This paper aims to solve large-scale and complex isogeometric topology optimization problems that consumesignificant computational resources. A novel isogeometric topology optimization method with a hybrid parallelstr...This paper aims to solve large-scale and complex isogeometric topology optimization problems that consumesignificant computational resources. A novel isogeometric topology optimization method with a hybrid parallelstrategy of CPU/GPU is proposed, while the hybrid parallel strategies for stiffness matrix assembly, equationsolving, sensitivity analysis, and design variable update are discussed in detail. To ensure the high efficiency ofCPU/GPU computing, a workload balancing strategy is presented for optimally distributing the workload betweenCPU and GPU. To illustrate the advantages of the proposedmethod, three benchmark examples are tested to verifythe hybrid parallel strategy in this paper. The results show that the efficiency of the hybrid method is faster thanserial CPU and parallel GPU, while the speedups can be up to two orders of magnitude.展开更多
Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio.In this paper,a full-scale isogeometric topology optimization(ITO)method ba...Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio.In this paper,a full-scale isogeometric topology optimization(ITO)method based on Kirchhoff-Love shells for designing cellular tshin-shell structures with excellent damage tolerance ability is proposed.This method utilizes high-order continuous nonuniform rational B-splines(NURBS)as basis functions for Kirchhoff-Love shell elements.The geometric and analysis models of thin shells are unified by isogeometric analysis(IGA)to avoid geometric approximation error and improve computational accuracy.The topological configurations of thin-shell structures are described by constructing the effective density field on the controlmesh.Local volume constraints are imposed in the proximity of each control point to obtain bone-like cellular structures.To facilitate numerical implementation,the p-norm function is used to aggregate local volume constraints into an equivalent global constraint.Several numerical examples are provided to demonstrate the effectiveness of the proposed method.After simulation and comparative analysis,the results indicate that the cellular thin-shell structures optimized by the proposed method exhibit great load-carrying behavior and high damage robustness.展开更多
This work puts forward an explicit isogeometric topology optimization(ITO)method using moving morphable components(MMC),which takes the suitably graded truncated hierarchical B-Spline based isogeometric analysis as th...This work puts forward an explicit isogeometric topology optimization(ITO)method using moving morphable components(MMC),which takes the suitably graded truncated hierarchical B-Spline based isogeometric analysis as the solver of physical unknown(SGTHB-ITO-MMC).By applying properly basis graded constraints to the hierarchical mesh of truncated hierarchical B-splines(THB),the convergence and robustness of the SGTHB-ITOMMC are simultaneously improved and the tiny holes occurred in optimized structure are eliminated,due to the improved accuracy around the explicit structural boundaries.Moreover,an efficient computational method is developed for the topological description functions(TDF)ofMMC under the admissible hierarchicalmesh,which consists of reducing the dimensionality strategy for design space and the locally computing strategy for hierarchical mesh.We apply the above SGTHB-ITO-MMC with improved efficiency to a series of 2D and 3Dcompliance design problems.The numerical results show that the proposed SGTHB-ITO-MMC method outperforms the traditional THB-ITO-MMCmethod in terms of convergence rate and efficiency.Therefore,the proposed SGTHB-ITO-MMC is an effective way of solving topology optimization(TO)problems.展开更多
Topological optimization plays a guiding role in the conceptual design process.This paper conducts research on structural topology optimization algorithm within the framework of isogeometric analysis.For multi-compone...Topological optimization plays a guiding role in the conceptual design process.This paper conducts research on structural topology optimization algorithm within the framework of isogeometric analysis.For multi-component structures,the Nitsche’smethod is used to glue differentmeshes to performisogeometricmulti-patch analysis.The discrete variable topology optimization algorithm based on integer programming is adopted in order to obtain clear boundaries for topology optimization.The sensitivity filtering method based on the Helmholtz equation is employed for averaging of curved elements’sensitivities.In addition,a simple averaging method along coupling interfaces is proposed in order to ensure the material distribution across coupling areas is reasonably smooth.Finally,the performance of the algorithm is demonstrated by numerical examples,and the effectiveness of the algorithm is verified by comparing it with the results obtained by single-patch and ABAQUS cases.展开更多
In this work,an acoustic topology optimizationmethod for structural surface design covered by porous materials is proposed.The analysis of acoustic problems is performed using the isogeometric boundary elementmethod.T...In this work,an acoustic topology optimizationmethod for structural surface design covered by porous materials is proposed.The analysis of acoustic problems is performed using the isogeometric boundary elementmethod.Taking the element density of porousmaterials as the design variable,the volume of porousmaterials as the constraint,and the minimum sound pressure or maximum scattered sound power as the design goal,the topology optimization is carried out by solid isotropic material with penalization(SIMP)method.To get a limpid 0–1 distribution,a smoothing Heaviside-like function is proposed.To obtain the gradient value of the objective function,a sensitivity analysis method based on the adjoint variable method(AVM)is proposed.To find the optimal solution,the optimization problems are solved by the method of moving asymptotes(MMA)based on gradient information.Numerical examples verify the effectiveness of the proposed topology optimization method in the optimization process of two-dimensional acoustic problems.Furthermore,the optimal distribution of sound-absorbingmaterials is highly frequency-dependent and usually needs to be performed within a frequency band.展开更多
Topology Optimization(TO)is a powerful numerical technique to determine the optimal material layout in a design domain,which has accepted considerable developments in recent years.The classic Finite Element Method(FEM...Topology Optimization(TO)is a powerful numerical technique to determine the optimal material layout in a design domain,which has accepted considerable developments in recent years.The classic Finite Element Method(FEM)is applied to compute the unknown structural responses in TO.However,several numerical deficiencies of the FEM significantly influence the effectiveness and efficiency of TO.In order to eliminate the negative influence of the FEM on TO,IsoGeometric Analysis(IGA)has become a promising alternative due to its unique feature that the Computer-Aided Design(CAD)model and Computer-Aided Engineering(CAE)model can be unified into a same mathematical model.In the paper,the main intention is to provide a comprehensive overview for the developments of Isogeometric Topology Optimization(ITO)in methods and applications.Finally,some prospects for the developments of ITO in the future are also presented.展开更多
In this paper,a new isogeometric topology optimization(ITO)method is proposed by using T-splines based isogeometric analysis(IGA).The arbitrarily shaped design domains,directly obtained from CAD,are represented by a s...In this paper,a new isogeometric topology optimization(ITO)method is proposed by using T-splines based isogeometric analysis(IGA).The arbitrarily shaped design domains,directly obtained from CAD,are represented by a single T-spline surface which overcomes the topological limitations of Non-Uniform Rational B-Spline(NURBS).The coefficients correlated with control points are directly used as design variables.Therefore,the T-spline basis functions applied for geometry description and calculation of structural response are simultaneously introduced to represent the density distribution.Several numerical examples show that the proposed approach leads to a coherent workflow to handle design problems of complicated structures.The optimized results are free of checkerboard patterns without additional stabilization and filtering techniques due to the properties of T-splines,which also simplified the post-processing.In addition,through performing local refinement,we can easily achieve multiresolution optimization and infill optimization within the T-splines based framework.In general,the proposed method provides a possibility to design,analyze,and optimize engineering structures in a uniform model,which has the potential to improve design efficiency and reduce the cost of product development.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
A combined shape and topology optimization algorithm based on isogeometric boundary element method for 3D acoustics is developed in this study.The key treatment involves using adjoint variable method in shape sensitiv...A combined shape and topology optimization algorithm based on isogeometric boundary element method for 3D acoustics is developed in this study.The key treatment involves using adjoint variable method in shape sensitivity analysis with respect to non-uniform rational basis splines control points,and in topology sensitivity analysis with respect to the artificial densities of sound absorption material.OpenMP tool in Fortran code is adopted to improve the efficiency of analysis.To consider the features and efficiencies of the two types of optimization methods,this study adopts a combined iteration scheme for the optimization process to investigate the simultaneous change of geometry shape and distribution of material to achieve better noise control.Numerical examples,such as sound barrier,simple tank,and BeTSSi submarine,are performed to validate the advantage of combined optimization in noise reduction,and to demonstrate the potential of the proposed method for engineering problems.展开更多
Topology optimization (TO) has developed rapidly recently. However, topology optimization with stress constraints still faces many challenges due to its highly non-linear properties which will cause inefficient comput...Topology optimization (TO) has developed rapidly recently. However, topology optimization with stress constraints still faces many challenges due to its highly non-linear properties which will cause inefficient computation, iterative oscillation, and convergence guarantee problems. At the same time, isogeometric analysis (IGA) is accepted by more and more researchers, and it has become one important tool in the field of topology optimization because of its high fidelity. In this paper, we focus on topology optimization with stress constraints based on isogeometric analysis to improve computation efficiency and stability. A new hybrid solver combining the alternating direction method of multipliers and the method of moving asymptotes (ADMM-MMA) is proposed to solve this problem. We first generate an initial feasible point by alternating direction method of multipliers (ADMM) in virtue of the rapid initial descent property. After that, we adopt the method of moving asymptotes (MMA) to get the final results. Several benchmark examples are used to verify the proposed method, and the results show its feasibility and effectiveness.展开更多
Isogeometric analysis(IGA),an approach that integrates CAE into conventional CAD design tools,has been used in structural optimization for 10 years,with plenty of excellent research results.This paper provides a compr...Isogeometric analysis(IGA),an approach that integrates CAE into conventional CAD design tools,has been used in structural optimization for 10 years,with plenty of excellent research results.This paper provides a comprehensive review on isogeometric shape and topology optimization,with a brief coverage of size optimization.For isogeometric shape optimization,attention is focused on the parametrization methods,mesh updating schemes and shape sensitivity analyses.Some interesting observations,e.g.the popularity of using direct(differential)method for shape sensitivity analysis and the possibility of developing a large scale,seamlessly integrated analysis-design platform,are discussed in the framework of isogeometric shape optimization.For isogeometric topology optimization(ITO),we discuss different types of ITOs,e.g.ITO using SIMP(Solid Isotropic Material with Penalization)method,ITO using level set method,ITO using moving morphable com-ponents(MMC),ITO with phase field model,etc.,their technical details and applications such as the spline filter,multi-resolution approach,multi-material problems and stress con-strained problems.In addition to the review in the last 10 years,the current developmental trend of isogeometric structural optimization is discussed.展开更多
This paper presents an effective fiber angle optimization method for two and multi-layered variable stiffness composites.A gradient-based fiber angle optimization method is developed based on isogeometric analysis(IGA...This paper presents an effective fiber angle optimization method for two and multi-layered variable stiffness composites.A gradient-based fiber angle optimization method is developed based on isogeometric analysis(IGA).Firstly,the element densities and fiber angles for two and multi-layered composites are synchronously optimized using an extended Bi-layered continuous fiber angle optimization method(XBi-CFAO).The densities and fiber angles in the base layer are attached to the control points.The structure response and sensitivity analysis are accomplished using the non-uniform rational B-spline(NURBS)based IGA.By the benefit of the B-spline space,this method is free from checkerboards,and no additional filtering is needed to smooth the sensitivity numbers.Then the curved fiber paths are generated using the streamline method and the discontinuous fiber paths are smoothed using a partitioned selection process.The proposed method in the paper can alleviate the phenomenon of fiber discontinuity,enhance information retention for the optimized fiber angles of the singular points and save calculating resources effectively.展开更多
This paper proposes a novel optimization framework in passive control techniques to reduce noise pollution.The geometries of the structures are represented by Catmull-Clark subdivision surfaces,which are able to build...This paper proposes a novel optimization framework in passive control techniques to reduce noise pollution.The geometries of the structures are represented by Catmull-Clark subdivision surfaces,which are able to build gap-free Computer-Aided Design models and meanwhile tackle the extraordinary points that are commonly encountered in geometricmodelling.The acoustic fields are simulated using the isogeometric boundary elementmethod,and a density-based topology optimization is conducted to optimize distribution of sound-absorbing materials adhered to structural surfaces.The approach enables one to perform acoustic optimization from Computer-Aided Design models directly without needingmeshing and volume parameterization,thereby avoiding the geometric errors and time-consuming preprocessing steps in conventional simulation and optimization methods.The effectiveness of the present method is demonstrated by three dimensional numerical examples.展开更多
We present an energy penalization method for isogeometric topology optimization using moving morphable components(ITO–MMC),propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetr...We present an energy penalization method for isogeometric topology optimization using moving morphable components(ITO–MMC),propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetric structures,and then extend the proposed energy penalization method to an ITO–MMC with a symmetric constraint.The energy penalization method can solve the problems of numerical instability and convergence for the ITO–MMC and the ITO–MMC subjected to the structural symmetric constraint with asymmetric loads.Topology optimization problems of asymmetric,bilateral symmetric,and periodic symmetric structures are discussed to validate the effectiveness of the proposed energy penalization approach.Compared with the conventional ITO–MMC,the energy penalization method for the ITO–MMC can improve the convergence rate from 18.6%to 44.5%for the optimization of the asymmetric structure.For the ITO–MMC under a bilateral symmetric constraint,the proposed method can reduce the objective value by 5.6%and obtain a final optimized topology that has a clear boundary with decreased iterations.For the ITO–MMC under a periodic symmetric constraint,the proposed energy penalization method can dramatically reduce the number of iterations and obtain a speedup of more than 2.展开更多
Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises.In this study,we develop an isogeometric analysis(IGA)-based level set model for the fonnulation a...Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises.In this study,we develop an isogeometric analysis(IGA)-based level set model for the fonnulation and solution of topology optimization in cases with maximum eigenfrequency.The proposed method is based on a combination of level set method and IGA technique,which uses the non-uniform rational B-spline(NURBS),description of geometry,to perfonn analysis.The same NURBS is used for geometry representation,but also for IGA-based dynamic analysis and parameterization of the level set surface,that is,the level set function.The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material.A modal track method,that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization.The validity and efficiency of the proposed method are illustrated by benchmark examples.展开更多
基金the National Key R&D Program of China(2020YFB1708300)the National Natural Science Foundation of China(52005192)the Project of Ministry of Industry and Information Technology(TC210804R-3).
文摘This paper aims to solve large-scale and complex isogeometric topology optimization problems that consumesignificant computational resources. A novel isogeometric topology optimization method with a hybrid parallelstrategy of CPU/GPU is proposed, while the hybrid parallel strategies for stiffness matrix assembly, equationsolving, sensitivity analysis, and design variable update are discussed in detail. To ensure the high efficiency ofCPU/GPU computing, a workload balancing strategy is presented for optimally distributing the workload betweenCPU and GPU. To illustrate the advantages of the proposedmethod, three benchmark examples are tested to verifythe hybrid parallel strategy in this paper. The results show that the efficiency of the hybrid method is faster thanserial CPU and parallel GPU, while the speedups can be up to two orders of magnitude.
基金supported by the National Key R&D Program of China(Grant Number 2020YFB1708300)China National Postdoctoral Program for Innovative Talents(Grant Number BX20220124)+1 种基金China Postdoctoral Science Foundation(Grant Number 2022M710055)the New Cornerstone Science Foundation through the XPLORER PRIZE,the Knowledge Innovation Program of Wuhan-Shuguang,the Young Top-Notch Talent Cultivation Program of Hubei Province and the Taihu Lake Innovation Fund for Future Technology(Grant Number HUST:2023-B-7).
文摘Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio.In this paper,a full-scale isogeometric topology optimization(ITO)method based on Kirchhoff-Love shells for designing cellular tshin-shell structures with excellent damage tolerance ability is proposed.This method utilizes high-order continuous nonuniform rational B-splines(NURBS)as basis functions for Kirchhoff-Love shell elements.The geometric and analysis models of thin shells are unified by isogeometric analysis(IGA)to avoid geometric approximation error and improve computational accuracy.The topological configurations of thin-shell structures are described by constructing the effective density field on the controlmesh.Local volume constraints are imposed in the proximity of each control point to obtain bone-like cellular structures.To facilitate numerical implementation,the p-norm function is used to aggregate local volume constraints into an equivalent global constraint.Several numerical examples are provided to demonstrate the effectiveness of the proposed method.After simulation and comparative analysis,the results indicate that the cellular thin-shell structures optimized by the proposed method exhibit great load-carrying behavior and high damage robustness.
基金supported by the National Key R&D Program of China (2020YFB1708300)the Project funded by the China Postdoctoral Science Foundation (2021M701310).
文摘This work puts forward an explicit isogeometric topology optimization(ITO)method using moving morphable components(MMC),which takes the suitably graded truncated hierarchical B-Spline based isogeometric analysis as the solver of physical unknown(SGTHB-ITO-MMC).By applying properly basis graded constraints to the hierarchical mesh of truncated hierarchical B-splines(THB),the convergence and robustness of the SGTHB-ITOMMC are simultaneously improved and the tiny holes occurred in optimized structure are eliminated,due to the improved accuracy around the explicit structural boundaries.Moreover,an efficient computational method is developed for the topological description functions(TDF)ofMMC under the admissible hierarchicalmesh,which consists of reducing the dimensionality strategy for design space and the locally computing strategy for hierarchical mesh.We apply the above SGTHB-ITO-MMC with improved efficiency to a series of 2D and 3Dcompliance design problems.The numerical results show that the proposed SGTHB-ITO-MMC method outperforms the traditional THB-ITO-MMCmethod in terms of convergence rate and efficiency.Therefore,the proposed SGTHB-ITO-MMC is an effective way of solving topology optimization(TO)problems.
基金supported by the Fundamental Research Funds for the Cen-tral Universities(No.JUSRP12038)the Natural Science Foundation of Jiangsu Province(No.BK20200611)the National Natural Science Foundation of China(No.12102146).
文摘Topological optimization plays a guiding role in the conceptual design process.This paper conducts research on structural topology optimization algorithm within the framework of isogeometric analysis.For multi-component structures,the Nitsche’smethod is used to glue differentmeshes to performisogeometricmulti-patch analysis.The discrete variable topology optimization algorithm based on integer programming is adopted in order to obtain clear boundaries for topology optimization.The sensitivity filtering method based on the Helmholtz equation is employed for averaging of curved elements’sensitivities.In addition,a simple averaging method along coupling interfaces is proposed in order to ensure the material distribution across coupling areas is reasonably smooth.Finally,the performance of the algorithm is demonstrated by numerical examples,and the effectiveness of the algorithm is verified by comparing it with the results obtained by single-patch and ABAQUS cases.
基金sponsored by Natural Science Foundation of Henan under Grant No.222300420498.
文摘In this work,an acoustic topology optimizationmethod for structural surface design covered by porous materials is proposed.The analysis of acoustic problems is performed using the isogeometric boundary elementmethod.Taking the element density of porousmaterials as the design variable,the volume of porousmaterials as the constraint,and the minimum sound pressure or maximum scattered sound power as the design goal,the topology optimization is carried out by solid isotropic material with penalization(SIMP)method.To get a limpid 0–1 distribution,a smoothing Heaviside-like function is proposed.To obtain the gradient value of the objective function,a sensitivity analysis method based on the adjoint variable method(AVM)is proposed.To find the optimal solution,the optimization problems are solved by the method of moving asymptotes(MMA)based on gradient information.Numerical examples verify the effectiveness of the proposed topology optimization method in the optimization process of two-dimensional acoustic problems.Furthermore,the optimal distribution of sound-absorbingmaterials is highly frequency-dependent and usually needs to be performed within a frequency band.
基金Supported by National Key R&D Program of China(Grant No.2020YFB1708304)and Fundamental Research Funds for the Central Universities of the Huazhong University of Science and Technology(Grant No.5003123021)and the Program for HUST Academic Frontier Youth Team(Grant No.2017QYTD04).
文摘Topology Optimization(TO)is a powerful numerical technique to determine the optimal material layout in a design domain,which has accepted considerable developments in recent years.The classic Finite Element Method(FEM)is applied to compute the unknown structural responses in TO.However,several numerical deficiencies of the FEM significantly influence the effectiveness and efficiency of TO.In order to eliminate the negative influence of the FEM on TO,IsoGeometric Analysis(IGA)has become a promising alternative due to its unique feature that the Computer-Aided Design(CAD)model and Computer-Aided Engineering(CAE)model can be unified into a same mathematical model.In the paper,the main intention is to provide a comprehensive overview for the developments of Isogeometric Topology Optimization(ITO)in methods and applications.Finally,some prospects for the developments of ITO in the future are also presented.
基金supported by the Natural Science Foundation of China(Project Nos.61972011 and 61572056).
文摘In this paper,a new isogeometric topology optimization(ITO)method is proposed by using T-splines based isogeometric analysis(IGA).The arbitrarily shaped design domains,directly obtained from CAD,are represented by a single T-spline surface which overcomes the topological limitations of Non-Uniform Rational B-Spline(NURBS).The coefficients correlated with control points are directly used as design variables.Therefore,the T-spline basis functions applied for geometry description and calculation of structural response are simultaneously introduced to represent the density distribution.Several numerical examples show that the proposed approach leads to a coherent workflow to handle design problems of complicated structures.The optimized results are free of checkerboard patterns without additional stabilization and filtering techniques due to the properties of T-splines,which also simplified the post-processing.In addition,through performing local refinement,we can easily achieve multiresolution optimization and infill optimization within the T-splines based framework.In general,the proposed method provides a possibility to design,analyze,and optimize engineering structures in a uniform model,which has the potential to improve design efficiency and reduce the cost of product development.
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This study was financially supported by the National Natural Science Foundation of China(NSFC)under Grant No.11772322the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No.XDB22040502.
文摘A combined shape and topology optimization algorithm based on isogeometric boundary element method for 3D acoustics is developed in this study.The key treatment involves using adjoint variable method in shape sensitivity analysis with respect to non-uniform rational basis splines control points,and in topology sensitivity analysis with respect to the artificial densities of sound absorption material.OpenMP tool in Fortran code is adopted to improve the efficiency of analysis.To consider the features and efficiencies of the two types of optimization methods,this study adopts a combined iteration scheme for the optimization process to investigate the simultaneous change of geometry shape and distribution of material to achieve better noise control.Numerical examples,such as sound barrier,simple tank,and BeTSSi submarine,are performed to validate the advantage of combined optimization in noise reduction,and to demonstrate the potential of the proposed method for engineering problems.
文摘Topology optimization (TO) has developed rapidly recently. However, topology optimization with stress constraints still faces many challenges due to its highly non-linear properties which will cause inefficient computation, iterative oscillation, and convergence guarantee problems. At the same time, isogeometric analysis (IGA) is accepted by more and more researchers, and it has become one important tool in the field of topology optimization because of its high fidelity. In this paper, we focus on topology optimization with stress constraints based on isogeometric analysis to improve computation efficiency and stability. A new hybrid solver combining the alternating direction method of multipliers and the method of moving asymptotes (ADMM-MMA) is proposed to solve this problem. We first generate an initial feasible point by alternating direction method of multipliers (ADMM) in virtue of the rapid initial descent property. After that, we adopt the method of moving asymptotes (MMA) to get the final results. Several benchmark examples are used to verify the proposed method, and the results show its feasibility and effectiveness.
基金This work was supported by National Natural Science Foundation of China(51705158)the Fundamental Research Funds for the Central Universities(2018MS45)Open Funds of National Engineering Research Center of Near-Net-Shape Forming for Metallic Materials(2018005).
文摘Isogeometric analysis(IGA),an approach that integrates CAE into conventional CAD design tools,has been used in structural optimization for 10 years,with plenty of excellent research results.This paper provides a comprehensive review on isogeometric shape and topology optimization,with a brief coverage of size optimization.For isogeometric shape optimization,attention is focused on the parametrization methods,mesh updating schemes and shape sensitivity analyses.Some interesting observations,e.g.the popularity of using direct(differential)method for shape sensitivity analysis and the possibility of developing a large scale,seamlessly integrated analysis-design platform,are discussed in the framework of isogeometric shape optimization.For isogeometric topology optimization(ITO),we discuss different types of ITOs,e.g.ITO using SIMP(Solid Isotropic Material with Penalization)method,ITO using level set method,ITO using moving morphable com-ponents(MMC),ITO with phase field model,etc.,their technical details and applications such as the spline filter,multi-resolution approach,multi-material problems and stress con-strained problems.In addition to the review in the last 10 years,the current developmental trend of isogeometric structural optimization is discussed.
基金This research work is supported by the National Key R&D Project of China(Grant Nos.2018YFB1700803 and 2018YFB1700804)managed by Qifu Wang.These supports are gratefully acknowledged.
文摘This paper presents an effective fiber angle optimization method for two and multi-layered variable stiffness composites.A gradient-based fiber angle optimization method is developed based on isogeometric analysis(IGA).Firstly,the element densities and fiber angles for two and multi-layered composites are synchronously optimized using an extended Bi-layered continuous fiber angle optimization method(XBi-CFAO).The densities and fiber angles in the base layer are attached to the control points.The structure response and sensitivity analysis are accomplished using the non-uniform rational B-spline(NURBS)based IGA.By the benefit of the B-spline space,this method is free from checkerboards,and no additional filtering is needed to smooth the sensitivity numbers.Then the curved fiber paths are generated using the streamline method and the discontinuous fiber paths are smoothed using a partitioned selection process.The proposed method in the paper can alleviate the phenomenon of fiber discontinuity,enhance information retention for the optimized fiber angles of the singular points and save calculating resources effectively.
基金We acknowledge the support of the National Natural Science Foundation of China(NSFC)under Grant Nos.51904202 and 11702238Stephane Bordas thanks the financial support of Intuitive modeling and SIMulation platform(IntuiSIM)(PoC17/12253887)grant by Luxembourg National Research Fund.
文摘This paper proposes a novel optimization framework in passive control techniques to reduce noise pollution.The geometries of the structures are represented by Catmull-Clark subdivision surfaces,which are able to build gap-free Computer-Aided Design models and meanwhile tackle the extraordinary points that are commonly encountered in geometricmodelling.The acoustic fields are simulated using the isogeometric boundary elementmethod,and a density-based topology optimization is conducted to optimize distribution of sound-absorbing materials adhered to structural surfaces.The approach enables one to perform acoustic optimization from Computer-Aided Design models directly without needingmeshing and volume parameterization,thereby avoiding the geometric errors and time-consuming preprocessing steps in conventional simulation and optimization methods.The effectiveness of the present method is demonstrated by three dimensional numerical examples.
基金the National Key Research and Development Programof China(2020YFB1708300)NationalNatural Science Foundation of China(52075184)+1 种基金Natural Science Foundation of Hubei Province(2019CFA059)Tencent XPLORER PRIZE.
基金This research was supported by the National Natural Science Foundation of China(Grant Nos.51675197 and 51705158)the National Engineering Research Center of Near-Net-Shape Forming for Metallic Materials,Ministry of Education Key Laboratory of High Efficient Near-Net-Shape Forming Technology and Equipment for Metallic Materials(Category B)Opening Foundation(Grant No.2018005)The support is gratefully acknowledged.
文摘We present an energy penalization method for isogeometric topology optimization using moving morphable components(ITO–MMC),propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetric structures,and then extend the proposed energy penalization method to an ITO–MMC with a symmetric constraint.The energy penalization method can solve the problems of numerical instability and convergence for the ITO–MMC and the ITO–MMC subjected to the structural symmetric constraint with asymmetric loads.Topology optimization problems of asymmetric,bilateral symmetric,and periodic symmetric structures are discussed to validate the effectiveness of the proposed energy penalization approach.Compared with the conventional ITO–MMC,the energy penalization method for the ITO–MMC can improve the convergence rate from 18.6%to 44.5%for the optimization of the asymmetric structure.For the ITO–MMC under a bilateral symmetric constraint,the proposed method can reduce the objective value by 5.6%and obtain a final optimized topology that has a clear boundary with decreased iterations.For the ITO–MMC under a periodic symmetric constraint,the proposed energy penalization method can dramatically reduce the number of iterations and obtain a speedup of more than 2.
基金the National Natural Science Foundation of China(Grant No.51675197).
文摘Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises.In this study,we develop an isogeometric analysis(IGA)-based level set model for the fonnulation and solution of topology optimization in cases with maximum eigenfrequency.The proposed method is based on a combination of level set method and IGA technique,which uses the non-uniform rational B-spline(NURBS),description of geometry,to perfonn analysis.The same NURBS is used for geometry representation,but also for IGA-based dynamic analysis and parameterization of the level set surface,that is,the level set function.The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material.A modal track method,that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization.The validity and efficiency of the proposed method are illustrated by benchmark examples.