We propose an optimal approach to solve the problem of multi-degree reduction of C-Brzier surfaces in the norm L2 with prescribed constraints. The control points of the degree-reduced C-Brzier surfaces can be explicit...We propose an optimal approach to solve the problem of multi-degree reduction of C-Brzier surfaces in the norm L2 with prescribed constraints. The control points of the degree-reduced C-Brzier surfaces can be explicitly obtained by using a matrix operation that is based on the transfer matrix of the C-Brzier basis. With prescribed boundary constraints, this method can be applied to piecewise continuous patches or to a single patch with the combination of surface subdivision. The resulting piecewise approximating patches are globally G1 continuous. Finally, numerical examples are presented to show the effectiveness of the method.展开更多
This article describes a study of the satellite module layout problem （SMLP）, which is a three-dimensional （3D） layout optimization problem with performance constraints that has proved to be non-deterministic poly...This article describes a study of the satellite module layout problem （SMLP）, which is a three-dimensional （3D） layout optimization problem with performance constraints that has proved to be non-deterministic polynomial-time hard （NP-hard）. To deal with this problem, we convert it into an unconstrained optimization problem using a quasi-physical strategy and the penalty function method. The energy landscape paving （ELP） method is a class of Monte-Carlo-based global optimization algorithm that has been successfully applied to solve many optimization problems. ELP can search for low-energy layouts via a random walk in complex energy landscapes. However, when ELP falls into the narrow and deep valleys of an energy landscape, it is difficult to escape. By putting forward a new update mechanism of the histogram function in ELP, we obtain an improved ELP method which can overcome this drawback. By incorporating the gradient method with local search into the improved ELP method, a new global search optimization method, hELP, is proposed for SMLP. Two representative instances from the literature are tested. Computational results show that the proposed hELP algorithm is an effective method for solving SMLP with performance constraints.展开更多
An effective design method of freeform micro lens array is presented for shaping varied laser beams into prescribed rectangular illumination. The variable separation mapping is applied to design concave freeform surfa...An effective design method of freeform micro lens array is presented for shaping varied laser beams into prescribed rectangular illumination. The variable separation mapping is applied to design concave freeform surfaces for constructing a freeform lens array. Several dedicated examples show that the designed freeform optical lens array can achieve a prescribed rectangular illumination pattern, especially without considering the initial states of incident laser beams. Both high collection efficiency and good spatial uniformity can be available simultaneously. Tolerance analysis is also performed to demonstrate that this optical device can well avoid fabricating difficulty in actual applications.展开更多
A new analytical method for springback of small curvature plane bending is addressed with unloading rule of classical elastic-plastic theory and principle of strain superposition.We start from strain analysis of plane...A new analytical method for springback of small curvature plane bending is addressed with unloading rule of classical elastic-plastic theory and principle of strain superposition.We start from strain analysis of plane bending which has initial curvature,and the theoretic derivation is on the widely applicable basic hypotheses.The results are unified to geometry constraint equations and springback equation of plane bending,which can be evolved to straight beam plane bending and pure bending.The expanding and setting round process is one of the situations of plane bending,which is a bend-stretching process of plane curved beam.In the present study,springback equation of plane bending is used to analyze the expanding and setting round process,and the results agree with the experimental data.With a reasonable prediction accuracy,this new analytical method for springback of plane bending can meet the needs of applications in engineering.展开更多
基金Project supported by the National Natural Science Foundation of China （Nos. 11401373, 61402281, and 11601322） and the Zhejiang Provincial Natural Science Foundation, China （No. LY16F020020）
文摘We propose an optimal approach to solve the problem of multi-degree reduction of C-Brzier surfaces in the norm L2 with prescribed constraints. The control points of the degree-reduced C-Brzier surfaces can be explicitly obtained by using a matrix operation that is based on the transfer matrix of the C-Brzier basis. With prescribed boundary constraints, this method can be applied to piecewise continuous patches or to a single patch with the combination of surface subdivision. The resulting piecewise approximating patches are globally G1 continuous. Finally, numerical examples are presented to show the effectiveness of the method.
基金Project supported by the National Natural Science Foundation of China （No. 61373016）, the Six Talent Peaks Project of Jiangsu Province, China （No. DZXX-041）, the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, and the Natural Science Foundation of Jiangsu Province, China （No. BK20141005）
文摘This article describes a study of the satellite module layout problem （SMLP）, which is a three-dimensional （3D） layout optimization problem with performance constraints that has proved to be non-deterministic polynomial-time hard （NP-hard）. To deal with this problem, we convert it into an unconstrained optimization problem using a quasi-physical strategy and the penalty function method. The energy landscape paving （ELP） method is a class of Monte-Carlo-based global optimization algorithm that has been successfully applied to solve many optimization problems. ELP can search for low-energy layouts via a random walk in complex energy landscapes. However, when ELP falls into the narrow and deep valleys of an energy landscape, it is difficult to escape. By putting forward a new update mechanism of the histogram function in ELP, we obtain an improved ELP method which can overcome this drawback. By incorporating the gradient method with local search into the improved ELP method, a new global search optimization method, hELP, is proposed for SMLP. Two representative instances from the literature are tested. Computational results show that the proposed hELP algorithm is an effective method for solving SMLP with performance constraints.
基金supported by the National Natural Science Foundation of China(No.61405037)the Science and Technology Project of Fujian Province(No.2015H4014)
文摘An effective design method of freeform micro lens array is presented for shaping varied laser beams into prescribed rectangular illumination. The variable separation mapping is applied to design concave freeform surfaces for constructing a freeform lens array. Several dedicated examples show that the designed freeform optical lens array can achieve a prescribed rectangular illumination pattern, especially without considering the initial states of incident laser beams. Both high collection efficiency and good spatial uniformity can be available simultaneously. Tolerance analysis is also performed to demonstrate that this optical device can well avoid fabricating difficulty in actual applications.
基金supported by the National Natural Science Foundation of China(Grant No.50805126)the Natural Science Foundation of Hebei Province(Grant No.E2009000389)
文摘A new analytical method for springback of small curvature plane bending is addressed with unloading rule of classical elastic-plastic theory and principle of strain superposition.We start from strain analysis of plane bending which has initial curvature,and the theoretic derivation is on the widely applicable basic hypotheses.The results are unified to geometry constraint equations and springback equation of plane bending,which can be evolved to straight beam plane bending and pure bending.The expanding and setting round process is one of the situations of plane bending,which is a bend-stretching process of plane curved beam.In the present study,springback equation of plane bending is used to analyze the expanding and setting round process,and the results agree with the experimental data.With a reasonable prediction accuracy,this new analytical method for springback of plane bending can meet the needs of applications in engineering.
