This paper proposes an effective reliability design optimizationmethod for fail-safe topology optimization(FSTO)considering uncertainty based on the moving morphable bars method to establish the ideal balance between ...This paper proposes an effective reliability design optimizationmethod for fail-safe topology optimization(FSTO)considering uncertainty based on the moving morphable bars method to establish the ideal balance between cost and robustness,reliability and structural safety.To this end,a performancemeasure approach(PMA)-based doubleloop optimization algorithmis developed tominimize the relative volume percentage while achieving the reliability criterion.To ensure the compliance value of the worst failure case can better approximate the quantified design requirement,a p-norm constraint approach with correction parameter is introduced.Finally,the significance of accounting for uncertainty in the fail-safe design is illustrated by contrasting the findings of the proposed reliabilitybased topology optimization(RBTO)method with those of the deterministic design method in three typical examples.Monte Carlo simulation shows that the relative error of the reliability index of the optimized structure does not exceed 3%.展开更多
This study proposes a non-probabilistic reliability-based topology optimization(NRBTO)method based on isogeometric analysis(IGA),considering the structural stiffness performance.In this study,a geometric model was con...This study proposes a non-probabilistic reliability-based topology optimization(NRBTO)method based on isogeometric analysis(IGA),considering the structural stiffness performance.In this study,a geometric model was constructed using non-uniform rational B-splines(NURBS),and the NURBS basis function was used as the shape function of the analytical model.In topology optimization,the classic finite element method(FEM)was replaced by a mesh-independent IGA method.The formulation of isogeometric topology optimization(ITO)based on the solid isotropic microstructures with penalization(SIMP)interpolation model was derived,and a sensitivity analysis was performed using the adjoint method.Considering the uncertainties of material properties and loads,the parameter uncertainty is quantified by interval theory,the propagation analysis is conducted using the interval parametric vertex method,the optimization feature distance is selected as the nonprobabilistic reliability-based index,and a sensitivity analysis is performed on the reliability index to establish a reliability-based topology optimization method based on isogeometric analysis.The method of moving asymptotes(MMA)is used to solve the optimization problem.Several numerical examples were used to verify the method’s effectiveness in practical applications.展开更多
The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is m...The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is mainly used for finite element analysis at present,and the effectiveness of the surrogate material model has been fully confirmed.However,there are some accuracy problems when dealing with boundary elements using the surrogate material model,which will affect the topology optimization results.In this study,a boundary element reconstruction(BER)model is proposed based on the surrogate material model under the MMC topology optimization framework to improve the accuracy of topology optimization.The proposed BER model can reconstruct the boundary elements by refining the local meshes and obtaining new nodes in boundary elements.Then the density of boundary elements is recalculated using the new node information,which is more accurate than the original model.Based on the new density of boundary elements,the material properties and volume information of the boundary elements are updated.Compared with other finite element analysis methods,the BER model is simple and feasible and can improve computational accuracy.Finally,the effectiveness and superiority of the proposed method are verified by comparing it with the optimization results of the original surrogate material model through several numerical examples.展开更多
Reliability and optimization are two key elements for structural design. The reliability~ based topology optimization （RBTO） is a powerful and promising methodology for finding the optimum topologies with the uncert...Reliability and optimization are two key elements for structural design. The reliability~ based topology optimization （RBTO） is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topol- ogy optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach （the performance measure approach, PMA） and the decoupled approaches （the so-called Hybrid method and the sequential optimization and reliability assessment, SORA）. For reliability analysis, the stochastic response surface method （SRSM） was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique. The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the de- terministic, RBTOs were compared with one another; and useful conclusions regarding validity, accuracy and efficiency were drawn.展开更多
Based on the level set model and the reliability theory, a numerical approach of reliability-based topology optimization for compliant mechanisms with multiple inputs and outputs is presented. A multi-objective topolo...Based on the level set model and the reliability theory, a numerical approach of reliability-based topology optimization for compliant mechanisms with multiple inputs and outputs is presented. A multi-objective topology optimal model of compliant mechanisms considering uncertainties of the loads, material properties, and member geometries is developed. The reliability analysis and topology optimization are integrated in the optimal iterative process. The reliabilities of the compliant mechanisms are evaluated by using the first order reliability method. Meanwhile, the problem of structural topology optimization is solved by the level set method which is flexible in handling complex topological changes and concise in describing the boundary shape of the mechanism. Numerical examples show the importance of considering the stochastic nature of the compliant mechanisms in the topology optimization process.展开更多
It is essential to consider the effects of incomplete measurement,inaccurate information and inadequate cognition on structural topology optimization.For the multi-material structural topology optimization with non-pr...It is essential to consider the effects of incomplete measurement,inaccurate information and inadequate cognition on structural topology optimization.For the multi-material structural topology optimization with non-probability uncertainty,the multi-material interpolation model is represented by the ordered rational approximation of mat erial properties(ordered RAMP).Combined with structural compliance minimization,the multi-material topology optimization with reliability constraints is established.The corresponding non-probability uncertainties are described by the evidence theory,and the uniformity processing method is introduced to convert the evidence variables into random variables.The first-order reliability method is employed to search the most probable point under the reliability index constraint,and then the random variables are equivalent to the deterministic variables according to the geometric meaning of the reliability index and sensitivity information.Therefore,the non-probabilistic reliability-based multi-material topology optimization is transformed into the conventional deterministic optimization format,followed by the ordered RAMP method to solve the optimization problem.Finally,through numerical examples of 2D and 3D structures,the feasibility and effectiveness of the proposed method are verified to consider the geometrical dimensions and external loading uncertainties.展开更多
Metalens technology has been applied extensively in miniaturized and integrated infrared imaging systems.However,due to the high phase dispersion of unit structures,metalens often exhibits chromatic aberration,making ...Metalens technology has been applied extensively in miniaturized and integrated infrared imaging systems.However,due to the high phase dispersion of unit structures,metalens often exhibits chromatic aberration,making broadband achromatic infrared imaging challenging to achieve.In this paper,six different unit structures based on chalcogenide glass are constructed,and their phase-dispersion parameters are analyzed to establish a database.On this basis,using chromatic aberration compensation and parameterized adjoint topology optimization,a broadband achromatic metalens with a numerical aperture of 0.5 is designed by arranging these six unit structures in the far-infrared band.Simulation results show that the metalens achieves near diffraction-limited focusing within the operating wavelength range of 9−11μm,demonstrating the good performance of achromatic aberration with flat focusing efficiency of 54%−58%across all wavelengths.展开更多
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
This study presents an extension of multiscale topology optimization by integrating both yield stress and local/global buckling considerations into the design process.Building upon established multiscale methodologies...This study presents an extension of multiscale topology optimization by integrating both yield stress and local/global buckling considerations into the design process.Building upon established multiscale methodologies,we develop a new framework incorporating yield stress limits either as constraints or objectives alongside previously established local and global buckling constraints.This approach significantly refines the optimization process,ensuring that the resulting designs meet mechanical performance criteria and adhere to critical material yield constraints.First,we establish local density-dependent von Mises yield surfaces based on local yield estimates from homogenization-based analysis to predict the local yield limits of the homogenized materials.Then,these local yield-based load factors are combined with local and global buckling criteria to obtain topology optimized designs that consider yield and buckling failure on all levels.This integration is crucial for the practical application of optimized structures in real-world scenarios,where material yield and stability behavior critically influence structural integrity and durability.Numerical examples demonstrate how optimized designs depend on the stiffness to yield ratio of the considered building material.Despite the foundational assumption of the separation of scales,the de-homogenized structures,even at relatively coarse length scales,exhibit a remarkably high degree of agreement with the corresponding homogenized predictions.展开更多
A data-driven model ofmultiple variable cutting(M-VCUT)level set-based substructure is proposed for the topology optimization of lattice structures.TheM-VCUTlevel setmethod is used to represent substructures,enriching...A data-driven model ofmultiple variable cutting(M-VCUT)level set-based substructure is proposed for the topology optimization of lattice structures.TheM-VCUTlevel setmethod is used to represent substructures,enriching their diversity of configuration while ensuring connectivity.To construct the data-driven model of substructure,a database is prepared by sampling the space of substructures spanned by several substructure prototypes.Then,for each substructure in this database,the stiffness matrix is condensed so that its degrees of freedomare reduced.Thereafter,the data-drivenmodel of substructures is constructed through interpolationwith compactly supported radial basis function(CS-RBF).The inputs of the data-driven model are the design variables of topology optimization,and the outputs are the condensed stiffness matrix and volume of substructures.During the optimization,this data-driven model is used,thus avoiding repeated static condensation that would requiremuch computation time.Several numerical examples are provided to verify the proposed method.展开更多
As primary load-bearing components extensively utilized in engineering applications,beam structures necessitate the design of their microstructural configurations to achieve lightweight objectives while satisfying div...As primary load-bearing components extensively utilized in engineering applications,beam structures necessitate the design of their microstructural configurations to achieve lightweight objectives while satisfying diverse mechanical performance requirements.Combining topology optimization with fully coupled homogenization beam theory,we provide a highly efficient design tool to access desirable periodic microstructures for beams.The present optimization framework comprehensively takes into account for key deformation modes,including tension,bending,torsion,and shear deformation,all within a unified formulation.Several numerical results prove that our method can be used to handle kinds of microstructure design for beam-like structures,e.g.,extreme tension(compression)-torsion stiffness,maximization of minimum critical buckling load,and minimization of structural compliance.When optimizing microstructures for macroscopic performance,we emphasize investigating the influence of shear stiffness on the optimized results.The novel chiral beam-like structures are fabricated and tested.The experimental results indicate that the optimized tension(compression)-torsion structure has excellent buffer characteristics,as compared with the traditional square tube.This proposed optimization framework can be further extended to other physical problems of Timoshenko beams.展开更多
Current topology optimization methods for nonlinear continuum structures often suffer from low computational efficiency and limited applicability to complex nonlinear problems.To address these issues,this paper propos...Current topology optimization methods for nonlinear continuum structures often suffer from low computational efficiency and limited applicability to complex nonlinear problems.To address these issues,this paper proposes an improved bi-directional evolutionary structural optimization(BESO)method tailored for maximizing stiffness in nonlinear structures.The optimization program is developed in Python and can be combined with Abaqus software to facilitate finite element analysis(FEA).To accelerate the speed of optimization,a novel adaptive evolutionary ratio(ER)strategy based on the BESO method is introduced,with four distinct adaptive ER functions proposed.The Newton-Raphson method is utilized for iteratively solving nonlinear equilibrium equations,and the sensitivity information for updating design variables is derived using the adjoint method.Additionally,this study extends topology optimization to account for both material nonlinearity and geometric nonlinearity,analyzing the effects of various nonlinearities.A series of comparative studies are conducted using benchmark cases to validate the effectiveness of the proposed method.The results show that the BESO method with adaptive ER significantly improves the optimization efficiency.Compared to the BESO method with a fixed ER,the convergence speed of the four adaptive ER BESO methods is increased by 37.3%,26.7%,12%and 18.7%,respectively.Given that Abaqus is a powerful FEA platform,this method has the potential to be extended to large-scale engineering structures and to address more complex optimization problems.This research proposes an improved BESO method with novel adaptive ER,which significantly accelerates the optimization process and enables its application to topology optimization of nonlinear structures.展开更多
Structural Reliability-Based Topology Optimization(RBTO),as an efficient design methodology,serves as a crucial means to ensure the development ofmodern engineering structures towards high performance,long service lif...Structural Reliability-Based Topology Optimization(RBTO),as an efficient design methodology,serves as a crucial means to ensure the development ofmodern engineering structures towards high performance,long service life,and high reliability.However,in practical design processes,topology optimization must not only account for the static performance of structures but also consider the impacts of various responses and uncertainties under complex dynamic conditions,which traditional methods often struggle accommodate.Therefore,this study proposes an RBTO framework based on a Kriging-assisted level set function and a novel Dynamic Hybrid Particle Swarm Optimization(DHPSO)algorithm.By leveraging the Kriging model as a surrogate,the high cost associated with repeatedly running finite element analysis processes is reduced,addressing the issue of minimizing structural compliance.Meanwhile,the DHPSO algorithm enables a better balance between the population’s developmental and exploratory capabilities,significantly accelerating convergence speed and enhancing global convergence performance.Finally,the proposed method is validated through three different structural examples,demonstrating its superior performance.Observed that the computational that,compared to the traditional Solid Isotropic Material with Penalization(SIMP)method,the proposed approach reduces the upper bound of structural compliance by approximately 30%.Additionally,the optimized results exhibit clear material interfaces without grayscale elements,and the stress concentration factor is reduced by approximately 42%.Consequently,the computational results fromdifferent examples verify the effectiveness and superiority of this study across various fields,achieving the goal of providing more precise optimization results within a shorter timeframe.展开更多
The integration of additive manufacturing(AM)and topology optimization(TO)has revolutionized the design and production of advanced equipment,providing innovative approaches to solving complex engineering challenges.In...The integration of additive manufacturing(AM)and topology optimization(TO)has revolutionized the design and production of advanced equipment,providing innovative approaches to solving complex engineering challenges.In the nuclear energy sector,achieving an optimal balance between the thermal and hydraulic performance of prismatic fuel elements has long been a key challenge.This study utilizes a coupled fluid-thermal TO method to design fuel elements with one,three,five,and seven inlets/outlets configurations suitable for AM.We systematically examine the impact of varying the number of inlets/outlets on the thermal-hydraulic performance of the elements.The results show that increasing the number of inlets/outlets can enhance the thermal performance of the fuel elements while sacrificing the hydraulic performance.Compared with the conventional design,the 5 inlets/outlets configuration achieved a coordinated improvement in both thermal and hydraulic performance,with a 2.38%enhancement in thermal performance and a 4.38%improvement in hydraulic performance.These findings highlight the significant potential of TO in improving the performance of fuel elements and strongly demonstrate the advantages of the collaborative application of AM and TO.展开更多
Inspired by natural biomimetic structures exemplified by femoral bones,the shell-infill composite design has emerged as a research focus in structural optimization.However,existing studies predominantly focus on unifo...Inspired by natural biomimetic structures exemplified by femoral bones,the shell-infill composite design has emerged as a research focus in structural optimization.However,existing studies predominantly focus on uniform-thickness shell designs and lack robust methodologies for generating high-resolution porous infill configurations.To address these challenges,a novel topology optimization framework for full-scale shell-filled composite structures is developed in this paper.First,a physics-driven,non-uniform partial differential equation(PDE)filter is developed,enabling precise control of variable-thickness shells by establishing explicit mapping relationships between shell thickness and filter radii.Second,this study addresses the convergence inefficiency of traditional full-scale topology optimization methods based on local volume constraints.It is revealed that a reduced influence radius exacerbates algorithm convergence challenges,thereby impeding the design of intricate porous structures.To overcome this bottleneck,a physics-driven stress skeleton generation method is developed.By integrating stress trajectories and rasterization processing,this method constructs an initial density field,effectively guiding material evolution and significantly enhancing convergence in porous structural optimization within the full-scale framework.Classical numerical examples demonstrate that our proposed optimization framework achieves biomimetic non-uniform shell thickness optimization and enables precise control of the shell thickness.Additionally,density preprocessing effectively eliminates intermediate density regions and void aggregation.Moreover,the generated trabecular-like infill patterns with spatially graded porosity,akin to multiscale topology optimization(MTO),provide an innovative solution for multifunctional,lightweight,complex shell-infill composite structures in aerospace and biomedical applications.展开更多
In this paper,a topology optimization method for coordinated stiffness and strength design is proposed under mass constraints,utilizing the Solid Isotropic Material with Penalization approach.Element densities are reg...In this paper,a topology optimization method for coordinated stiffness and strength design is proposed under mass constraints,utilizing the Solid Isotropic Material with Penalization approach.Element densities are regulated through sensitivity filtering tomitigate numerical instabilities associatedwith stress concentrations.Ap-norm aggregation function is employed to globalize local stress constraints,and a normalization technique linearly weights strain energy and stress,transforming the multi-objective problem into a single-objective formulation.The sensitivity of the objective function with respect to design variables is rigorously derived.Three numerical examples are presented,comparing the optimized structures in terms of strain energy,mass,and stress across five different mathematical models with varying combinations of optimization objectives.The results validate the effectiveness and feasibility of the proposed method for achieving a balanced design between structural stiffness and strength.This approach offers a new perspective for future research on stiffness-strength coordinated structural optimization.展开更多
The application of multi-material topology optimization affords greater design flexibility compared to traditional single-material methods.However,density-based topology optimization methods encounter three unique cha...The application of multi-material topology optimization affords greater design flexibility compared to traditional single-material methods.However,density-based topology optimization methods encounter three unique challenges when inertial loads become dominant:non-monotonous behavior of the objective function,possible unconstrained characterization of the optimal solution,and parasitic effects.Herein,an improved Guide-Weight approach is introduced,which effectively addresses the structural topology optimization problem when subjected to inertial loads.Smooth and fast convergence of the compliance is achieved by the approach,while also maintaining the effectiveness of the volume constraints.The rational approximation of material properties model and smooth design are utilized to guarantee clear boundaries of the final structure,facilitating its seamless integration into manufacturing processes.The framework provided by the alternating active-phase algorithm is employed to decompose the multi-material topological problem under inertial loading into a set of sub-problems.The optimization of multi-material under inertial loads is accomplished through the effective resolution of these sub-problems using the improved Guide-Weight method.The effectiveness of the proposed approach is demonstrated through numerical examples involving two-phase and multi-phase materials.展开更多
This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element couplin...This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element coupling stress resulting from the combination of mechanical and thermal loading,using geometric nonlinear finite element analysis.A topological model is then developed to minimize compliance while meeting displacement and frequency constraints to fulfill design requirements of structural members.Since the conventional Lagrange multiplier search method is unable to handle convergence instability arising from large deformation,a novel Lagrange multiplier search method is proposed.Additionally,the proposed method can be extended to multi-constrained geometrically nonlinear topology optimization,accommodating multiple physical field couplings.展开更多
Recent progress in topology optimization(TO)has seen a growing integration of machine learning to accelerate computation.Among these,online learning stands out as a promising strategy for large-scale TO tasks,as it el...Recent progress in topology optimization(TO)has seen a growing integration of machine learning to accelerate computation.Among these,online learning stands out as a promising strategy for large-scale TO tasks,as it eliminates the need for pre-collected training datasets by updating surrogate models dynamically using intermediate optimization data.Stress-constrained lightweight design is an important class of problem with broad engineering relevance.Most existing frameworks use pixel or voxel-based representations and employ the finite element method(FEM)for analysis.The limited continuity across finite elements often compromises the accuracy of stress evaluation.To overcome this limitation,isogeometric analysis is employed as it enables smooth representation of structures and thus more accurate stress computation.However,the complexity of the stress-constrained design problem together with the isogeometric representation results in a large computational cost.This work proposes a multi-grid,single-mesh online learning framework for isogeometric topology optimization(ITO),leveraging the Fourier Neural Operator(FNO)as a surrogate model.Operating entirely within the isogeometric analysis setting,the framework provides smooth geometry representation and precise stress computation,without requiring traditional mesh generation.A localized training approach is employed to enhance scalability,while a multi-grid decomposition scheme incorporates global structural context into local predictions to boost FNO accuracy.By learning the mapping from spatial features to sensitivity fields,the framework enables efficient single-resolution optimization,avoiding the computational burden of two-resolution simulations.The proposed method is validated through 2D stress-constrained design examples,and the effect of key parameters is studied.展开更多
Parameterized level-set method(PLSM)has been proposed and developed for many years,and is renowned for its efficacy in ad-dressing topology optimization challenges associated with intricate boundaries and nucleation o...Parameterized level-set method(PLSM)has been proposed and developed for many years,and is renowned for its efficacy in ad-dressing topology optimization challenges associated with intricate boundaries and nucleation of new holes.However,most pertinent investigations in the field rely predominantly on fixed background mesh,which is never remeshed.Consequently,the mesh element partitioned by material interface during the optimization process necessitates approximation by using artificial interpolation models to obtain its element stiffness or other properties.This paper introduces a novel approach to topology op-timization by integrating the PLSM with body-fitted adaptive mesh and Helmholtz-type filter.Primarily,combining the PLSM with body-fitted adaptive mesh enables the regeneration of mesh based on the zero level-set interface.This not only precludes the direct traversal of the material interface through the mesh element during the topology optimization process,but also improves the accuracy of calculation.Additionally,the incorporation of a Helmholtz-type partial differential equation filter,relying solely on mesh information essential for finite element discretization,serves to regulate the topological complexity and the minimum feature size of the optimized structure.Leveraging these advantages,the topology optimization program demonstrates its versa-tility by successfully addressing various design problems,encompassing the minimum mean compliance problem and minimum energy dissipation problem.Ultimately,the result of numerical example indicates that the optimized structure exhibits a dis-tinct and smooth boundary,affirming the effective control over both topological complexity and the minimum feature size of the optimized structure.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12172114)Natural Science Foundation of Anhui Province(Grant No.2008085QA21)+1 种基金Fundamental Research Funds for the Central Universities(Grant No.JZ2022HGTB0291)China Postdoctoral Science Foundation(Grant No.2022M712358).
文摘This paper proposes an effective reliability design optimizationmethod for fail-safe topology optimization(FSTO)considering uncertainty based on the moving morphable bars method to establish the ideal balance between cost and robustness,reliability and structural safety.To this end,a performancemeasure approach(PMA)-based doubleloop optimization algorithmis developed tominimize the relative volume percentage while achieving the reliability criterion.To ensure the compliance value of the worst failure case can better approximate the quantified design requirement,a p-norm constraint approach with correction parameter is introduced.Finally,the significance of accounting for uncertainty in the fail-safe design is illustrated by contrasting the findings of the proposed reliabilitybased topology optimization(RBTO)method with those of the deterministic design method in three typical examples.Monte Carlo simulation shows that the relative error of the reliability index of the optimized structure does not exceed 3%.
基金supported by the National Natural Science Foundation of China(Grant Nos.12472114,12132001,52192632)the Defense Industrial Technology Development Program(Grant No.JCKY2023204A005)the Aeronautical Science Foundation of China(Grant No.20240029051001).
文摘This study proposes a non-probabilistic reliability-based topology optimization(NRBTO)method based on isogeometric analysis(IGA),considering the structural stiffness performance.In this study,a geometric model was constructed using non-uniform rational B-splines(NURBS),and the NURBS basis function was used as the shape function of the analytical model.In topology optimization,the classic finite element method(FEM)was replaced by a mesh-independent IGA method.The formulation of isogeometric topology optimization(ITO)based on the solid isotropic microstructures with penalization(SIMP)interpolation model was derived,and a sensitivity analysis was performed using the adjoint method.Considering the uncertainties of material properties and loads,the parameter uncertainty is quantified by interval theory,the propagation analysis is conducted using the interval parametric vertex method,the optimization feature distance is selected as the nonprobabilistic reliability-based index,and a sensitivity analysis is performed on the reliability index to establish a reliability-based topology optimization method based on isogeometric analysis.The method of moving asymptotes(MMA)is used to solve the optimization problem.Several numerical examples were used to verify the method’s effectiveness in practical applications.
基金supported by the Science and Technology Research Project of Henan Province(242102241055)the Industry-University-Research Collaborative Innovation Base on Automobile Lightweight of“Science and Technology Innovation in Central Plains”(2024KCZY315)the Opening Fund of State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment(GZ2024A03-ZZU).
文摘The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is mainly used for finite element analysis at present,and the effectiveness of the surrogate material model has been fully confirmed.However,there are some accuracy problems when dealing with boundary elements using the surrogate material model,which will affect the topology optimization results.In this study,a boundary element reconstruction(BER)model is proposed based on the surrogate material model under the MMC topology optimization framework to improve the accuracy of topology optimization.The proposed BER model can reconstruct the boundary elements by refining the local meshes and obtaining new nodes in boundary elements.Then the density of boundary elements is recalculated using the new node information,which is more accurate than the original model.Based on the new density of boundary elements,the material properties and volume information of the boundary elements are updated.Compared with other finite element analysis methods,the BER model is simple and feasible and can improve computational accuracy.Finally,the effectiveness and superiority of the proposed method are verified by comparing it with the optimization results of the original surrogate material model through several numerical examples.
基金Project supported by the National Natural Science Foundation of China(Nos.51275040 and 50905017)the Programme of Introducing Talents of Discipline to Universities(No.B12022)
文摘Reliability and optimization are two key elements for structural design. The reliability~ based topology optimization （RBTO） is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topol- ogy optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach （the performance measure approach, PMA） and the decoupled approaches （the so-called Hybrid method and the sequential optimization and reliability assessment, SORA）. For reliability analysis, the stochastic response surface method （SRSM） was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique. The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the de- terministic, RBTOs were compared with one another; and useful conclusions regarding validity, accuracy and efficiency were drawn.
基金Supported by the National Natural Science Foundation of China (Grant No. 50775073)the Teaching and Research Award Program for Outstanding Young Teacher in Higher Education Institutions of the Ministry of Education of China+2 种基金the Guangdong Hong Kong Technology Cooperation Funding (Dongguan Project 20061682)the Research Project of Ministry of Education and Guangdong Province (Grant No. 2006D90304001)the Natural Science Foundation of Guangdong Province, China (Grant No. 05006494)
文摘Based on the level set model and the reliability theory, a numerical approach of reliability-based topology optimization for compliant mechanisms with multiple inputs and outputs is presented. A multi-objective topology optimal model of compliant mechanisms considering uncertainties of the loads, material properties, and member geometries is developed. The reliability analysis and topology optimization are integrated in the optimal iterative process. The reliabilities of the compliant mechanisms are evaluated by using the first order reliability method. Meanwhile, the problem of structural topology optimization is solved by the level set method which is flexible in handling complex topological changes and concise in describing the boundary shape of the mechanism. Numerical examples show the importance of considering the stochastic nature of the compliant mechanisms in the topology optimization process.
基金supported by the Natural Science Foundation of China(Grant No.51705268)Shandong Provincial Natural Science Foundation,China(Grant No.ZR2016EEB20)China Postdoctoral Science Foundation Funded Project(Grant No.2017M612191)。
文摘It is essential to consider the effects of incomplete measurement,inaccurate information and inadequate cognition on structural topology optimization.For the multi-material structural topology optimization with non-probability uncertainty,the multi-material interpolation model is represented by the ordered rational approximation of mat erial properties(ordered RAMP).Combined with structural compliance minimization,the multi-material topology optimization with reliability constraints is established.The corresponding non-probability uncertainties are described by the evidence theory,and the uniformity processing method is introduced to convert the evidence variables into random variables.The first-order reliability method is employed to search the most probable point under the reliability index constraint,and then the random variables are equivalent to the deterministic variables according to the geometric meaning of the reliability index and sensitivity information.Therefore,the non-probabilistic reliability-based multi-material topology optimization is transformed into the conventional deterministic optimization format,followed by the ordered RAMP method to solve the optimization problem.Finally,through numerical examples of 2D and 3D structures,the feasibility and effectiveness of the proposed method are verified to consider the geometrical dimensions and external loading uncertainties.
文摘Metalens technology has been applied extensively in miniaturized and integrated infrared imaging systems.However,due to the high phase dispersion of unit structures,metalens often exhibits chromatic aberration,making broadband achromatic infrared imaging challenging to achieve.In this paper,six different unit structures based on chalcogenide glass are constructed,and their phase-dispersion parameters are analyzed to establish a database.On this basis,using chromatic aberration compensation and parameterized adjoint topology optimization,a broadband achromatic metalens with a numerical aperture of 0.5 is designed by arranging these six unit structures in the far-infrared band.Simulation results show that the metalens achieves near diffraction-limited focusing within the operating wavelength range of 9−11μm,demonstrating the good performance of achromatic aberration with flat focusing efficiency of 54%−58%across all wavelengths.
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 Villum Fonden through the Villum Investigator Project“AMSTRAD”(Grant No.VIL54487).
文摘This study presents an extension of multiscale topology optimization by integrating both yield stress and local/global buckling considerations into the design process.Building upon established multiscale methodologies,we develop a new framework incorporating yield stress limits either as constraints or objectives alongside previously established local and global buckling constraints.This approach significantly refines the optimization process,ensuring that the resulting designs meet mechanical performance criteria and adhere to critical material yield constraints.First,we establish local density-dependent von Mises yield surfaces based on local yield estimates from homogenization-based analysis to predict the local yield limits of the homogenized materials.Then,these local yield-based load factors are combined with local and global buckling criteria to obtain topology optimized designs that consider yield and buckling failure on all levels.This integration is crucial for the practical application of optimized structures in real-world scenarios,where material yield and stability behavior critically influence structural integrity and durability.Numerical examples demonstrate how optimized designs depend on the stiffness to yield ratio of the considered building material.Despite the foundational assumption of the separation of scales,the de-homogenized structures,even at relatively coarse length scales,exhibit a remarkably high degree of agreement with the corresponding homogenized predictions.
基金supported by the National Natural Science Foundation of China(Grant No.12272144).
文摘A data-driven model ofmultiple variable cutting(M-VCUT)level set-based substructure is proposed for the topology optimization of lattice structures.TheM-VCUTlevel setmethod is used to represent substructures,enriching their diversity of configuration while ensuring connectivity.To construct the data-driven model of substructure,a database is prepared by sampling the space of substructures spanned by several substructure prototypes.Then,for each substructure in this database,the stiffness matrix is condensed so that its degrees of freedomare reduced.Thereafter,the data-drivenmodel of substructures is constructed through interpolationwith compactly supported radial basis function(CS-RBF).The inputs of the data-driven model are the design variables of topology optimization,and the outputs are the condensed stiffness matrix and volume of substructures.During the optimization,this data-driven model is used,thus avoiding repeated static condensation that would requiremuch computation time.Several numerical examples are provided to verify the proposed method.
基金supported by the National Natural Science Foundation of China(grant number 11902015)the Open Fund of Deceleration and Landing Laboratory of the Fifth Academy of Aerospace Science and Technology Group(grant number EDL19092138)the Ministry of Education Chunhui Plan(HZKY20220014).
文摘As primary load-bearing components extensively utilized in engineering applications,beam structures necessitate the design of their microstructural configurations to achieve lightweight objectives while satisfying diverse mechanical performance requirements.Combining topology optimization with fully coupled homogenization beam theory,we provide a highly efficient design tool to access desirable periodic microstructures for beams.The present optimization framework comprehensively takes into account for key deformation modes,including tension,bending,torsion,and shear deformation,all within a unified formulation.Several numerical results prove that our method can be used to handle kinds of microstructure design for beam-like structures,e.g.,extreme tension(compression)-torsion stiffness,maximization of minimum critical buckling load,and minimization of structural compliance.When optimizing microstructures for macroscopic performance,we emphasize investigating the influence of shear stiffness on the optimized results.The novel chiral beam-like structures are fabricated and tested.The experimental results indicate that the optimized tension(compression)-torsion structure has excellent buffer characteristics,as compared with the traditional square tube.This proposed optimization framework can be further extended to other physical problems of Timoshenko beams.
基金Supported by National Natural Science Foundation of China(Grant No.52105271).
文摘Current topology optimization methods for nonlinear continuum structures often suffer from low computational efficiency and limited applicability to complex nonlinear problems.To address these issues,this paper proposes an improved bi-directional evolutionary structural optimization(BESO)method tailored for maximizing stiffness in nonlinear structures.The optimization program is developed in Python and can be combined with Abaqus software to facilitate finite element analysis(FEA).To accelerate the speed of optimization,a novel adaptive evolutionary ratio(ER)strategy based on the BESO method is introduced,with four distinct adaptive ER functions proposed.The Newton-Raphson method is utilized for iteratively solving nonlinear equilibrium equations,and the sensitivity information for updating design variables is derived using the adjoint method.Additionally,this study extends topology optimization to account for both material nonlinearity and geometric nonlinearity,analyzing the effects of various nonlinearities.A series of comparative studies are conducted using benchmark cases to validate the effectiveness of the proposed method.The results show that the BESO method with adaptive ER significantly improves the optimization efficiency.Compared to the BESO method with a fixed ER,the convergence speed of the four adaptive ER BESO methods is increased by 37.3%,26.7%,12%and 18.7%,respectively.Given that Abaqus is a powerful FEA platform,this method has the potential to be extended to large-scale engineering structures and to address more complex optimization problems.This research proposes an improved BESO method with novel adaptive ER,which significantly accelerates the optimization process and enables its application to topology optimization of nonlinear structures.
基金fundings supported by Sichuan Science and Technology Program(2025YFHZ0065).
文摘Structural Reliability-Based Topology Optimization(RBTO),as an efficient design methodology,serves as a crucial means to ensure the development ofmodern engineering structures towards high performance,long service life,and high reliability.However,in practical design processes,topology optimization must not only account for the static performance of structures but also consider the impacts of various responses and uncertainties under complex dynamic conditions,which traditional methods often struggle accommodate.Therefore,this study proposes an RBTO framework based on a Kriging-assisted level set function and a novel Dynamic Hybrid Particle Swarm Optimization(DHPSO)algorithm.By leveraging the Kriging model as a surrogate,the high cost associated with repeatedly running finite element analysis processes is reduced,addressing the issue of minimizing structural compliance.Meanwhile,the DHPSO algorithm enables a better balance between the population’s developmental and exploratory capabilities,significantly accelerating convergence speed and enhancing global convergence performance.Finally,the proposed method is validated through three different structural examples,demonstrating its superior performance.Observed that the computational that,compared to the traditional Solid Isotropic Material with Penalization(SIMP)method,the proposed approach reduces the upper bound of structural compliance by approximately 30%.Additionally,the optimized results exhibit clear material interfaces without grayscale elements,and the stress concentration factor is reduced by approximately 42%.Consequently,the computational results fromdifferent examples verify the effectiveness and superiority of this study across various fields,achieving the goal of providing more precise optimization results within a shorter timeframe.
基金supported by National Natural Science Foundation of China(Grant No.1257021702)National Key Research and Development Program of China(Grant No.2022YFB4603101).
文摘The integration of additive manufacturing(AM)and topology optimization(TO)has revolutionized the design and production of advanced equipment,providing innovative approaches to solving complex engineering challenges.In the nuclear energy sector,achieving an optimal balance between the thermal and hydraulic performance of prismatic fuel elements has long been a key challenge.This study utilizes a coupled fluid-thermal TO method to design fuel elements with one,three,five,and seven inlets/outlets configurations suitable for AM.We systematically examine the impact of varying the number of inlets/outlets on the thermal-hydraulic performance of the elements.The results show that increasing the number of inlets/outlets can enhance the thermal performance of the fuel elements while sacrificing the hydraulic performance.Compared with the conventional design,the 5 inlets/outlets configuration achieved a coordinated improvement in both thermal and hydraulic performance,with a 2.38%enhancement in thermal performance and a 4.38%improvement in hydraulic performance.These findings highlight the significant potential of TO in improving the performance of fuel elements and strongly demonstrate the advantages of the collaborative application of AM and TO.
基金supported by the Defense Industrial Technology Development Program.
文摘Inspired by natural biomimetic structures exemplified by femoral bones,the shell-infill composite design has emerged as a research focus in structural optimization.However,existing studies predominantly focus on uniform-thickness shell designs and lack robust methodologies for generating high-resolution porous infill configurations.To address these challenges,a novel topology optimization framework for full-scale shell-filled composite structures is developed in this paper.First,a physics-driven,non-uniform partial differential equation(PDE)filter is developed,enabling precise control of variable-thickness shells by establishing explicit mapping relationships between shell thickness and filter radii.Second,this study addresses the convergence inefficiency of traditional full-scale topology optimization methods based on local volume constraints.It is revealed that a reduced influence radius exacerbates algorithm convergence challenges,thereby impeding the design of intricate porous structures.To overcome this bottleneck,a physics-driven stress skeleton generation method is developed.By integrating stress trajectories and rasterization processing,this method constructs an initial density field,effectively guiding material evolution and significantly enhancing convergence in porous structural optimization within the full-scale framework.Classical numerical examples demonstrate that our proposed optimization framework achieves biomimetic non-uniform shell thickness optimization and enables precise control of the shell thickness.Additionally,density preprocessing effectively eliminates intermediate density regions and void aggregation.Moreover,the generated trabecular-like infill patterns with spatially graded porosity,akin to multiscale topology optimization(MTO),provide an innovative solution for multifunctional,lightweight,complex shell-infill composite structures in aerospace and biomedical applications.
基金funded by National Nature Science Foundation of China(92266203)National Nature Science Foundation of China(52205278)+1 种基金Key Projects of Shijiazhuang Basic Research Program(241791077A)Central Guide Local Science and Technology Development Fund Project of Hebei Province(246Z1022G).
文摘In this paper,a topology optimization method for coordinated stiffness and strength design is proposed under mass constraints,utilizing the Solid Isotropic Material with Penalization approach.Element densities are regulated through sensitivity filtering tomitigate numerical instabilities associatedwith stress concentrations.Ap-norm aggregation function is employed to globalize local stress constraints,and a normalization technique linearly weights strain energy and stress,transforming the multi-objective problem into a single-objective formulation.The sensitivity of the objective function with respect to design variables is rigorously derived.Three numerical examples are presented,comparing the optimized structures in terms of strain energy,mass,and stress across five different mathematical models with varying combinations of optimization objectives.The results validate the effectiveness and feasibility of the proposed method for achieving a balanced design between structural stiffness and strength.This approach offers a new perspective for future research on stiffness-strength coordinated structural optimization.
基金supported by the National Natural Science Foundation of China(Grant No.52172356)the Hunan Provincial Natural Science Foundation of China(Grant No.2022JJ10012).
文摘The application of multi-material topology optimization affords greater design flexibility compared to traditional single-material methods.However,density-based topology optimization methods encounter three unique challenges when inertial loads become dominant:non-monotonous behavior of the objective function,possible unconstrained characterization of the optimal solution,and parasitic effects.Herein,an improved Guide-Weight approach is introduced,which effectively addresses the structural topology optimization problem when subjected to inertial loads.Smooth and fast convergence of the compliance is achieved by the approach,while also maintaining the effectiveness of the volume constraints.The rational approximation of material properties model and smooth design are utilized to guarantee clear boundaries of the final structure,facilitating its seamless integration into manufacturing processes.The framework provided by the alternating active-phase algorithm is employed to decompose the multi-material topological problem under inertial loading into a set of sub-problems.The optimization of multi-material under inertial loads is accomplished through the effective resolution of these sub-problems using the improved Guide-Weight method.The effectiveness of the proposed approach is demonstrated through numerical examples involving two-phase and multi-phase materials.
基金supported by grants from the National Natural Science Foundation of China (51478130)the Guangzhou Municipal Education Bureau’s Scientific Research Project, China (2024312217)+1 种基金the China Scholarship Council (201808440070)the 111 Project of China (D21021).
文摘This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element coupling stress resulting from the combination of mechanical and thermal loading,using geometric nonlinear finite element analysis.A topological model is then developed to minimize compliance while meeting displacement and frequency constraints to fulfill design requirements of structural members.Since the conventional Lagrange multiplier search method is unable to handle convergence instability arising from large deformation,a novel Lagrange multiplier search method is proposed.Additionally,the proposed method can be extended to multi-constrained geometrically nonlinear topology optimization,accommodating multiple physical field couplings.
基金supported by the Hong Kong Research Grants under Competitive Earmarked Research Grant No.16206320.
文摘Recent progress in topology optimization(TO)has seen a growing integration of machine learning to accelerate computation.Among these,online learning stands out as a promising strategy for large-scale TO tasks,as it eliminates the need for pre-collected training datasets by updating surrogate models dynamically using intermediate optimization data.Stress-constrained lightweight design is an important class of problem with broad engineering relevance.Most existing frameworks use pixel or voxel-based representations and employ the finite element method(FEM)for analysis.The limited continuity across finite elements often compromises the accuracy of stress evaluation.To overcome this limitation,isogeometric analysis is employed as it enables smooth representation of structures and thus more accurate stress computation.However,the complexity of the stress-constrained design problem together with the isogeometric representation results in a large computational cost.This work proposes a multi-grid,single-mesh online learning framework for isogeometric topology optimization(ITO),leveraging the Fourier Neural Operator(FNO)as a surrogate model.Operating entirely within the isogeometric analysis setting,the framework provides smooth geometry representation and precise stress computation,without requiring traditional mesh generation.A localized training approach is employed to enhance scalability,while a multi-grid decomposition scheme incorporates global structural context into local predictions to boost FNO accuracy.By learning the mapping from spatial features to sensitivity fields,the framework enables efficient single-resolution optimization,avoiding the computational burden of two-resolution simulations.The proposed method is validated through 2D stress-constrained design examples,and the effect of key parameters is studied.
基金supported by the National Natural Science Foundation of China(Grant Nos.12372200 and 12072242).
文摘Parameterized level-set method(PLSM)has been proposed and developed for many years,and is renowned for its efficacy in ad-dressing topology optimization challenges associated with intricate boundaries and nucleation of new holes.However,most pertinent investigations in the field rely predominantly on fixed background mesh,which is never remeshed.Consequently,the mesh element partitioned by material interface during the optimization process necessitates approximation by using artificial interpolation models to obtain its element stiffness or other properties.This paper introduces a novel approach to topology op-timization by integrating the PLSM with body-fitted adaptive mesh and Helmholtz-type filter.Primarily,combining the PLSM with body-fitted adaptive mesh enables the regeneration of mesh based on the zero level-set interface.This not only precludes the direct traversal of the material interface through the mesh element during the topology optimization process,but also improves the accuracy of calculation.Additionally,the incorporation of a Helmholtz-type partial differential equation filter,relying solely on mesh information essential for finite element discretization,serves to regulate the topological complexity and the minimum feature size of the optimized structure.Leveraging these advantages,the topology optimization program demonstrates its versa-tility by successfully addressing various design problems,encompassing the minimum mean compliance problem and minimum energy dissipation problem.Ultimately,the result of numerical example indicates that the optimized structure exhibits a dis-tinct and smooth boundary,affirming the effective control over both topological complexity and the minimum feature size of the optimized structure.
