Based on the two-scale asymptotic analysis method for elastic structures of composite materials formed by entirely basic configurations, the finite element formulation and its error estimates are presented in this pap...Based on the two-scale asymptotic analysis method for elastic structures of composite materials formed by entirely basic configurations, the finite element formulation and its error estimates are presented in this paper. Meanwhile, the approximate formulas of Du are also set up.展开更多
In this paper,the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic(TSA)exp...In this paper,the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic(TSA)expression of the displacement and the increment of temperature for composite materials with a small periodic configuration under the condition of thermoelasticity are briefly shown at first,then the multi-scale finite element algorithms based on TSA are discussed.Finally the numerical results evaluated by the multi-scale computational method are shown.It demonstrates that the basic configuration and the increment of temperature strongly influence the local strains and local stresses inside a basic cell.展开更多
The Griewank function is a typical multimodal benchmark function,composed of a quadratic convex function and an oscillatory nonconvex function.The comparative importance of Griewank's two major parts alters in dif...The Griewank function is a typical multimodal benchmark function,composed of a quadratic convex function and an oscillatory nonconvex function.The comparative importance of Griewank's two major parts alters in different dimensions.Different from most test functions,an unusual phenomenon appears when optimizing the Griewank function.The Griewank function first becomes more difficult and then becomes easier to optimize with the increase of dimension.In this study,from the methodology perspective,this phenomenon is explained by structural,mathematical,and quantum analyses.Furthermore,frequency transformation and amplitude transformation are implemented on the Griewank function to make a generalization.The multi-scale quantum harmonic oscillator algorithm(MQHOA)with quantum tunnel effect is used to verify its characteristics.Experimental results indicate that the Griewank function's two-scale structure is the main reason for this phenomenon.The quantum tunneling mechanism mentioned in this paper is an effective method which can be generalized to analyze the generation and variation of solutions for numerous swarm optimization algorithms.展开更多
By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M...By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.展开更多
The optimization of two-scale structures can adapt to the different needs of materials in various regions by reasonably arranging different microstructures at the macro scale,thereby considerably improving structural ...The optimization of two-scale structures can adapt to the different needs of materials in various regions by reasonably arranging different microstructures at the macro scale,thereby considerably improving structural performance.Here,a multiple variable cutting(M-VCUT)level set-based data-driven model of microstructures is presented,and a method based on this model is proposed for the optimal design of two-scale structures.The geometry of the microstructure is described using the M-VCUT level set method,and the effective mechanical properties of microstructures are computed by the homogenization method.Then,a database of microstructures containing their geometric and mechanical parameters is constructed.The two sets of parameters are adopted as input and output datasets,and a mapping relationship between the two datasets is established to build the data-driven model of microstructures.During the optimization of two-scale structures,the data-driven model is used for macroscale finite element and sensitivity analyses.The efficiency of the analysis and optimization of two-scale structures is improved because the computational costs of invoking such a data-driven model are much smaller than those of homogenization.展开更多
The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-sc...The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.展开更多
The novel laminated Ti-TiBw/Ti composites composed of pure Ti layers and TiBw/Ti composite layers have been successfully fabricated by reactive hot pressing. Herein, two-scale structures formed： the pure Ti layer and...The novel laminated Ti-TiBw/Ti composites composed of pure Ti layers and TiBw/Ti composite layers have been successfully fabricated by reactive hot pressing. Herein, two-scale structures formed： the pure Ti layer and TiBw/Ti composite layer together constructed a laminated structure at a macro scale. Furthermore, TiBw reinforcement was distributed around Ti particles and then formed a network microstructure in TiBw/Ti composite layer at a micro scale. The laminated Ti-TiBw/Ti composites reveal a superior combination of high strength and high elongation due to two-scale structures compared with the pure Ti, and a further enhancement in ductility compared with the network structured composites. Moreover, the elastic modulus of the laminated composites can be predicted by H-S upper bound, which is consistent with the experimental values.展开更多
文摘Based on the two-scale asymptotic analysis method for elastic structures of composite materials formed by entirely basic configurations, the finite element formulation and its error estimates are presented in this paper. Meanwhile, the approximate formulas of Du are also set up.
基金The project supported by the National Natural Science Foundation of China(19932030)Special Funds for Major State Basic Research Projects
文摘In this paper,the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic(TSA)expression of the displacement and the increment of temperature for composite materials with a small periodic configuration under the condition of thermoelasticity are briefly shown at first,then the multi-scale finite element algorithms based on TSA are discussed.Finally the numerical results evaluated by the multi-scale computational method are shown.It demonstrates that the basic configuration and the increment of temperature strongly influence the local strains and local stresses inside a basic cell.
基金Project supported by the Natural Science Foundation of Huai'an,China(No.HAB201828)the Fundamental Research Funds for the Central Universities of China(No.2019NYB22)the Open Foundation of Jiangsu Key Laboratory of Media Design and Software Technology,China(Nos.19ST0204 and 18ST0203)。
文摘The Griewank function is a typical multimodal benchmark function,composed of a quadratic convex function and an oscillatory nonconvex function.The comparative importance of Griewank's two major parts alters in different dimensions.Different from most test functions,an unusual phenomenon appears when optimizing the Griewank function.The Griewank function first becomes more difficult and then becomes easier to optimize with the increase of dimension.In this study,from the methodology perspective,this phenomenon is explained by structural,mathematical,and quantum analyses.Furthermore,frequency transformation and amplitude transformation are implemented on the Griewank function to make a generalization.The multi-scale quantum harmonic oscillator algorithm(MQHOA)with quantum tunnel effect is used to verify its characteristics.Experimental results indicate that the Griewank function's two-scale structure is the main reason for this phenomenon.The quantum tunneling mechanism mentioned in this paper is an effective method which can be generalized to analyze the generation and variation of solutions for numerous swarm optimization algorithms.
基金supported by the National Natural Science Foundation of China(Grant No.12272144).
文摘By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.
基金supported by the National Natural Science Foundation of China(Grant No.12272144).
文摘The optimization of two-scale structures can adapt to the different needs of materials in various regions by reasonably arranging different microstructures at the macro scale,thereby considerably improving structural performance.Here,a multiple variable cutting(M-VCUT)level set-based data-driven model of microstructures is presented,and a method based on this model is proposed for the optimal design of two-scale structures.The geometry of the microstructure is described using the M-VCUT level set method,and the effective mechanical properties of microstructures are computed by the homogenization method.Then,a database of microstructures containing their geometric and mechanical parameters is constructed.The two sets of parameters are adopted as input and output datasets,and a mapping relationship between the two datasets is established to build the data-driven model of microstructures.During the optimization of two-scale structures,the data-driven model is used for macroscale finite element and sensitivity analyses.The efficiency of the analysis and optimization of two-scale structures is improved because the computational costs of invoking such a data-driven model are much smaller than those of homogenization.
基金supported by the National Natural Science Foundation of China(Nos.10801042 and 11171257)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20104410120001)
文摘The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.
基金Funded by the National Natural Science Foundation of China(Nos.51101042,51271064 and 51228102)
文摘The novel laminated Ti-TiBw/Ti composites composed of pure Ti layers and TiBw/Ti composite layers have been successfully fabricated by reactive hot pressing. Herein, two-scale structures formed： the pure Ti layer and TiBw/Ti composite layer together constructed a laminated structure at a macro scale. Furthermore, TiBw reinforcement was distributed around Ti particles and then formed a network microstructure in TiBw/Ti composite layer at a micro scale. The laminated Ti-TiBw/Ti composites reveal a superior combination of high strength and high elongation due to two-scale structures compared with the pure Ti, and a further enhancement in ductility compared with the network structured composites. Moreover, the elastic modulus of the laminated composites can be predicted by H-S upper bound, which is consistent with the experimental values.
