally,in order to find a more reasonable modeling method for MMTO,this paper studies the characteristics of surrogate modeling as regression task and classification task.Through the training of 297 models,our findings show that the regression task yields slightly better results than the classification task in most cases.Furthermore,The results indicate that the prediction accuracy is primarily influenced by factors such as the TO problem,material category,and data scale.Conversely,factors such as the domain size and the material property have minimal impact on the accuracy.展开更多
We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods...We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods mainly contain shape and topology schemes,with the former changing the surface geometric profile of the structure and the latter changing thematerial distribution topology or hole topology of the structure.In the present acoustic performance optimization,the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure,the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter,and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge.The topology and shape sensitivities of the approach are calculated using the adjoint variable method,which ensures the efficiency of the optimization.The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization.Numerical examples are given to validate the effectiveness of the presented optimization approach.展开更多
This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encounter...This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.展开更多
Material and structure made by additive manufacturing(AM)have received much attention lately due to their flexibility and ability to customize complex structures.This study first implements multiple objective topology...Material and structure made by additive manufacturing(AM)have received much attention lately due to their flexibility and ability to customize complex structures.This study first implements multiple objective topology optimization simulations based on a projectile perforation model,and a new topologic projectile is obtained.Then two types of 316L stainless steel projectiles(the solid and the topology)are printed in a selective laser melt(SLM)machine to evaluate the penetration performance of the projectiles by the ballistic test.The experiment results show that the dimensionless specific kinetic energy value of topologic projectiles is higher than that of solid projectiles,indicating the better penetration ability of the topologic projectiles.Finally,microscopic studies(scanning electron microscope and X-ray micro-CT)are performed on the remaining projectiles to investigate the failure mechanism of the internal structure of the topologic projectiles.An explicit dynamics simulation was also performed,and the failure locations of the residual topologic projectiles were in good agreement with the experimental results,which can better guide the design of new projectiles combining AM and topology optimization in the future.展开更多
This paper aims to solve large-scale and complex isogeometric topology optimization problems that consumesignificant computational resources. A novel isogeometric topology optimization method with a hybrid parallelstr...This paper aims to solve large-scale and complex isogeometric topology optimization problems that consumesignificant computational resources. A novel isogeometric topology optimization method with a hybrid parallelstrategy of CPU/GPU is proposed, while the hybrid parallel strategies for stiffness matrix assembly, equationsolving, sensitivity analysis, and design variable update are discussed in detail. To ensure the high efficiency ofCPU/GPU computing, a workload balancing strategy is presented for optimally distributing the workload betweenCPU and GPU. To illustrate the advantages of the proposedmethod, three benchmark examples are tested to verifythe hybrid parallel strategy in this paper. The results show that the efficiency of the hybrid method is faster thanserial CPU and parallel GPU, while the speedups can be up to two orders of magnitude.展开更多
Previous studies have shown that deep learning is very effective in detecting known attacks.However,when facing unknown attacks,models such as Deep Neural Networks(DNN)combined with Long Short-Term Memory(LSTM),Convol...Previous studies have shown that deep learning is very effective in detecting known attacks.However,when facing unknown attacks,models such as Deep Neural Networks(DNN)combined with Long Short-Term Memory(LSTM),Convolutional Neural Networks(CNN)combined with LSTM,and so on are built by simple stacking,which has the problems of feature loss,low efficiency,and low accuracy.Therefore,this paper proposes an autonomous detectionmodel for Distributed Denial of Service attacks,Multi-Scale Convolutional Neural Network-Bidirectional Gated Recurrent Units-Single Headed Attention(MSCNN-BiGRU-SHA),which is based on a Multistrategy Integrated Zebra Optimization Algorithm(MI-ZOA).The model undergoes training and testing with the CICDDoS2019 dataset,and its performance is evaluated on a new GINKS2023 dataset.The hyperparameters for Conv_filter and GRU_unit are optimized using the Multi-strategy Integrated Zebra Optimization Algorithm(MIZOA).The experimental results show that the test accuracy of the MSCNN-BiGRU-SHA model based on the MIZOA proposed in this paper is as high as 0.9971 in the CICDDoS 2019 dataset.The evaluation accuracy of the new dataset GINKS2023 created in this paper is 0.9386.Compared to the MSCNN-BiGRU-SHA model based on the Zebra Optimization Algorithm(ZOA),the detection accuracy on the GINKS2023 dataset has improved by 5.81%,precisionhas increasedby 1.35%,the recallhas improvedby 9%,and theF1scorehas increasedby 5.55%.Compared to the MSCNN-BiGRU-SHA models developed using Grid Search,Random Search,and Bayesian Optimization,the MSCNN-BiGRU-SHA model optimized with the MI-ZOA exhibits better performance in terms of accuracy,precision,recall,and F1 score.展开更多
Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy absorption.However,when subjected to significant stretching...Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy absorption.However,when subjected to significant stretching,NPR metamaterials designed under small strain assumption may experience a rapid degradation in NPR performance.To address this issue,this study aims to design metamaterials maintaining a targeted NPR under large deformation by taking advantage of the geometry nonlinearity mechanism.A representative periodic unit cell is modeled considering geometry nonlinearity,and its topology is designed using a gradient-free method.The unit cell microstructural topologies are described with the material-field series-expansion(MFSE)method.The MFSE method assumes spatial correlation of the material distribution,which greatly reduces the number of required design variables.To conveniently design metamaterials with desired NPR under large deformation,we propose a two-stage gradient-free metamaterial topology optimization method,which fully takes advantage of the dimension reduction benefits of the MFSE method and the Kriging surrogate model technique.Initially,we use homogenization to find a preliminary NPR design under a small deformation assumption.In the second stage,we begin with this preliminary design and minimize deviations in NPR from a targeted value under large deformation.Using this strategy and solution technique,we successfully obtain a group of NPR metamaterials that can sustain different desired NPRs in the range of[−0.8,−0.1]under uniaxial stretching up to 20% strain.Furthermore,typical microstructure designs are fabricated and tested through experiments.The experimental results show good consistency with our numerical results,demonstrating the effectiveness of the present gradientfree NPR metamaterial design strategy.展开更多
文摘The optimization of civil engineering structures is critical for enhancing structural performance and material efficiency in engineering applications.Structural optimization approaches seek to determine the optimal design,by considering material performance,cost,and structural safety.The design approaches aim to reduce the built environment’s energy use and carbon emissions.This comprehensive review examines optimization techniques,including size,shape,topology,and multi-objective approaches,by integrating these methodologies.The trends and advancements that contribute to developing more efficient,cost-effective,and reliable structural designs were identified.The review also discusses emerging technologies,such as machine learning applications with different optimization techniques.Optimization of truss,frame,tensegrity,reinforced concrete,origami,pantographic,and adaptive structures are covered and discussed.Optimization techniques are explained,including metaheuristics,genetic algorithm,particle swarm,ant-colony,harmony search algorithm,and their applications with mentioned structure types.Linear and non-linear structures,including geometric and material nonlinearity,are distinguished.The role of optimization in active structures,structural design,seismic design,form-finding,and structural control is taken into account,and the most recent techniques and advancements are mentioned.
基金supported by the National Key R&D Program of China(2023YFB2504601)National Natural Science Foundation of China(52205267).
文摘Due to the high-order B-spline basis functions utilized in isogeometric analysis(IGA)and the repeatedly updating global stiffness matrix of topology optimization,Isogeometric topology optimization(ITO)intrinsically suffers from the computationally demanding process.In this work,we address the efficiency problem existing in the assembling stiffness matrix and sensitivity analysis using B˙ezier element stiffness mapping.The Element-wise and Interaction-wise parallel computing frameworks for updating the global stiffness matrix are proposed for ITO with B˙ezier element stiffness mapping,which differs from these ones with the traditional Gaussian integrals utilized.Since the explicit stiffness computation formula derived from B˙ezier element stiffness mapping possesses a typical parallel structure,the presented GPU-enabled ITO method can greatly accelerate the computation speed while maintaining its high memory efficiency unaltered.Numerical examples demonstrate threefold speedup:1)the assembling stiffness matrix is accelerated by 10×maximumly with the proposed GPU strategy;2)the solution efficiency of a sparse linear system is enhanced by up to 30×with Eigen replaced by AMGCL;3)the efficiency of sensitivity analysis is promoted by 100×with GPU applied.Therefore,the proposed method is a promising way to enhance the numerical efficiency of ITO for both single-patch and multiple-patch design problems.
基金supported by the Aeronautical Science Foundation of China(Grant No.2020Z009063001)the Fundamental Research Funds for the Central Universities(Grant No.DUT22GF303).
文摘Topology optimization of thermal-fluid coupling problems has received widespread attention.This article proposes a novel topology optimization method for laminar two-fluid heat exchanger design.The proposed method utilizes an artificial density field to create two permeability interpolation functions that exhibit opposing trends,ensuring separation between the two fluid domains.Additionally,a Gaussian function is employed to construct an interpolation function for the thermal conductivity coefficient.Furthermore,a computational program has been developed on the OpenFOAM platform for the topology optimization of two-fluid heat exchangers.This program leverages parallel computing,significantly reducing the time required for the topology optimization process.To enhance computational speed and reduce the number of constraint conditions,we replaced the conventional pressure drop constraint condition in the optimization problem with a pressure inlet/outlet boundary condition.The 3D optimization results demonstrate the characteristic features of a surface structure,providing valuable guidance for designing heat exchangers that achieve high heat exchange efficiency while minimizing excessive pressure loss.At the same time,a new structure appears in large-scale topology optimization,which proves the effectiveness and stability of the topology optimization program written in this paper in large-scale calculation.
基金This study is financially supported by StateKey Laboratory of Alternate Electrical Power System with Renewable Energy Sources(Grant No.LAPS22012).
文摘This paper aims to propose a topology optimization method on generating porous structures comprising multiple materials.The mathematical optimization formulation is established under the constraints of individual volume fraction of constituent phase or total mass,as well as the local volume fraction of all phases.The original optimization problem with numerous constraints is converted into a box-constrained optimization problem by incorporating all constraints to the augmented Lagrangian function,avoiding the parameter dependence in the conventional aggregation process.Furthermore,the local volume percentage can be precisely satisfied.The effects including the globalmass bound,the influence radius and local volume percentage on final designs are exploited through numerical examples.The numerical results also reveal that porous structures keep a balance between the bulk design and periodic design in terms of the resulting compliance.All results,including those for irregular structures andmultiple volume fraction constraints,demonstrate that the proposedmethod can provide an efficient solution for multiple material infill structures.
基金the National Natural Science Foundation of China and the Natural Science Foundation of Jiangsu Province.It was also supported in part by Young Elite Scientists Sponsorship Program by CAST.
文摘Large cavity structures are widely employed in aerospace engineering, such as thin-walled cylinders, blades andwings. Enhancing performance of aerial vehicles while reducing manufacturing costs and fuel consumptionhas become a focal point for contemporary researchers. Therefore, this paper aims to investigate the topologyoptimization of large cavity structures as a means to enhance their performance, safety, and efficiency. By usingthe variable density method, lightweight design is achieved without compromising structural strength. Theoptimization model considers both concentrated and distributed loads, and utilizes techniques like sensitivityfiltering and projection to obtain a robust optimized configuration. The mechanical properties are checked bycomparing the stress distribution and displacement of the unoptimized and optimized structures under the sameload. The results confirm that the optimized structures exhibit improved mechanical properties, thus offering keyinsights for engineering lightweight, high-strength large cavity structures.
基金Supported by 2021 Zhanjiang University of Science and Technology"Brand Enhancement Plan"Project:Network Series Course Teaching Team(PPJH202102JXTD)2022 Zhanjiang University of Science and Technology"Brand Enhancement Plan"Project:Network Engineering(PPJHKCSZ-2022301)+1 种基金2023 Zhanjiang Science and Technology Bureau Project:Design and Simulation of Zhanjiang Mangrove Wetland Monitoring Network System(2023B01017)2022 Zhanjiang University of Science and Technology Quality Engineering Project:Audiovisual Language Teaching and Research Office(ZLGC202203).
文摘Background With the development of the Internet,the topology optimization of wireless sensor networks has received increasing attention.However,traditional optimization methods often overlook the energy imbalance caused by node loads,which affects network performance.Methods To improve the overall performance and efficiency of wireless sensor networks,a new method for optimizing the wireless sensor network topology based on K-means clustering and firefly algorithms is proposed.The K-means clustering algorithm partitions nodes by minimizing the within-cluster variance,while the firefly algorithm is an optimization algorithm based on swarm intelligence that simulates the flashing interaction between fireflies to guide the search process.The proposed method first introduces the K-means clustering algorithm to cluster nodes and then introduces a firefly algorithm to dynamically adjust the nodes.Results The results showed that the average clustering accuracies in the Wine and Iris data sets were 86.59%and 94.55%,respectively,demonstrating good clustering performance.When calculating the node mortality rate and network load balancing standard deviation,the proposed algorithm showed dead nodes at approximately 50 iterations,with an average load balancing standard deviation of 1.7×10^(4),proving its contribution to extending the network lifespan.Conclusions This demonstrates the superiority of the proposed algorithm in significantly improving the energy efficiency and load balancing of wireless sensor networks to extend the network lifespan.The research results indicate that wireless sensor networks have theoretical and practical significance in fields such as monitoring,healthcare,and agriculture.
基金Project supported by the Open Fund of Wuhan National Research Center for Optoelectronics(Grant No.2022WNLOKF012)the National College Students Innovation Innovation and Entrepreneurship Training Program(Grant No.2023102930147).
文摘A broadband polarization-independent terahertz multifunctional coding metasurface based on topological optimization using liquid crystal(LC)is proposed.The metasurface can achieve reconfigurability for beam steering and vortex beam generation within a frequency range of 0.68 THz–0.72 THz.Firstly,the metasurface unit is topologically optimized using the non-dominant sequencing genetic algorithms(NSGA-II)multi-objective optimization algorithm.By applying the LC’s electrically tunable refractive index properties,the metasurface unit enables polarization-independent 2-bit coding within a frequency range of 0.68 THz–0.72 THz.Then,based on the designed metasurface unit,the array arrangement of the metasurface is reverse-designed to achieve beam steering and vortex beam generation.The results show that,for beam steering,not only can polarization-independent steering of both single-and multi-beam be achieved within the 35°elevation angle range,but also independent control of the target angle of each beam in the multi-beam steering.For vortex beam generation,the metasurfaces can achieve the generation of single-and multi-vortex beams with topological charges l=±1,±2 within the 35elevation angle range,and the generation angles of each vortex beam in the multi-vortex beam can be independently controlled.This provides flexibility and diversity in the generation of vortex beams.Therefore,the proposed terahertz LC metasurface can realize flexible control of reconfigurable functions and has certain application prospects in terahertz communication,phased array radar,and vortex radar.
基金Supported by National Natural Science Foundation of China (Grant Nos.12072219,12202303,12272254)Shanxi Provincial Excellent Talents Science and Technology Innovation Project of China (Grant No.201805D211033)。
文摘The current research of sandwich structures under dynamic loading mainly focus on the response characteristic of structure.The micro-topology of core layers would sufficiently influence the property of sandwich structure.However,the micro deformation and topology mechanism of structural deformation and energy absorption are unclear.In this paper,based on the bi-directional evolutionary structural optimization method and periodic base cell(PBC)technology,a topology optimization frame work is proposed to optimize the core layer of sandwich beams.The objective of the present optimization problem is to maximize shear stiffness of PBC with a volume constraint.The effects of the volume fraction,filter radius,and initial PBC aspect ratio on the micro-topology of the core were discussed.The dynamic response process,core compression,and energy absorption capacity of the sandwich beams under blast impact loading were analyzed by the finite element method.The results demonstrated that the overpressure action stage was coupled with the core compression stage.Under the same loading and mass per unit area,the sandwich beam with a 20%volume fraction core layer had the best blast resistance.The filter radius has a slight effect on the shear stiffness and blast resistances of the sandwich beams.But increasing the filter radius could slightly improve the bending stiffness.Upon changing the initial PBC aspect ratio,there are three ways for PBC evolution:The first is to change the angle between the adjacent bars,the second is to further form holes in the bars,and the third is to combine the first two ways.However,not all three ways can improve the energy absorption capacity of the structure.Changing the aspect ratio of the PBC arbitrarily may lead to worse results.More studies are necessary for further detailed optimization.This research proposes a new topology sandwich beam structure by micro-topology optimization,which has sufficient shear stiffness.The micro mechanism of structural energy absorption is clarified,it is significant for structural energy absorption design.
基金Supported by National Natural Science Foundation of China (Grant No.51875545)Innovation Grant of Changchun Institute of Optics+2 种基金Fine Mechanics and Physics (CIOMP)CAS Project for Young Scientists in Basic Research of China (Grant No.YSBR-066)Science and Technology Development Program of Jilin Province of China (Grant No.SKL202302020)。
文摘This paper presents a topology optimization approach for the surface flows on variable design domains.Via this approach,the matching between the pattern of a surface flow and the 2-manifold used to define the pattern can be optimized,where the 2-manifold is implicitly defined on another fixed 2-manifold named as the base manifold.The fiber bundle topology optimization approach is developed based on the description of the topological structure of the surface flow by using the differential geometry concept of the fiber bundle.The material distribution method is used to achieve the evolution of the pattern of the surface flow.The evolution of the implicit 2-manifold is realized via a homeomorphous map.The design variable of the pattern of the surface flow and that of the implicit 2-manifold are regularized by two sequentially implemented surface-PDE filters.The two surface-PDE filters are coupled,because they are defined on the implicit 2-manifold and base manifold,respectively.The surface Navier-Stokes equations,defined on the implicit 2-manifold,are used to describe the surface flow.The fiber bundle topology optimization problem is analyzed using the continuous adjoint method implemented on the first-order Sobolev space.Several numerical examples have been provided to demonstrate this approach,where the combination of the viscous dissipation and pressure drop is used as the design objective.
基金Project supported by the National Natural Science Foundation of China (Nos.12072007,12072006,12132001,and 52192632)the Ningbo Natural Science Foundation of Zhejiang Province of China (No.202003N4018)the Defense Industrial Technology Development Program of China (Nos.JCKY2019205A006,JCKY2019203A003,and JCKY2021204A002)。
文摘A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific problem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analysis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples.
基金supported by the National Natural Science Foundation of China(Nos.52171327,11991032,52201386,and 51805537)。
文摘Chiral metamaterials have been proven to possess many appealing mechanical phenomena,such as negative Poisson's ratio,high-impact resistance,and energy absorption.This work extends the applications of chiral metamaterials to underwater sound insulation.Various chiral metamaterials with low acoustic impedance and proper stiffness are inversely designed using the topology optimization scheme.Low acoustic impedance enables the metamaterials to have a high and broadband sound transmission loss(STL),while proper stiffness guarantees its robust acoustic performance under a hydrostatic pressure.As proof-of-concept demonstrations,two specimens are fabricated and tested in a water-filled impedance tube.Experimental results show that,on average,over 95%incident sound energy can be isolated by the specimens in a broad frequency range from 1 k Hz to 5 k Hz,while the sound insulation performance keeps stable under a certain hydrostatic pressure.This work may provide new insights for chiral metamaterials into the underwater applications with sound insulation.
基金supported by the National Natural Science Foundation of China(Grant No.12272144).
文摘By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.
基金supported by the National Natural Science Foundation of China(Grant 52175236).
文摘This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design.The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads.The topology optimization formula is combined with the ordered solid isotropic material with penalization(ordered-SIMP)multi-material interpolation model.The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function.Furthermore,the sequential optimization and reliability assessment(SORA)is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization(DTO)problem.Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point(MPP).In each cycle,the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle.The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method(MMA)is used to update design variables.Finally,the validity and feasibility of the method are verified by the numerical example of L-shape beam design,T-shape structure design,steering knuckle,and 3D T-shaped beam.
基金supported in part by National Natural Science Foundation of China under Grant Nos.51675525,52005505,and 62001502Post-Graduate Scientific Research Innovation Project of Hunan Province under Grant No.XJCX2023185.
文摘In recent years,there has been significant research on the application of deep learning(DL)in topology optimization(TO)to accelerate structural design.However,these methods have primarily focused on solving binary TO problems,and effective solutions for multi-material topology optimization(MMTO)which requires a lot of computing resources are still lacking.Therefore,this paper proposes the framework of multiphase topology optimization using deep learning to accelerate MMTO design.The framework employs convolutional neural network(CNN)to construct a surrogate model for solving MMTO,and the obtained surrogate model can rapidly generate multi-material structure topologies in negligible time without any iterations.The performance evaluation results show that the proposed method not only outputs multi-material topologies with clear material boundary but also reduces the calculation cost with high prediction accuracy.Additionally,in order to find a more reasonable modeling method for MMTO,this paper studies the characteristics of surrogate modeling as regression task and classification task.Through the training of 297 models,our findings show that the regression task yields slightly better results than the classification task in most cases.Furthermore,The results indicate that the prediction accuracy is primarily influenced by factors such as the TO problem,material category,and data scale.Conversely,factors such as the domain size and the material property have minimal impact on the accuracy.
基金supported by the National Natural Science Foundation of China (NSFC)under Grant Nos.12172350,11772322 and 11702238。
文摘We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods mainly contain shape and topology schemes,with the former changing the surface geometric profile of the structure and the latter changing thematerial distribution topology or hole topology of the structure.In the present acoustic performance optimization,the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure,the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter,and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge.The topology and shape sensitivities of the approach are calculated using the adjoint variable method,which ensures the efficiency of the optimization.The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization.Numerical examples are given to validate the effectiveness of the presented optimization approach.
基金financially supported by the National Key R&D Program (2022YFB4201302)Guang Dong Basic and Applied Basic Research Foundation (2022A1515240057)the Huaneng Technology Funds (HNKJ20-H88).
文摘This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.
基金sponsored by the National Key Research and Development Program of China[Grant Nos.2020YFC0826804 and 2022YFC3320504]the National Natural Science Foundation of China[Grant No.11772059]。
文摘Material and structure made by additive manufacturing(AM)have received much attention lately due to their flexibility and ability to customize complex structures.This study first implements multiple objective topology optimization simulations based on a projectile perforation model,and a new topologic projectile is obtained.Then two types of 316L stainless steel projectiles(the solid and the topology)are printed in a selective laser melt(SLM)machine to evaluate the penetration performance of the projectiles by the ballistic test.The experiment results show that the dimensionless specific kinetic energy value of topologic projectiles is higher than that of solid projectiles,indicating the better penetration ability of the topologic projectiles.Finally,microscopic studies(scanning electron microscope and X-ray micro-CT)are performed on the remaining projectiles to investigate the failure mechanism of the internal structure of the topologic projectiles.An explicit dynamics simulation was also performed,and the failure locations of the residual topologic projectiles were in good agreement with the experimental results,which can better guide the design of new projectiles combining AM and topology optimization in the future.
基金the National Key R&D Program of China(2020YFB1708300)the National Natural Science Foundation of China(52005192)the Project of Ministry of Industry and Information Technology(TC210804R-3).
文摘This paper aims to solve large-scale and complex isogeometric topology optimization problems that consumesignificant computational resources. A novel isogeometric topology optimization method with a hybrid parallelstrategy of CPU/GPU is proposed, while the hybrid parallel strategies for stiffness matrix assembly, equationsolving, sensitivity analysis, and design variable update are discussed in detail. To ensure the high efficiency ofCPU/GPU computing, a workload balancing strategy is presented for optimally distributing the workload betweenCPU and GPU. To illustrate the advantages of the proposedmethod, three benchmark examples are tested to verifythe hybrid parallel strategy in this paper. The results show that the efficiency of the hybrid method is faster thanserial CPU and parallel GPU, while the speedups can be up to two orders of magnitude.
基金supported by Science and Technology Innovation Programfor Postgraduate Students in IDP Subsidized by Fundamental Research Funds for the Central Universities(Project No.ZY20240335)support of the Research Project of the Key Technology of Malicious Code Detection Based on Data Mining in APT Attack(Project No.2022IT173)the Research Project of the Big Data Sensitive Information Supervision Technology Based on Convolutional Neural Network(Project No.2022011033).
文摘Previous studies have shown that deep learning is very effective in detecting known attacks.However,when facing unknown attacks,models such as Deep Neural Networks(DNN)combined with Long Short-Term Memory(LSTM),Convolutional Neural Networks(CNN)combined with LSTM,and so on are built by simple stacking,which has the problems of feature loss,low efficiency,and low accuracy.Therefore,this paper proposes an autonomous detectionmodel for Distributed Denial of Service attacks,Multi-Scale Convolutional Neural Network-Bidirectional Gated Recurrent Units-Single Headed Attention(MSCNN-BiGRU-SHA),which is based on a Multistrategy Integrated Zebra Optimization Algorithm(MI-ZOA).The model undergoes training and testing with the CICDDoS2019 dataset,and its performance is evaluated on a new GINKS2023 dataset.The hyperparameters for Conv_filter and GRU_unit are optimized using the Multi-strategy Integrated Zebra Optimization Algorithm(MIZOA).The experimental results show that the test accuracy of the MSCNN-BiGRU-SHA model based on the MIZOA proposed in this paper is as high as 0.9971 in the CICDDoS 2019 dataset.The evaluation accuracy of the new dataset GINKS2023 created in this paper is 0.9386.Compared to the MSCNN-BiGRU-SHA model based on the Zebra Optimization Algorithm(ZOA),the detection accuracy on the GINKS2023 dataset has improved by 5.81%,precisionhas increasedby 1.35%,the recallhas improvedby 9%,and theF1scorehas increasedby 5.55%.Compared to the MSCNN-BiGRU-SHA models developed using Grid Search,Random Search,and Bayesian Optimization,the MSCNN-BiGRU-SHA model optimized with the MI-ZOA exhibits better performance in terms of accuracy,precision,recall,and F1 score.
基金the support of the National Science Foundation of China(12372120,12172075)the Liaoning Revitalization Talents Program(XLYC2007027)Fundamental Research Funds for the Central Universities(DUT21RC(3)067).
文摘Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy absorption.However,when subjected to significant stretching,NPR metamaterials designed under small strain assumption may experience a rapid degradation in NPR performance.To address this issue,this study aims to design metamaterials maintaining a targeted NPR under large deformation by taking advantage of the geometry nonlinearity mechanism.A representative periodic unit cell is modeled considering geometry nonlinearity,and its topology is designed using a gradient-free method.The unit cell microstructural topologies are described with the material-field series-expansion(MFSE)method.The MFSE method assumes spatial correlation of the material distribution,which greatly reduces the number of required design variables.To conveniently design metamaterials with desired NPR under large deformation,we propose a two-stage gradient-free metamaterial topology optimization method,which fully takes advantage of the dimension reduction benefits of the MFSE method and the Kriging surrogate model technique.Initially,we use homogenization to find a preliminary NPR design under a small deformation assumption.In the second stage,we begin with this preliminary design and minimize deviations in NPR from a targeted value under large deformation.Using this strategy and solution technique,we successfully obtain a group of NPR metamaterials that can sustain different desired NPRs in the range of[−0.8,−0.1]under uniaxial stretching up to 20% strain.Furthermore,typical microstructure designs are fabricated and tested through experiments.The experimental results show good consistency with our numerical results,demonstrating the effectiveness of the present gradientfree NPR metamaterial design strategy.
