Materials mechanics and structural dynamics provide theoretical support for the structural optimization of amusement facilities.The design code system guides the design process,covering aspects such as strength and fa...Materials mechanics and structural dynamics provide theoretical support for the structural optimization of amusement facilities.The design code system guides the design process,covering aspects such as strength and fatigue life.This paper introduces optimization methods like standardized module interfaces and variable density methods,as well as topics related to finite element simulation,reliability enhancement,innovative practices,and their significance.展开更多
A concept of the independent-continuous topological variable is proposed to establish its corresponding smooth model of structural topological optimization. The method can overcome difficulties that are encountered in...A concept of the independent-continuous topological variable is proposed to establish its corresponding smooth model of structural topological optimization. The method can overcome difficulties that are encountered in conventional models and algorithms for the optimization of the structural topology. Its application to truss topological optimization with stress and displacement constraints is satisfactory, with convergence faster than that of sectional optimizations.展开更多
In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topolo...In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multidisplacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.展开更多
The objective and constraint functions related to structural optimization designs are classified into economic and performance indexes in this paper.The influences of their different roles in model construction of str...The objective and constraint functions related to structural optimization designs are classified into economic and performance indexes in this paper.The influences of their different roles in model construction of structural topology optimization are also discussed.Furthermore,two structural topology optimization models,optimizing a performance index under the limitation of an economic index,represented by the minimum compliance with a volume constraint（MCVC）model,and optimizing an economic index under the limitation of a performance index,represented by the minimum weight with a displacement constraint（MWDC）model,are presented.Based on a comparison of numerical example results,the conclusions can be summarized as follows：（1）under the same external loading and displacement performance conditions,the results of the MWDC model are almost equal to those of the MCVC model;（2）the MWDC model overcomes the difficulties and shortcomings of the MCVC model;this makes the MWDC model more feasible in model construction;（3）constructing a model of minimizing an economic index under the limitations of performance indexes is better at meeting the needs of practical engineering problems and completely satisfies safety and economic requirements in mechanical engineering,which have remained unchanged since the early days of mechanical engineering.展开更多
This paper proposes a multiscale isogeometric topology optimization(ITO)method where the configuration and layout of microstructures are optimized simultaneously.At micro scale,a shape deformation method is presented ...This paper proposes a multiscale isogeometric topology optimization(ITO)method where the configuration and layout of microstructures are optimized simultaneously.At micro scale,a shape deformation method is presented to transform a prototype microstructure(PM)for obtaining a series of graded microstructures(GMs),where microstructural skeleton based on the level set framework is applied to retain more topology features and improve the connectability.For the macro scale calculation,the effective mechanical properties can be estimated by means of the numerical homogenization method.By adopting identical non-uniform rational basis splines(NURBS)as basis functions for both parameterized level set model and isogeometric calculation model,the isogeometric analysis(IGA)is integrated into the level set method,which contributes to improving the accuracy and efficiency.Numerical examples demonstrate that,the proposed method is effective in improving the performance and manufacturability.展开更多
High-resolution laser additive manufacturing(LAM)significantly releases design free-dom,promoting the development of topology optimization(TO)and advancing structural design methods.In order to fully take advantage of...High-resolution laser additive manufacturing(LAM)significantly releases design free-dom,promoting the development of topology optimization(TO)and advancing structural design methods.In order to fully take advantage of voxelated forming methods and establish the quantitative relationship between the mechanical properties of printing components and multiple process factors(laser-and process-parameters),the concurrent optimization design method based on LAM should cover the process-performance relationship.This study proposes a novel artificial intelligence-facilitated TO method for LAM to concurrently design microscale material property and macroscale structural topology of 3D components by adopting heuristic and gradient-based algorithms.The process–structure–property relationship of selective laser sintering is established by the back propagation neural network,and it is integrated into the TO algorithm for providing a systematic design scheme of structural topology and process parameter.Compared with the classical optimization method,numerical examples show that this method is able to improve the mechanical performance of the macrostructure significantly.In addition,the collaborative design method is able to be widely applied for complex functional part design and optimization,as well as case studies on artificial intelligence-facilitated product evaluation.展开更多
Because of descriptive nonlinearity and computational inefficiency,topology optimization with fatigue life under aperiodic loads has developed slowly.A fatigue constraint topology optimization method based on bidirect...Because of descriptive nonlinearity and computational inefficiency,topology optimization with fatigue life under aperiodic loads has developed slowly.A fatigue constraint topology optimization method based on bidirectional evolutionary structural optimization(BESO)under an aperiodic load is proposed in this paper.In viewof the severe nonlinearity of fatigue damagewith respect to design variables,effective stress cycles are extracted through transient dynamic analysis.Based on the Miner cumulative damage theory and life requirements,a fatigue constraint is first quantified and then transformed into a stress problem.Then,a normalized termination criterion is proposed by approximatemaximum stress measured by global stress using a P-normaggregation function.Finally,optimization examples show that the proposed algorithm can not only meet the requirements of fatigue life but also obtain a reasonable configuration.展开更多
Stress-based topology optimization is one of the most concerns of structural optimization and receives much attention in a wide range of engineering designs.To solve the inherent issues of stress-based topology optimi...Stress-based topology optimization is one of the most concerns of structural optimization and receives much attention in a wide range of engineering designs.To solve the inherent issues of stress-based topology optimization,many schemes are added to the conventional bi-directional evolutionary structural optimization(BESO)method in the previous studies.However,these schemes degrade the generality of BESO and increase the computational cost.This study proposes an improved topology optimization method for the continuum structures considering stress minimization in the framework of the conventional BESO method.A global stress measure constructed by p-norm function is treated as the objective function.To stabilize the optimization process,both qp-relaxation and sensitivity weight scheme are introduced.Design variables are updated by the conventional BESO method.Several 2D and 3D examples are used to demonstrate the validity of the proposed method.The results show that the optimization process can be stabilized by qp-relaxation.The value of q and p are crucial to reasonable solutions.The proposed sensitivity weight scheme further stabilizes the optimization process and evenly distributes the stress field.The computational efficiency of the proposed method is higher than the previous methods because it keeps the generality of BESO and does not need additional schemes.展开更多
When describing the mechanical behavior of some engineering materials,such as composites,grains,biological materials and cellular solids,the Cosserat continuum theory has more powerful capabilities compared with the c...When describing the mechanical behavior of some engineering materials,such as composites,grains,biological materials and cellular solids,the Cosserat continuum theory has more powerful capabilities compared with the classical Cauchy elasticity since an additional local rotation of point and its counterpart(couple stress)are considered in the Cosserat elasticity to represent the material microscale effects.In this paper,a parameterized level set topology optimization method is developed based on the Cosserat elasticity for the minimum compliance problem of the Cosserat solids.The influence of material characteristic length and Cosserat shear modulus on the optimized structure is investigated in detail.It can be found that the microstructural constants in the Cosserat elasticity have a significant impact on the optimized topology configurations.In addition,the minimum feature size and the geometric complexity of the optimized structure can be controlled implicitly by adjusting the parameters of the characteristic length and Cosserat shear modulus easily.Furthermore,the optimized structure obtained by the developed Cosserat elasticity based parameterized level set method will degenerate to the result by using the classical Cauchy elasticity based parameterized level set method when the Cosserat shear modulus approaches zero.展开更多
This study investigates structural topology optimization of thermoelastic structures considering two kinds of objectives ofminimumstructural compliance and elastic strain energy with a specified available volume const...This study investigates structural topology optimization of thermoelastic structures considering two kinds of objectives ofminimumstructural compliance and elastic strain energy with a specified available volume constraint.To explicitly express the configuration evolution in the structural topology optimization under combination of mechanical and thermal load conditions,the moving morphable components(MMC)framework is adopted.Based on the characteristics of the MMC framework,the number of design variables can be reduced substantially.Corresponding optimization formulation in the MMC topology optimization framework and numerical solution procedures are developed for several numerical examples.Different optimization results are obtained with structural compliance and elastic strain energy as objectives,respectively,for thermoelastic problems.The effectiveness of the proposed optimization formulation is validated by the numerical examples.It is revealed that for the optimization design of the thermoelastic structural strength,the objective function with the minimum structural strain energy can achieve a better performance than that from structural compliance design.展开更多
In this paper,a new algorithm combining the features of bi-direction evolutionary structural optimization(BESO)and reinforcement learning(RL)is proposed for continuum structural topology optimization(STO).In contrast ...In this paper,a new algorithm combining the features of bi-direction evolutionary structural optimization(BESO)and reinforcement learning(RL)is proposed for continuum structural topology optimization(STO).In contrast to conventional approaches which only generate a certain quasi-optimal solution,the goal of the combined method is to provide more quasi-optimal solutions for designers such as the idea of generative design.Two key components were adopted.First,besides sensitivity,value function updated by Monte-Carlo reinforcement learning was utilized to measure the importance of each element,which made the solving process convergent and closer to the optimum.Second,ε-greedy policy added a random perturbation to the main search direction so as to extend the search ability.Finally,the quality and diversity of solutions could be guaranteed by controlling the value of compliance as well as Intersection-over-Union(IoU).Results of several 2D and 3D compliance minimization problems,including a geometrically nonlinear case,show that the combined method is capable of generating a group of good and different solutions that satisfy various possible requirements in engineering design within acceptable computation cost.展开更多
This work presents a moving morphable component(MMC)-based framework for solving topology optimization problems considering both single-frequency and band-frequency steady-state structural dynamic responses.In this wo...This work presents a moving morphable component(MMC)-based framework for solving topology optimization problems considering both single-frequency and band-frequency steady-state structural dynamic responses.In this work,a set of morphable components are introduced as the basic building blocks for topology optimization,and the optimized structural layout can be found by optimizing the parameters characterizing the locations and geometries of the components explicitly.The degree of freedom(DOF)elimination technique is also employed to delete unnecessary DOFs at each iteration.Since the proposed approach solves the corresponding optimization problems in an explicit way,some challenging issues(e.g.,the large computational burden related to finite element analysis and sensitivity analysis,the localized eigenmodes in low material density regions,and the impact of excitation frequency on the optimization process)associated with the traditional approaches can be circumvented naturally.Numerical results show that the proposed approach is effective for solving topology optimization problems involving structural dynamic behaviors,especially when high-frequency responses are considered.展开更多
Additive manufacturing(AM)has made significant progress in recent years and has been successfully applied in various fields owing to its ability to manufacture complex geometries.This method efficiently expands the de...Additive manufacturing(AM)has made significant progress in recent years and has been successfully applied in various fields owing to its ability to manufacture complex geometries.This method efficiently expands the design space,allowing for the creation of products with better performance than ever before.With the emergence of new manufacturing technologies,new design methods are required to efficiently utilize the expanded design space.Therefore,topology optimization methods have attracted the attention of researchers because of their ability to generate new and optimized designs without requiring prior experience.The combination of AM and topology optimization has proven to be a powerful tool for structural innovation in design and manufacturing.However,it is important to note that AM does not eliminate all manufacturing restrictions but instead replaces them with a different set of design considerations that designers must consider for the successful implementation of these technologies.This has motivated research on topology optimization methods that incorporate manufacturable constraints for AM structures.In this paper,we present a survey of the latest studies in this research area,with a particular focus on developments in China.Additionally,we discuss the existing research gaps and future development trends.展开更多
A number of critical problems of topology optimization concerning the thermostructural coupling field axe studied at length. The governing equations and topology optimization model for the thermal-structural coupling ...A number of critical problems of topology optimization concerning the thermostructural coupling field axe studied at length. The governing equations and topology optimization model for the thermal-structural coupling field axe derived, with an adjoint method for sensitivity analysis of the thermo-structural coupling field proposed. The optimization algorithm for coupling field topology optimization is investigated and a flowchart of coupling field topology optimization presented. The theory and algorithms axe implemented and verified by two numerical examples.展开更多
Natural frequency and dynamic stiffness under transient loading are two key performances for structural design related to automotive,aviation and construction industries.This article aims to tackle the multi-objective...Natural frequency and dynamic stiffness under transient loading are two key performances for structural design related to automotive,aviation and construction industries.This article aims to tackle the multi-objective topological optimization problem considering dynamic stiffness and natural frequency using modified version of bi-directional evolutionary structural optimization(BESO).The conventional BESO is provided with constant evolutionary volume ratio(EVR),whereas low EVR greatly retards the optimization process and high EVR improperly removes the efficient elements.To address the issue,the modified BESO with variable EVR is introduced.To compromise the natural frequency and the dynamic stiffness,a weighting scheme of sensitivity numbers is employed to form the Pareto solution space.Several numerical examples demonstrate that the optimal solutions obtained from the modified BESO method have good agreement with those from the classic BESO method.Most importantly,the dynamic removal strategy with the variable EVR sharply springs up the optimization process.Therefore,it is concluded that the modified BESO method with variable EVR can solve structural design problems using multi-objective optimization.展开更多
This work analyzes the implementation of a continuous method of structural topology optimization(STO)using open-source software for all stages of the topology optimization problem:modeling,sensitivity analysis and opt...This work analyzes the implementation of a continuous method of structural topology optimization(STO)using open-source software for all stages of the topology optimization problem:modeling,sensitivity analysis and optimization.Its implementation involves three main components:numerical analysis using the Finite Element Method(FEM),sensitivity analysis using an Adjoint method and an optimization solver.In order to allow the automated numerical solution of Partial Differential Equations(PDEs)and perform a sensitivity analysis,FEniCS and Dolfin Adjoint software are used as tools,which are open-source code.For the optimization process,Ipopt(Interior Point OPTimizer)is used,which is a software package for nonlinear optimization scale designed to find(local)solutions of mathematical optimization problems.The topological optimization method used is based on the SIMP-Solid IsotropicMaterial with Penalization interpolation.The considered problem is the minimization of compliance/maximization of stiffness,considering the examples of recurrent structures in the literature in 2D and 3D.A density filtering algorithm based on Helmholtz formulation is used.The complete code involves 51 lines of programming and is presented and commented in detail in this article.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
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
The jacket structure and transition piece comprise the supporting structure of a bottom-fixed offshore wind turbine(OWT)connected to the steel tower,which determines the overall structural dynamic performance of the e...The jacket structure and transition piece comprise the supporting structure of a bottom-fixed offshore wind turbine(OWT)connected to the steel tower,which determines the overall structural dynamic performance of the entire OWT.Ideally,optimal performance can be realized by effectively coordinating two components,notwithstanding their separate design processes.In pursuit of this objective,this paper proposes a concurrent design methodology for the jacket structure and transition piece by exploiting topology optimization(TO).The TO for a three-legged jacket foundation is formulated by minimizing static compliance.In contrast to conventional TO,two separated volume fractions are imposed upon the structural design domain of the jacket structure and transition piece to ensure continuity.A 5 MW(megawatt)OWT supported by a four-legged or three-legged jacket substructure is under investigation.The external loads are derived from various design load cases that are acquired using the commercial software platform DNV Bladed(Det Norske Veritas).Through a comparative analysis of the fundamental frequency and maximum nodal deformation,it was found that the optimized solution demonstrates a reduced weight and superior stiffness.The findings demonstrate the present concurrent design approach using TO can yield significant benefits by reducing the overall design cycle and enhancing the feasibility of the final design.展开更多
This paper presents a deep learning-based topology optimization method for the joint design of material layout and fiber orientation in continuous fiber-reinforced composite structure(CFRCS).The proposed method mainly...This paper presents a deep learning-based topology optimization method for the joint design of material layout and fiber orientation in continuous fiber-reinforced composite structure(CFRCS).The proposed method mainly includes three steps:(1)a ResUNet-involved generative and adversarial network(ResUNet-GAN)is developed to establish the end-to-end mapping from structural design parameters to fiber-reinforced composite optimized structure,and a fiber orientation chromatogram is presented to represent continuous fiber angles;(2)to avoid the local optimum problem,the independent continuous mapping method(ICM method)considering the improved principal stress orientation interpolated continuous fiber angle optimization(PSO-CFAO)strategy is utilized to construct CFRCS topology optimization dataset;(3)the well-trained ResUNet-GAN is deployed to design the optimal structural material distribution together with the corresponding continuous fiber orientations.Numerical simulations for benchmark structure verify that the proposed method greatly improves the design efficiency of CFRCS along with high design accuracy.Furthermore,the CFRCS topology configuration designed by ResUNet-GAN is fabricated by additive manufacturing.Compression experiments of the specimens show that both the stiffness structure and peak load of the CFRCS topology configuration designed by the proposed method have significantly enhanced.The proposed deep learning-based topology optimization method will provide great flexibility in CFRCS for engineering applications.展开更多
文摘Materials mechanics and structural dynamics provide theoretical support for the structural optimization of amusement facilities.The design code system guides the design process,covering aspects such as strength and fatigue life.This paper introduces optimization methods like standardized module interfaces and variable density methods,as well as topics related to finite element simulation,reliability enhancement,innovative practices,and their significance.
基金The project supported by State Key Laboratory of Structural Analyses of Industrial Equipment
文摘A concept of the independent-continuous topological variable is proposed to establish its corresponding smooth model of structural topological optimization. The method can overcome difficulties that are encountered in conventional models and algorithms for the optimization of the structural topology. Its application to truss topological optimization with stress and displacement constraints is satisfactory, with convergence faster than that of sectional optimizations.
基金supported by the National Natural Science Foundation of China (10872036)the High Technological Research and Development Program of China (2008AA04Z118)the Airspace Natural Science Foundation (2007ZA23007)
文摘In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multidisplacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.
基金supported by the National Natural Science Foundation of China(Grant 11172013)
文摘The objective and constraint functions related to structural optimization designs are classified into economic and performance indexes in this paper.The influences of their different roles in model construction of structural topology optimization are also discussed.Furthermore,two structural topology optimization models,optimizing a performance index under the limitation of an economic index,represented by the minimum compliance with a volume constraint（MCVC）model,and optimizing an economic index under the limitation of a performance index,represented by the minimum weight with a displacement constraint（MWDC）model,are presented.Based on a comparison of numerical example results,the conclusions can be summarized as follows：（1）under the same external loading and displacement performance conditions,the results of the MWDC model are almost equal to those of the MCVC model;（2）the MWDC model overcomes the difficulties and shortcomings of the MCVC model;this makes the MWDC model more feasible in model construction;（3）constructing a model of minimizing an economic index under the limitations of performance indexes is better at meeting the needs of practical engineering problems and completely satisfies safety and economic requirements in mechanical engineering,which have remained unchanged since the early days of mechanical engineering.
基金National Key R&D Program of China(2018YFB1700803,2018YFB1700804).
文摘This paper proposes a multiscale isogeometric topology optimization(ITO)method where the configuration and layout of microstructures are optimized simultaneously.At micro scale,a shape deformation method is presented to transform a prototype microstructure(PM)for obtaining a series of graded microstructures(GMs),where microstructural skeleton based on the level set framework is applied to retain more topology features and improve the connectability.For the macro scale calculation,the effective mechanical properties can be estimated by means of the numerical homogenization method.By adopting identical non-uniform rational basis splines(NURBS)as basis functions for both parameterized level set model and isogeometric calculation model,the isogeometric analysis(IGA)is integrated into the level set method,which contributes to improving the accuracy and efficiency.Numerical examples demonstrate that,the proposed method is effective in improving the performance and manufacturability.
基金supported by National Natural Science Foundation of China(U1930207)Key Project of National Natural Science Foundation of China(51790171)+2 种基金National Natural Science Foundation of China for Excellent Young Scholars(11722219)National Natural Science Foundation of China for Young Scholars(51905439)111 Project(B21013)。
文摘High-resolution laser additive manufacturing(LAM)significantly releases design free-dom,promoting the development of topology optimization(TO)and advancing structural design methods.In order to fully take advantage of voxelated forming methods and establish the quantitative relationship between the mechanical properties of printing components and multiple process factors(laser-and process-parameters),the concurrent optimization design method based on LAM should cover the process-performance relationship.This study proposes a novel artificial intelligence-facilitated TO method for LAM to concurrently design microscale material property and macroscale structural topology of 3D components by adopting heuristic and gradient-based algorithms.The process–structure–property relationship of selective laser sintering is established by the back propagation neural network,and it is integrated into the TO algorithm for providing a systematic design scheme of structural topology and process parameter.Compared with the classical optimization method,numerical examples show that this method is able to improve the mechanical performance of the macrostructure significantly.In addition,the collaborative design method is able to be widely applied for complex functional part design and optimization,as well as case studies on artificial intelligence-facilitated product evaluation.
基金Chinese National Natural Science Foundation(No.51890881)Science and Technology Project of Hebei Education Department(Nos.ZD2020156,QN2018228).
文摘Because of descriptive nonlinearity and computational inefficiency,topology optimization with fatigue life under aperiodic loads has developed slowly.A fatigue constraint topology optimization method based on bidirectional evolutionary structural optimization(BESO)under an aperiodic load is proposed in this paper.In viewof the severe nonlinearity of fatigue damagewith respect to design variables,effective stress cycles are extracted through transient dynamic analysis.Based on the Miner cumulative damage theory and life requirements,a fatigue constraint is first quantified and then transformed into a stress problem.Then,a normalized termination criterion is proposed by approximatemaximum stress measured by global stress using a P-normaggregation function.Finally,optimization examples show that the proposed algorithm can not only meet the requirements of fatigue life but also obtain a reasonable configuration.
基金supported by National Natural Science Foundation of China[Grant No.51575399]the National Key Research and Development Program of China[Grant No.2016YFB0101602].
文摘Stress-based topology optimization is one of the most concerns of structural optimization and receives much attention in a wide range of engineering designs.To solve the inherent issues of stress-based topology optimization,many schemes are added to the conventional bi-directional evolutionary structural optimization(BESO)method in the previous studies.However,these schemes degrade the generality of BESO and increase the computational cost.This study proposes an improved topology optimization method for the continuum structures considering stress minimization in the framework of the conventional BESO method.A global stress measure constructed by p-norm function is treated as the objective function.To stabilize the optimization process,both qp-relaxation and sensitivity weight scheme are introduced.Design variables are updated by the conventional BESO method.Several 2D and 3D examples are used to demonstrate the validity of the proposed method.The results show that the optimization process can be stabilized by qp-relaxation.The value of q and p are crucial to reasonable solutions.The proposed sensitivity weight scheme further stabilizes the optimization process and evenly distributes the stress field.The computational efficiency of the proposed method is higher than the previous methods because it keeps the generality of BESO and does not need additional schemes.
基金This work was supported by the National Natural Science Foundation of China(Grants 12072242,11772237,and 11472196)the Hubei Provincial Natural Science Foundation(Grant 2020CFB816)the Fundamental Research Funds for the Central Universities(Grant 2042018kf0016).
文摘When describing the mechanical behavior of some engineering materials,such as composites,grains,biological materials and cellular solids,the Cosserat continuum theory has more powerful capabilities compared with the classical Cauchy elasticity since an additional local rotation of point and its counterpart(couple stress)are considered in the Cosserat elasticity to represent the material microscale effects.In this paper,a parameterized level set topology optimization method is developed based on the Cosserat elasticity for the minimum compliance problem of the Cosserat solids.The influence of material characteristic length and Cosserat shear modulus on the optimized structure is investigated in detail.It can be found that the microstructural constants in the Cosserat elasticity have a significant impact on the optimized topology configurations.In addition,the minimum feature size and the geometric complexity of the optimized structure can be controlled implicitly by adjusting the parameters of the characteristic length and Cosserat shear modulus easily.Furthermore,the optimized structure obtained by the developed Cosserat elasticity based parameterized level set method will degenerate to the result by using the classical Cauchy elasticity based parameterized level set method when the Cosserat shear modulus approaches zero.
基金Financial supports for this research were provided by the National Nat-ural Science Foundation of China(Nos.11672057,12002278,U1906233)the National Key R&D Program of China(2017YFC0307201)+1 种基金the Key R&D Program of Shandong Province(2019JZZY010801)the Fundamental Research Funds for the Central Universities(NWPU-G2020KY05308)。
文摘This study investigates structural topology optimization of thermoelastic structures considering two kinds of objectives ofminimumstructural compliance and elastic strain energy with a specified available volume constraint.To explicitly express the configuration evolution in the structural topology optimization under combination of mechanical and thermal load conditions,the moving morphable components(MMC)framework is adopted.Based on the characteristics of the MMC framework,the number of design variables can be reduced substantially.Corresponding optimization formulation in the MMC topology optimization framework and numerical solution procedures are developed for several numerical examples.Different optimization results are obtained with structural compliance and elastic strain energy as objectives,respectively,for thermoelastic problems.The effectiveness of the proposed optimization formulation is validated by the numerical examples.It is revealed that for the optimization design of the thermoelastic structural strength,the objective function with the minimum structural strain energy can achieve a better performance than that from structural compliance design.
文摘In this paper,a new algorithm combining the features of bi-direction evolutionary structural optimization(BESO)and reinforcement learning(RL)is proposed for continuum structural topology optimization(STO).In contrast to conventional approaches which only generate a certain quasi-optimal solution,the goal of the combined method is to provide more quasi-optimal solutions for designers such as the idea of generative design.Two key components were adopted.First,besides sensitivity,value function updated by Monte-Carlo reinforcement learning was utilized to measure the importance of each element,which made the solving process convergent and closer to the optimum.Second,ε-greedy policy added a random perturbation to the main search direction so as to extend the search ability.Finally,the quality and diversity of solutions could be guaranteed by controlling the value of compliance as well as Intersection-over-Union(IoU).Results of several 2D and 3D compliance minimization problems,including a geometrically nonlinear case,show that the combined method is capable of generating a group of good and different solutions that satisfy various possible requirements in engineering design within acceptable computation cost.
基金Financial support from the National Natural Science Foundation of China (11821202,11872141,11922204,12002073)the National Key Research and Development Plan (2020YFB1709401)+1 种基金the Fundamental Research Funds for the Central Universities[DUT20RC (3)020]the 111 Project (B14013)is gratefully acknowledged.
文摘This work presents a moving morphable component(MMC)-based framework for solving topology optimization problems considering both single-frequency and band-frequency steady-state structural dynamic responses.In this work,a set of morphable components are introduced as the basic building blocks for topology optimization,and the optimized structural layout can be found by optimizing the parameters characterizing the locations and geometries of the components explicitly.The degree of freedom(DOF)elimination technique is also employed to delete unnecessary DOFs at each iteration.Since the proposed approach solves the corresponding optimization problems in an explicit way,some challenging issues(e.g.,the large computational burden related to finite element analysis and sensitivity analysis,the localized eigenmodes in low material density regions,and the impact of excitation frequency on the optimization process)associated with the traditional approaches can be circumvented naturally.Numerical results show that the proposed approach is effective for solving topology optimization problems involving structural dynamic behaviors,especially when high-frequency responses are considered.
基金supported by National Natural Science Foundation of China(Grant Nos.12272076,U2341232,11332004,and U1808215)the 111 Project of China(Grant No.B14013).
文摘Additive manufacturing(AM)has made significant progress in recent years and has been successfully applied in various fields owing to its ability to manufacture complex geometries.This method efficiently expands the design space,allowing for the creation of products with better performance than ever before.With the emergence of new manufacturing technologies,new design methods are required to efficiently utilize the expanded design space.Therefore,topology optimization methods have attracted the attention of researchers because of their ability to generate new and optimized designs without requiring prior experience.The combination of AM and topology optimization has proven to be a powerful tool for structural innovation in design and manufacturing.However,it is important to note that AM does not eliminate all manufacturing restrictions but instead replaces them with a different set of design considerations that designers must consider for the successful implementation of these technologies.This has motivated research on topology optimization methods that incorporate manufacturable constraints for AM structures.In this paper,we present a survey of the latest studies in this research area,with a particular focus on developments in China.Additionally,we discuss the existing research gaps and future development trends.
基金Project supported by the National Natural Postdoctor Scientific Foundation (No.2005037347)973 Project of China (No.2003CB716207).
文摘A number of critical problems of topology optimization concerning the thermostructural coupling field axe studied at length. The governing equations and topology optimization model for the thermal-structural coupling field axe derived, with an adjoint method for sensitivity analysis of the thermo-structural coupling field proposed. The optimization algorithm for coupling field topology optimization is investigated and a flowchart of coupling field topology optimization presented. The theory and algorithms axe implemented and verified by two numerical examples.
基金funded by the National Natural Science Foundation of China(Grant No.51505096)the Natural Science Foundation of Heilongjiang Province(Grant No.LH2020E064).
文摘Natural frequency and dynamic stiffness under transient loading are two key performances for structural design related to automotive,aviation and construction industries.This article aims to tackle the multi-objective topological optimization problem considering dynamic stiffness and natural frequency using modified version of bi-directional evolutionary structural optimization(BESO).The conventional BESO is provided with constant evolutionary volume ratio(EVR),whereas low EVR greatly retards the optimization process and high EVR improperly removes the efficient elements.To address the issue,the modified BESO with variable EVR is introduced.To compromise the natural frequency and the dynamic stiffness,a weighting scheme of sensitivity numbers is employed to form the Pareto solution space.Several numerical examples demonstrate that the optimal solutions obtained from the modified BESO method have good agreement with those from the classic BESO method.Most importantly,the dynamic removal strategy with the variable EVR sharply springs up the optimization process.Therefore,it is concluded that the modified BESO method with variable EVR can solve structural design problems using multi-objective optimization.
文摘This work analyzes the implementation of a continuous method of structural topology optimization(STO)using open-source software for all stages of the topology optimization problem:modeling,sensitivity analysis and optimization.Its implementation involves three main components:numerical analysis using the Finite Element Method(FEM),sensitivity analysis using an Adjoint method and an optimization solver.In order to allow the automated numerical solution of Partial Differential Equations(PDEs)and perform a sensitivity analysis,FEniCS and Dolfin Adjoint software are used as tools,which are open-source code.For the optimization process,Ipopt(Interior Point OPTimizer)is used,which is a software package for nonlinear optimization scale designed to find(local)solutions of mathematical optimization problems.The topological optimization method used is based on the SIMP-Solid IsotropicMaterial with Penalization interpolation.The considered problem is the minimization of compliance/maximization of stiffness,considering the examples of recurrent structures in the literature in 2D and 3D.A density filtering algorithm based on Helmholtz formulation is used.The complete code involves 51 lines of programming and is presented and commented in detail in this article.
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 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supports were received from the National Key Research and Development Program of China(2024YFE0208600)New Energy Joint Laboratory of China Southern Power Grid Corporation(GDXNY2024KF03)+2 种基金the National Natural Science Foundation of China(Grant No.U24B2090)National Key R&D Program(No.2022YFB4201300)Science and Technology Project of Huaneng Group(HNKJ24-H78).
文摘The jacket structure and transition piece comprise the supporting structure of a bottom-fixed offshore wind turbine(OWT)connected to the steel tower,which determines the overall structural dynamic performance of the entire OWT.Ideally,optimal performance can be realized by effectively coordinating two components,notwithstanding their separate design processes.In pursuit of this objective,this paper proposes a concurrent design methodology for the jacket structure and transition piece by exploiting topology optimization(TO).The TO for a three-legged jacket foundation is formulated by minimizing static compliance.In contrast to conventional TO,two separated volume fractions are imposed upon the structural design domain of the jacket structure and transition piece to ensure continuity.A 5 MW(megawatt)OWT supported by a four-legged or three-legged jacket substructure is under investigation.The external loads are derived from various design load cases that are acquired using the commercial software platform DNV Bladed(Det Norske Veritas).Through a comparative analysis of the fundamental frequency and maximum nodal deformation,it was found that the optimized solution demonstrates a reduced weight and superior stiffness.The findings demonstrate the present concurrent design approach using TO can yield significant benefits by reducing the overall design cycle and enhancing the feasibility of the final design.
基金supported by the National Natural Science Foundation of China(Grant No.11872080)Beijing Natural Science Foundation(Grant No.3192005).
文摘This paper presents a deep learning-based topology optimization method for the joint design of material layout and fiber orientation in continuous fiber-reinforced composite structure(CFRCS).The proposed method mainly includes three steps:(1)a ResUNet-involved generative and adversarial network(ResUNet-GAN)is developed to establish the end-to-end mapping from structural design parameters to fiber-reinforced composite optimized structure,and a fiber orientation chromatogram is presented to represent continuous fiber angles;(2)to avoid the local optimum problem,the independent continuous mapping method(ICM method)considering the improved principal stress orientation interpolated continuous fiber angle optimization(PSO-CFAO)strategy is utilized to construct CFRCS topology optimization dataset;(3)the well-trained ResUNet-GAN is deployed to design the optimal structural material distribution together with the corresponding continuous fiber orientations.Numerical simulations for benchmark structure verify that the proposed method greatly improves the design efficiency of CFRCS along with high design accuracy.Furthermore,the CFRCS topology configuration designed by ResUNet-GAN is fabricated by additive manufacturing.Compression experiments of the specimens show that both the stiffness structure and peak load of the CFRCS topology configuration designed by the proposed method have significantly enhanced.The proposed deep learning-based topology optimization method will provide great flexibility in CFRCS for engineering applications.
