Based on the traditional re-entrant honeycomb,a novel re-entrant octagon honeycomb(ROH)is proposed.The deformation mode of the honeycomb under quasi-static compression is analyzed by numerical simulation,and the resul...Based on the traditional re-entrant honeycomb,a novel re-entrant octagon honeycomb(ROH)is proposed.The deformation mode of the honeycomb under quasi-static compression is analyzed by numerical simulation,and the results are in good agreement with the experimental ones.The deformation modes,mechanical properties,and energy absorption characteristics of ROH along the impact and perpendicular directions gradient design are investigated under different velocities.The results indicated that the deformation mode of ROH is affected by gradient design along the direction of impact and impact speed.In addition,gradient design along the direction of impact can increase the initial peak stress of ROH and accelerate its densification phase.Gradient design perpendicular to the impact direction can enhance the energy absorption performance of ROH,especially for ROH,with wall thickness increasing from the inside outwards.Compared to ROH with uniform wall thickness at the same relative density,ROH with a gradient design can increase the plateau stress by over half.With the elevation of impact velocity,the plateau stress and specific energy absorption exhibit an upward trend,aligning with the dynamic performance pattern observed in conventional honeycombs.The results can be used as a reference for the design and application of honeycomb and provide a new idea for developing more efficient and reliable energy-absorbing materials.展开更多
Based on the analyses of the severity of cutting process as well as the failure mechanisms of ceramic tools, a model for designing functionally gradient ceramic tool materials with symmetrical distribution is presente...Based on the analyses of the severity of cutting process as well as the failure mechanisms of ceramic tools, a model for designing functionally gradient ceramic tool materials with symmetrical distribution is presented, by which a Al 2O 3/(W,Ti)C ceramic tool material FG 2 was developed. Multi objective optimization method was employed in designing the compositional distribution of this ceramic tool material. The results of both continuous and intermittent cutting tests are indicative of the much better cutting behavior of the functionally gradient ceramic tool FG 2 than that of the common ceramic tool SG 4.展开更多
This paper proposes a gradient conformal design technique to modify the multi-directional stiffness characteristics of 3D printed chiral metamaterials,using various airfoil shapes.The method ensures the integrity of c...This paper proposes a gradient conformal design technique to modify the multi-directional stiffness characteristics of 3D printed chiral metamaterials,using various airfoil shapes.The method ensures the integrity of chiral cell nodal circles while improving load transmission efficiency and enhancing manufacturing precision for 3D printing applications.A parametric design framework,integrating finite element analysis and optimization modules,is developed to enhance the wing’s multidirectional stiffness.The optimization process demonstrates that the distribution of chiral structural ligaments and nodal circles significantly affects wing deformation.The stiffness gradient optimization results reveal a variation of over 78%in tail stiffness performance between the best and worst parameter combinations.Experimental outcomes suggest that this strategy can develop metamaterials with enhanced deformability,offering a promising approach for designing morphing wings.展开更多
This paper presents the generalized reduced gradient method （GRG） and its realization forms. The application example of GRG in the optimization design of a single-stage cylindrical gear reducer is introduced. The al...This paper presents the generalized reduced gradient method （GRG） and its realization forms. The application example of GRG in the optimization design of a single-stage cylindrical gear reducer is introduced. The algo- rithm of the GRG method is realized in Vissim software. Based on the mathematical model of the single-stage cylin- drical gear reducer, the simulation structure of the optimization design was achieved. The experiment results show that the GRG method has fewer iterations and higher precision. The GRG method is very suitable for solving mechanical optimization design.展开更多
Based on a level set model and the homogenization theory, an optimization al- gorithm for ?nding the optimal con?guration of the microstructure with speci?ed properties is proposed, which extends current resea...Based on a level set model and the homogenization theory, an optimization al- gorithm for ?nding the optimal con?guration of the microstructure with speci?ed properties is proposed, which extends current research on the level set method for structure topology opti- mization. The method proposed employs a level set model to implicitly describe the material interfaces of the microstructure and a Hamilton-Jacobi equation to continuously evolve the ma- terial interfaces until an optimal design is achieved. Meanwhile, the moving velocities of level set are obtained by conducting sensitivity analysis and gradient projection. Besides, how to handle the violated constraints is also discussed in the level set method for topological optimization, and a return-mapping algorithm is constructed. Numerical examples show that the method exhibits outstanding ?exibility of handling topological changes and ?delity of material interface represen- tation as compared with other conventional methods in literatures.展开更多
The genetic/gradient-based hybrid algorithm is introduced and used in the design studies of aeroelastic optimization of large aircraft wings to attain skin distribution,stiffness distribution and design sensitivity.Th...The genetic/gradient-based hybrid algorithm is introduced and used in the design studies of aeroelastic optimization of large aircraft wings to attain skin distribution,stiffness distribution and design sensitivity.The program of genetic algorithm is developed by the authors while the gradient-based algorithm borrows from the modified method for feasible direction in MSC/NASTRAN software.In the hybrid algorithm,the genetic algorithm is used to perform global search to avoid to fall into local optima,and then the excellent individuals of every generation optimized by the genetic algorithm are further fine-tuned by the modified method for feasible direction to attain the local optima and hence to get global optima.Moreover,the application effects of hybrid genetic algorithm in aeroelastic multidisciplinary design optimization of large aircraft wing are discussed,which satisfy multiple constraints of strength,displacement,aileron efficiency,and flutter speed.The application results show that the genetic/gradient-based hybrid algorithm is available for aeroelastic optimization of large aircraft wings in initial design phase as well as detailed design phase,and the optimization results are very consistent.Therefore,the design modifications can be decreased using the genetic/gradient-based hybrid algorithm.展开更多
When trying to fit data to functions of the eigensystem of a pde-eigenvalue problem, such as Maxwell’s equation, numerical differentiation is ineffective and analytic gradients must be supplied. In our motivating exa...When trying to fit data to functions of the eigensystem of a pde-eigenvalue problem, such as Maxwell’s equation, numerical differentiation is ineffective and analytic gradients must be supplied. In our motivating example of trying to determine the chemical composition of the layers of specialty optical fibers, the function involved fitting the higher order derivatives with respect to frequency of the positive eigenvalues. The computation of the gradient was the most time consuming part of the minimization problem. It was realized that if one interchanged the order of differentiation, and differentiated first with respect to the design parameters, fewer derivatives of the eigenvectors would be required and one could take full advantage that each grid point was affected by only a few variables. As the model was expanded to cover a fiber wrapped around a spool, the bandwidth of the linearized symmetric eigenvalue problem increased. At the heart of each of the iterative methods used to find the few positive eigenvalues was a symmetric, banded, indefinite matrix. Here we present an algorithm for this problem which reduces a symmetric banded matrix to a block diagonal matrix of 1 x 1 and 2 x 2 blocks. Fillin outside the band because of pivoting for stability is prevented by a sequence of planar transformations. Computationally the algorithm is compared to the block unsymmetric banded solver and the block positive definite symmetric band solver in LAPACK.展开更多
This study presents a new method for designing algorithm for a triplet lens with one or two elements that are made of a gradient index medium (GRIN). This method is based upon considering a well-known designed triplet...This study presents a new method for designing algorithm for a triplet lens with one or two elements that are made of a gradient index medium (GRIN). This method is based upon considering a well-known designed triplet lens (Cooke triplet lens) as a target lens for designing of the Hybrid Triplet Lens (HTL). Our design was based upon keeping the total optical path length for the axial ray fixed for each case of design. The results showed that several designs for the HTL have the same total powers of the target lens. These designs depend on the variation of the GRIN element parameter values and the order of the GRIN element position in the system. These HTL designs have been evaluated by considering several optical merit functions, i.e., the root mean square (RMS) spot radius, wave front error and the spherical aberration. To achieve the optimal design, these functions are compared for the target lens and the HTL designs through a wide range of field angles.展开更多
基金This work is supported by the National Natural Science Foundation of China(No.11902232).
文摘Based on the traditional re-entrant honeycomb,a novel re-entrant octagon honeycomb(ROH)is proposed.The deformation mode of the honeycomb under quasi-static compression is analyzed by numerical simulation,and the results are in good agreement with the experimental ones.The deformation modes,mechanical properties,and energy absorption characteristics of ROH along the impact and perpendicular directions gradient design are investigated under different velocities.The results indicated that the deformation mode of ROH is affected by gradient design along the direction of impact and impact speed.In addition,gradient design along the direction of impact can increase the initial peak stress of ROH and accelerate its densification phase.Gradient design perpendicular to the impact direction can enhance the energy absorption performance of ROH,especially for ROH,with wall thickness increasing from the inside outwards.Compared to ROH with uniform wall thickness at the same relative density,ROH with a gradient design can increase the plateau stress by over half.With the elevation of impact velocity,the plateau stress and specific energy absorption exhibit an upward trend,aligning with the dynamic performance pattern observed in conventional honeycombs.The results can be used as a reference for the design and application of honeycomb and provide a new idea for developing more efficient and reliable energy-absorbing materials.
文摘Based on the analyses of the severity of cutting process as well as the failure mechanisms of ceramic tools, a model for designing functionally gradient ceramic tool materials with symmetrical distribution is presented, by which a Al 2O 3/(W,Ti)C ceramic tool material FG 2 was developed. Multi objective optimization method was employed in designing the compositional distribution of this ceramic tool material. The results of both continuous and intermittent cutting tests are indicative of the much better cutting behavior of the functionally gradient ceramic tool FG 2 than that of the common ceramic tool SG 4.
基金Supported by National Natural Science Foundation of China(Grant Nos.52075026 and 52192632)the Fundamental Research Funds for the Central Universities(Grant No.YWF-22-L-1119)。
文摘This paper proposes a gradient conformal design technique to modify the multi-directional stiffness characteristics of 3D printed chiral metamaterials,using various airfoil shapes.The method ensures the integrity of chiral cell nodal circles while improving load transmission efficiency and enhancing manufacturing precision for 3D printing applications.A parametric design framework,integrating finite element analysis and optimization modules,is developed to enhance the wing’s multidirectional stiffness.The optimization process demonstrates that the distribution of chiral structural ligaments and nodal circles significantly affects wing deformation.The stiffness gradient optimization results reveal a variation of over 78%in tail stiffness performance between the best and worst parameter combinations.Experimental outcomes suggest that this strategy can develop metamaterials with enhanced deformability,offering a promising approach for designing morphing wings.
文摘This paper presents the generalized reduced gradient method （GRG） and its realization forms. The application example of GRG in the optimization design of a single-stage cylindrical gear reducer is introduced. The algo- rithm of the GRG method is realized in Vissim software. Based on the mathematical model of the single-stage cylin- drical gear reducer, the simulation structure of the optimization design was achieved. The experiment results show that the GRG method has fewer iterations and higher precision. The GRG method is very suitable for solving mechanical optimization design.
基金Project supported by the National Natural Science Foundation of China (Nos. 59805001 and 10332010) and the KeyScience and Technology Research Project of Ministry of Education of China (No. 104060).
文摘Based on a level set model and the homogenization theory, an optimization al- gorithm for ?nding the optimal con?guration of the microstructure with speci?ed properties is proposed, which extends current research on the level set method for structure topology opti- mization. The method proposed employs a level set model to implicitly describe the material interfaces of the microstructure and a Hamilton-Jacobi equation to continuously evolve the ma- terial interfaces until an optimal design is achieved. Meanwhile, the moving velocities of level set are obtained by conducting sensitivity analysis and gradient projection. Besides, how to handle the violated constraints is also discussed in the level set method for topological optimization, and a return-mapping algorithm is constructed. Numerical examples show that the method exhibits outstanding ?exibility of handling topological changes and ?delity of material interface represen- tation as compared with other conventional methods in literatures.
基金Supported by the National Natural Science Foundation of China(1117202591116)
文摘The genetic/gradient-based hybrid algorithm is introduced and used in the design studies of aeroelastic optimization of large aircraft wings to attain skin distribution,stiffness distribution and design sensitivity.The program of genetic algorithm is developed by the authors while the gradient-based algorithm borrows from the modified method for feasible direction in MSC/NASTRAN software.In the hybrid algorithm,the genetic algorithm is used to perform global search to avoid to fall into local optima,and then the excellent individuals of every generation optimized by the genetic algorithm are further fine-tuned by the modified method for feasible direction to attain the local optima and hence to get global optima.Moreover,the application effects of hybrid genetic algorithm in aeroelastic multidisciplinary design optimization of large aircraft wing are discussed,which satisfy multiple constraints of strength,displacement,aileron efficiency,and flutter speed.The application results show that the genetic/gradient-based hybrid algorithm is available for aeroelastic optimization of large aircraft wings in initial design phase as well as detailed design phase,and the optimization results are very consistent.Therefore,the design modifications can be decreased using the genetic/gradient-based hybrid algorithm.
文摘When trying to fit data to functions of the eigensystem of a pde-eigenvalue problem, such as Maxwell’s equation, numerical differentiation is ineffective and analytic gradients must be supplied. In our motivating example of trying to determine the chemical composition of the layers of specialty optical fibers, the function involved fitting the higher order derivatives with respect to frequency of the positive eigenvalues. The computation of the gradient was the most time consuming part of the minimization problem. It was realized that if one interchanged the order of differentiation, and differentiated first with respect to the design parameters, fewer derivatives of the eigenvectors would be required and one could take full advantage that each grid point was affected by only a few variables. As the model was expanded to cover a fiber wrapped around a spool, the bandwidth of the linearized symmetric eigenvalue problem increased. At the heart of each of the iterative methods used to find the few positive eigenvalues was a symmetric, banded, indefinite matrix. Here we present an algorithm for this problem which reduces a symmetric banded matrix to a block diagonal matrix of 1 x 1 and 2 x 2 blocks. Fillin outside the band because of pivoting for stability is prevented by a sequence of planar transformations. Computationally the algorithm is compared to the block unsymmetric banded solver and the block positive definite symmetric band solver in LAPACK.
文摘This study presents a new method for designing algorithm for a triplet lens with one or two elements that are made of a gradient index medium (GRIN). This method is based upon considering a well-known designed triplet lens (Cooke triplet lens) as a target lens for designing of the Hybrid Triplet Lens (HTL). Our design was based upon keeping the total optical path length for the axial ray fixed for each case of design. The results showed that several designs for the HTL have the same total powers of the target lens. These designs depend on the variation of the GRIN element parameter values and the order of the GRIN element position in the system. These HTL designs have been evaluated by considering several optical merit functions, i.e., the root mean square (RMS) spot radius, wave front error and the spherical aberration. To achieve the optimal design, these functions are compared for the target lens and the HTL designs through a wide range of field angles.
