To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection techniq...To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).展开更多
Arches are widely used when large spans are necessary, e.g. to overpass large rivers, and further possess unquestioned aesthetics advantages. Their structural efficiency depends primarily on optimal material exploitat...Arches are widely used when large spans are necessary, e.g. to overpass large rivers, and further possess unquestioned aesthetics advantages. Their structural efficiency depends primarily on optimal material exploitation, i.e. minimization of internal stress eccentricity,and on minimization of structural material volume. An efficient structure, under these terms, further requires simpler and lighter scaffolding, contributing in minimizing construction costs.Although arches have millenary use and many researches dealing with this typology are available in literature, there is still scope for design optimization. The proposed study is framed within this context. Investigation is limited to statically determinate plane arches under vertical load. The problem of finding the profile of an equal strength catenary subjected to its self-weight is spread out to the case of an inverted catenary of equal strength under its self-weight and an external constant load. In the first optimization step, constant normal stress is imposed at all sections, to maximize material exploitation, and the resulting arch centerline shape is computed in closed form. In the second step, the ensemble of foundations and arch is considered and optimized, taking the linear combination of arch weight and thrust as objective function. The linear combination is dependent on a single variable, and minima of the objective function(i.e. optimal geometric shape parameters) are computed and charted to be simply used in the design process.展开更多
A body frame composed of thin sheet metal is a crucial structure that determines the safety performance of a vehicle.Designing a correct weight and high-performance automotive body is an emerging engineering problem.T...A body frame composed of thin sheet metal is a crucial structure that determines the safety performance of a vehicle.Designing a correct weight and high-performance automotive body is an emerging engineering problem.To improve the performance of the automotive frame,we attempt to reconstruct its design criteria based on statistical and mechanical approaches.At first,a fundamental study on the frame strength is conducted and a cross-sectional shape optimization problem is developed for designing the cross-sectional shape of an automobile frame having a very high mass efficiency for strength.Shape optimization is carried out using the nonlinear finite element method and a meta-modeling-based genetic algorithm.Data analysis of the obtained set of optimal results is performed to identify the dominant design variables by employing the smoothing spline analysis of variance,the principal component analysis,and the self-organizing map technique.The relationship between the cross-sectional shape and the objective function is also analyzed by hierarchical clustering.A design guideline is obtained from these statistical approach results.A comparison between the statistically obtained design guideline and the conventional one based on the designers’experience is performed based on mechanical interpretation of the optimal cross-sectional frame.Finally,a mechanically reasonable new general-purpose design guideline is proposed for the cross-sectional shape of the automotive frame.展开更多
We consider optimal shape design in Stokes flow using H^(1) shape gradient flows based on the distributed Eulerian derivatives.MINI element is used for discretizations of Stokes equation and Galerkin finite element is...We consider optimal shape design in Stokes flow using H^(1) shape gradient flows based on the distributed Eulerian derivatives.MINI element is used for discretizations of Stokes equation and Galerkin finite element is used for discretizations of distributed and boundary H^(1) shape gradient flows.Convergence analysis with a priori error estimates is provided under general and different regularity assumptions.We investigate the performances of shape gradient descent algorithms for energy dissipation minimization and obstacle flow.Numerical comparisons in 2D and 3D show that the distributed H1 shape gradient flow is more accurate than the popular boundary type.The corresponding distributed shape gradient algorithm is more effective.展开更多
A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization...A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.展开更多
We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods...We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods mainly contain shape and topology schemes,with the former changing the surface geometric profile of the structure and the latter changing thematerial distribution topology or hole topology of the structure.In the present acoustic performance optimization,the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure,the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter,and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge.The topology and shape sensitivities of the approach are calculated using the adjoint variable method,which ensures the efficiency of the optimization.The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization.Numerical examples are given to validate the effectiveness of the presented optimization approach.展开更多
We consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts.Specifically,we model polymer selfassembly using the self-consistent field t...We consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts.Specifically,we model polymer selfassembly using the self-consistent field theory and derive,in a non-parametric setting,the sensitivity of the dissimilarity between the desired and the actual morphologies to arbitrary perturbations in the guiding pattern shape.The sensitivity is then used for the optimization of the confining pattern shapes such that the dissimilarity between the desired and the actual morphologies is minimized.The efficiency and robustness of the proposed gradient-based algorithm are demonstrated in a number of examples related to templating vertical interconnect accesses(VIA).展开更多
In this paper, we use Physics-Informed Neural Networks (PINNs) to solve shape optimization problems. These problems are based on incompressible Navier-Stokes equations and phase-field equations. The phase-field functi...In this paper, we use Physics-Informed Neural Networks (PINNs) to solve shape optimization problems. These problems are based on incompressible Navier-Stokes equations and phase-field equations. The phase-field function is used to describe the state of the fluids, and the optimal shape optimization is obtained by using the shape sensitivity analysis based on the phase-field function. The sharp interface is also presented by a continuous function between zero and one with a large gradient. To avoid the numerical solutions falling into the trivial solution, the hard boundary condition is implemented for our PINNs’ training. Finally, numerical results are given to prove the feasibility and effectiveness of the proposed numerical method.展开更多
An effective optimization method for the shape/sizing design of composite wing structures is presented with satisfying weight-cutting results. After decoupling, a kind of two-layer cycled optimization strategy suitabl...An effective optimization method for the shape/sizing design of composite wing structures is presented with satisfying weight-cutting results. After decoupling, a kind of two-layer cycled optimization strategy suitable for these integrated shape/sizing optimization is obtained. The uniform design method is used to provide sample points, and approximation models for shape design variables. And the results of sizing optimization are construct- ed with the quadratic response surface method （QRSM）. The complex method based on QRSM is used to opti- mize the shape design variables and the criteria method is adopted to optimize the sizing design variables. Compared with the conventional method, the proposed algorithm is more effective and feasible for solving complex composite optimization problems and has good efficiency in weight cutting.展开更多
Aim To introduce a new method of adaptive shape optimization (ASOP) based on three-dimensional structure boundary strength and optimize an engine bearing cap with the method. Methods Using the normal substance's p...Aim To introduce a new method of adaptive shape optimization (ASOP) based on three-dimensional structure boundary strength and optimize an engine bearing cap with the method. Methods Using the normal substance's property of thermal expansion and cooling shrinkage,the load which is proportional to the difference between the nodes' stress and their respective objective stress were applied to the corresponding variable nodes on the boundary.The thermal load made the nodes whose stress is greater than their objective stress expand along the boundary's normal direction and the nodes whose stress is less than objec- tive stress shrink in the opposite direction , This process would repeat until the stress on the boundary nodes was converge to the objective stress. Results The satisfied results have been obtained when optimizing an engine bearing cap.The mass of the bearing cap is reduced to 55 percent of the total. Conclusion ASOP is an efficient,practical and reliable method which is suitable for optimizing the shape of the continuous structures.展开更多
As an advanced 4^(th) generation synchrotron radiation facility,the Shenzhen Innovation Light-source Facility(SILF)storage ring is based on multi-bend achromat(MBA)lattices,enabling one to two orders of magnitude redu...As an advanced 4^(th) generation synchrotron radiation facility,the Shenzhen Innovation Light-source Facility(SILF)storage ring is based on multi-bend achromat(MBA)lattices,enabling one to two orders of magnitude reduction in beam emittance compared to the 3^(rd) generation storage ring.This significantly enhance the radiation brightness and coherence.The multipole magnets of many types for SILF storage ring are under preliminary design,which require high integral field homogeneity.As a result,a dedicated pole tip optimization procedure with high efficiency is developed for quadrupole and sextupole magnets with Opera-2D^(■)python script.The procedure considers also the 3D field effect which makes the optimization more straightforward.In this paper,the design of the quadrupole and sextupole magnets for SILF storage ring is first presented,followed by a detailed description of the implemented pole shape optimization method.展开更多
The optimization of wings typically relies on computationally intensive high-fidelity simulations,which restrict the quick exploration of design spaces.To address this problem,this paper introduces a methodology dedic...The optimization of wings typically relies on computationally intensive high-fidelity simulations,which restrict the quick exploration of design spaces.To address this problem,this paper introduces a methodology dedicated to optimizing box wing configurations using low-fidelity data driven machine learning approach.This technique showcases its practicality through the utilization of a tailored low-fidelity machine learning technique,specifically designed for early-stage wing configuration.By employing surrogate model trained on small dataset derived from low-fidelity simulations,our method aims to predict outputs within an acceptable range.This strategy significantly mitigates computational costs and expedites the design exploration process.The methodology's validation relies on its successful application in optimizing the box wing of PARSIFAL,serving as a benchmark,while the primary focus remains on optimizing the newly designed box wing by Bionica.Applying this method to the Bionica configuration led to a notable 14%improvement in overall aerodynamic effciency.Furthermore,all the optimized results obtained from machine learning model undergo rigorous assessments through the high-fidelity RANS analysis for confirmation.This methodology introduces innovative approach that aims to streamline computational processes,potentially reducing the time and resources required compared to traditional optimization methods.展开更多
The multi-objective optimization method was used for shape optimization of cement sand and gravel （CSG） dams in this study. The economic efficiency, the sensitivities of maximum horizontal displacement and maximum s...The multi-objective optimization method was used for shape optimization of cement sand and gravel （CSG） dams in this study. The economic efficiency, the sensitivities of maximum horizontal displacement and maximum settlement of the dam to water level changes, the overall stability, and the overall strength security were taken into account during the optimization process. Three weight coefficient selection schemes were adopted to conduct shape optimization of a dam, and the case studies lead to the conclusion that both the upstream-and downstream dam slope ratios for the optimal cross-section equal 1：0.7, which is consistent with the empirically observed range of 1：0.6 to 1;0.8 for the upstream and downstream dam slope ratios of CSG dams. Therefore, the present study is of certain reference value for designing CSG dams.展开更多
A new approach for the solution of truss shape and topology optimization problems under local and global stability constraints is proposed.By employing the cross sectional areas of each bar and some shape parameters a...A new approach for the solution of truss shape and topology optimization problems under local and global stability constraints is proposed.By employing the cross sectional areas of each bar and some shape parameters as topology design variables,the difficulty arising from the jumping of buckling length phenomenon can be easily overcome without the necessity of introduc- ing the overlapping bars into the initial ground structure.Therefore computational efforts can be saved for the solution of this kind of problem.By modifying the elements of the stiffness matrix using Sigmoid function,the continuity of the objective and constraint functions with respect to shape design parameters can be restored to some extent.Some numerical examples demonstrate the effectiveness of the proposed method.展开更多
Subsea tunnel lining structures should be designed to sustain the loads transmitted from surrounding ground and groundwater during excavation. Extremely high pore-water pressure reduces the effective strength of the c...Subsea tunnel lining structures should be designed to sustain the loads transmitted from surrounding ground and groundwater during excavation. Extremely high pore-water pressure reduces the effective strength of the country rock that surrounds a tunnel, thereby lowering the arching effect and stratum stability of the structure. In this paper, the mechanical behavior and shape optimization of the lining structure for the Xiang＇an tunnel excavated in weathered slots are examined. Eight cross sections with different geometric parameters are adopted to study the mechanical behavior and shape optimization of the lining structure. The hyperstatic reaction method is used through finite element analysis software ANSYS. The mechanical behavior of the lining structure is evidently affected by the geometric parameters of crosssectional shape. The minimum safety factor of the lining structure elements is set to be the objective function. The efficient tunnel shape to maximize the minimum safety factor is identified. The minimum safety factor increases significantly after optimization. The optimized cross section significantly improves the mechanical characteristics of the lining structure and effectively reduces its deformation. Force analyses of optimization process and program are conducted parametrically so that the method can be applied to the optimization design of other similar structures. The results obtained from this study enhance our understanding of the mechanical behavior of the lining structure for subsea tunnels. These results are also beneficial to the optimal design of lining structures in general.展开更多
As a type of autonomous underwater vehicle(AUV),underwater gliders(UG)are getting increasing attention in ocean exploration.To save energy and satisfy the mission requirements of a longer voyage,shape optimization for...As a type of autonomous underwater vehicle(AUV),underwater gliders(UG)are getting increasing attention in ocean exploration.To save energy and satisfy the mission requirements of a longer voyage,shape optimization for UGs has become a key technique and research focus.In this paper,a conventional UG,including its fuselage and hydrofoil,is optimized,which aims to decrease the average resistance in one motion cycle.To operate the optimization progress for the complex object,multiple free form deformation(FFD)volumes are established for geometric parameterization.High-fidelity simulation models are employed for objective function evaluation and gradients calculation.And sequential quadratic programming(SQP)method is adopted as an optimization algorithm.The optimization results show that there exists a UG with symmetrical and non-horizontal hydrofoils that has lower resistance.展开更多
Tailor rolled blank （TRB） is a type of emerging material to produce lightweight vehicle parts. Transitional zoners shape is an important parameter for tailor rolled blank. It not only affects mold design and the loc...Tailor rolled blank （TRB） is a type of emerging material to produce lightweight vehicle parts. Transitional zoners shape is an important parameter for tailor rolled blank. It not only affects mold design and the local carrying capacity of the stamping parts, but also determines the maximum value and variation characteristics of rolling force. How to get the best transitional zone＇s shape is a key problem for production of tailor rolled blank. A double power function is put forward using for transitional curve, which is continuous and smooth at all connection points inde- pendent of its parameters, so the sudden change of mechanical parameters during rolling and forming process can be avoided. At the same time, the velocity formula and restriction for arbitrary transitional curve are derived to preset vertical velocity of the roller and judge whether the curve can be rolled successfully or not. Then, the finite element method （FEM） is used to verify the precision of velocity formula and study the mechanical characteristics of different curves. Finally, a method to obtain the optimal curve equation is put forward and verified.展开更多
In this paper,a Double-stage Surrogate-based Shape Optimization(DSSO)strategy for Blended-Wing-Body Underwater Gliders(BWBUGs)is proposed to reduce the computational cost.In this strategy,a double-stage surrogate mode...In this paper,a Double-stage Surrogate-based Shape Optimization(DSSO)strategy for Blended-Wing-Body Underwater Gliders(BWBUGs)is proposed to reduce the computational cost.In this strategy,a double-stage surrogate model is developed to replace the high-dimensional objective in shape optimization.Specifically,several First-stage Surrogate Models(FSMs)are built for the sectional airfoils,and the second-stage surrogate model is constructed with respect to the outputs of FSMs.Besides,a Multi-start Space Reduction surrogate-based global optimization method is applied to search for the optimum.In order to validate the efficiency of the proposed method,DSSO is first compared with an ordinary One-stage Surrogate-based Optimization strategy by using the same optimization method.Then,the other three popular surrogate-based optimization methods and three heuristic algorithms are utilized to make comparisons.Results indicate that the lift-to-drag ratio of the BWBUG is improved by 9.35%with DSSO,which outperforms the comparison methods.Besides,DSSO reduces more than 50%of the time that other methods used when obtaining the same level of results.Furthermore,some considerations of the proposed strategy are further discussed and some characteristics of DSSO are identified.展开更多
The hull form optimization concerns one of the most important applications of wave-making resistance theories.In recent years,scholars can determine the hull form by using the optimization method based on the computat...The hull form optimization concerns one of the most important applications of wave-making resistance theories.In recent years,scholars can determine the hull form by using the optimization method based on the computational fluid dynamics(CFD)and other mathematical techniques.In this paper,the hull form optimization method based on the Rankine source method and nonlinear programming(NLP)is discussed;in the optimization process,a hull form modification function is introduced to represent an improved hull surface and to generate a new smooth hull surface by changing its frame lines and bow stem profiles under the prescribed design constraints. Numerical example is given for a practical container hull form.Finally,shape optimization of bow bulls is shown for non-protruding and protruding bow bulls.This study presents a simplified and practical design method to the select frame lines of bow bulls.展开更多
Smoothly stitching multiple surfaces mainly represented by B-spline or NURBS together is an extremely important issue in complex surfaces modeling and reverse engineering. In recent years, a lot of progress has been m...Smoothly stitching multiple surfaces mainly represented by B-spline or NURBS together is an extremely important issue in complex surfaces modeling and reverse engineering. In recent years, a lot of progress has been made in smooth join of non-trimmed surface patches, while there has been seldom research on smoothly stitching trimmed surface patches together. This paper studies the problem of global continuity adjustment, damaged hole repair and local shape optimization for complex trimmed surface model, and presents a uniform scheme to deal with continuity adjustment of trimmed surfaces and geometric repair of local broken region. Constrained B-spline surface refitting technique and trim calculation are first utilized to achieve global G^1 continuity, and then local shape optimization functional is adopted to reduce fitting error and improve local quality of refitted surface patch. The proposed approach is applied to a discontinuity ship hull surface model with an irregular hole, and the result demonstrates the validation of our method. Furthermore, on the premise of global continuity, the proposed locally repairing damaged surface model provides a better foundation for following research work, such as topology recovery technique for complex surface model after geometric repair.展开更多
基金supported by the the National Science and Technology Council(Grant Number:NSTC 112-2221-E239-022).
文摘To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).
基金the research project “OptArch e689983,H2020-MSCA-RISE-2015/H2020-MSCA-RISE-20”
文摘Arches are widely used when large spans are necessary, e.g. to overpass large rivers, and further possess unquestioned aesthetics advantages. Their structural efficiency depends primarily on optimal material exploitation, i.e. minimization of internal stress eccentricity,and on minimization of structural material volume. An efficient structure, under these terms, further requires simpler and lighter scaffolding, contributing in minimizing construction costs.Although arches have millenary use and many researches dealing with this typology are available in literature, there is still scope for design optimization. The proposed study is framed within this context. Investigation is limited to statically determinate plane arches under vertical load. The problem of finding the profile of an equal strength catenary subjected to its self-weight is spread out to the case of an inverted catenary of equal strength under its self-weight and an external constant load. In the first optimization step, constant normal stress is imposed at all sections, to maximize material exploitation, and the resulting arch centerline shape is computed in closed form. In the second step, the ensemble of foundations and arch is considered and optimized, taking the linear combination of arch weight and thrust as objective function. The linear combination is dependent on a single variable, and minima of the objective function(i.e. optimal geometric shape parameters) are computed and charted to be simply used in the design process.
文摘A body frame composed of thin sheet metal is a crucial structure that determines the safety performance of a vehicle.Designing a correct weight and high-performance automotive body is an emerging engineering problem.To improve the performance of the automotive frame,we attempt to reconstruct its design criteria based on statistical and mechanical approaches.At first,a fundamental study on the frame strength is conducted and a cross-sectional shape optimization problem is developed for designing the cross-sectional shape of an automobile frame having a very high mass efficiency for strength.Shape optimization is carried out using the nonlinear finite element method and a meta-modeling-based genetic algorithm.Data analysis of the obtained set of optimal results is performed to identify the dominant design variables by employing the smoothing spline analysis of variance,the principal component analysis,and the self-organizing map technique.The relationship between the cross-sectional shape and the objective function is also analyzed by hierarchical clustering.A design guideline is obtained from these statistical approach results.A comparison between the statistically obtained design guideline and the conventional one based on the designers’experience is performed based on mechanical interpretation of the optimal cross-sectional frame.Finally,a mechanically reasonable new general-purpose design guideline is proposed for the cross-sectional shape of the automotive frame.
基金This work was supported in part by the National Natural Science Foundation of China under grants(No.11571115 and No.12071149)Natural Science Foundation of Shanghai(No.19ZR1414100)Science and Technology Commission of Shanghai Municipality(No.18dz2271000).
文摘We consider optimal shape design in Stokes flow using H^(1) shape gradient flows based on the distributed Eulerian derivatives.MINI element is used for discretizations of Stokes equation and Galerkin finite element is used for discretizations of distributed and boundary H^(1) shape gradient flows.Convergence analysis with a priori error estimates is provided under general and different regularity assumptions.We investigate the performances of shape gradient descent algorithms for energy dissipation minimization and obstacle flow.Numerical comparisons in 2D and 3D show that the distributed H1 shape gradient flow is more accurate than the popular boundary type.The corresponding distributed shape gradient algorithm is more effective.
基金supported by a Major Research Project in Higher Education Institutions in Henan Province,with Project Number 23A560015.
文摘A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.
基金supported by the National Natural Science Foundation of China (NSFC)under Grant Nos.12172350,11772322 and 11702238。
文摘We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods mainly contain shape and topology schemes,with the former changing the surface geometric profile of the structure and the latter changing thematerial distribution topology or hole topology of the structure.In the present acoustic performance optimization,the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure,the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter,and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge.The topology and shape sensitivities of the approach are calculated using the adjoint variable method,which ensures the efficiency of the optimization.The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization.Numerical examples are given to validate the effectiveness of the presented optimization approach.
文摘We consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts.Specifically,we model polymer selfassembly using the self-consistent field theory and derive,in a non-parametric setting,the sensitivity of the dissimilarity between the desired and the actual morphologies to arbitrary perturbations in the guiding pattern shape.The sensitivity is then used for the optimization of the confining pattern shapes such that the dissimilarity between the desired and the actual morphologies is minimized.The efficiency and robustness of the proposed gradient-based algorithm are demonstrated in a number of examples related to templating vertical interconnect accesses(VIA).
文摘In this paper, we use Physics-Informed Neural Networks (PINNs) to solve shape optimization problems. These problems are based on incompressible Navier-Stokes equations and phase-field equations. The phase-field function is used to describe the state of the fluids, and the optimal shape optimization is obtained by using the shape sensitivity analysis based on the phase-field function. The sharp interface is also presented by a continuous function between zero and one with a large gradient. To avoid the numerical solutions falling into the trivial solution, the hard boundary condition is implemented for our PINNs’ training. Finally, numerical results are given to prove the feasibility and effectiveness of the proposed numerical method.
文摘An effective optimization method for the shape/sizing design of composite wing structures is presented with satisfying weight-cutting results. After decoupling, a kind of two-layer cycled optimization strategy suitable for these integrated shape/sizing optimization is obtained. The uniform design method is used to provide sample points, and approximation models for shape design variables. And the results of sizing optimization are construct- ed with the quadratic response surface method （QRSM）. The complex method based on QRSM is used to opti- mize the shape design variables and the criteria method is adopted to optimize the sizing design variables. Compared with the conventional method, the proposed algorithm is more effective and feasible for solving complex composite optimization problems and has good efficiency in weight cutting.
文摘Aim To introduce a new method of adaptive shape optimization (ASOP) based on three-dimensional structure boundary strength and optimize an engine bearing cap with the method. Methods Using the normal substance's property of thermal expansion and cooling shrinkage,the load which is proportional to the difference between the nodes' stress and their respective objective stress were applied to the corresponding variable nodes on the boundary.The thermal load made the nodes whose stress is greater than their objective stress expand along the boundary's normal direction and the nodes whose stress is less than objec- tive stress shrink in the opposite direction , This process would repeat until the stress on the boundary nodes was converge to the objective stress. Results The satisfied results have been obtained when optimizing an engine bearing cap.The mass of the bearing cap is reduced to 55 percent of the total. Conclusion ASOP is an efficient,practical and reliable method which is suitable for optimizing the shape of the continuous structures.
文摘As an advanced 4^(th) generation synchrotron radiation facility,the Shenzhen Innovation Light-source Facility(SILF)storage ring is based on multi-bend achromat(MBA)lattices,enabling one to two orders of magnitude reduction in beam emittance compared to the 3^(rd) generation storage ring.This significantly enhance the radiation brightness and coherence.The multipole magnets of many types for SILF storage ring are under preliminary design,which require high integral field homogeneity.As a result,a dedicated pole tip optimization procedure with high efficiency is developed for quadrupole and sextupole magnets with Opera-2D^(■)python script.The procedure considers also the 3D field effect which makes the optimization more straightforward.In this paper,the design of the quadrupole and sextupole magnets for SILF storage ring is first presented,followed by a detailed description of the implemented pole shape optimization method.
基金The funding for this publication was provided by Johannes Kepler University(JKU),Linz.Special thanks to Prof.Zongmin DENG from Beihang University for his invaluable guidance,insightful feedback,and constructive criticism,which greatly enhanced the quality of this manuscript.We extend our heartfelt gratitude to the PARSIFAL team for providing the supporting materials,which inspired this study.
文摘The optimization of wings typically relies on computationally intensive high-fidelity simulations,which restrict the quick exploration of design spaces.To address this problem,this paper introduces a methodology dedicated to optimizing box wing configurations using low-fidelity data driven machine learning approach.This technique showcases its practicality through the utilization of a tailored low-fidelity machine learning technique,specifically designed for early-stage wing configuration.By employing surrogate model trained on small dataset derived from low-fidelity simulations,our method aims to predict outputs within an acceptable range.This strategy significantly mitigates computational costs and expedites the design exploration process.The methodology's validation relies on its successful application in optimizing the box wing of PARSIFAL,serving as a benchmark,while the primary focus remains on optimizing the newly designed box wing by Bionica.Applying this method to the Bionica configuration led to a notable 14%improvement in overall aerodynamic effciency.Furthermore,all the optimized results obtained from machine learning model undergo rigorous assessments through the high-fidelity RANS analysis for confirmation.This methodology introduces innovative approach that aims to streamline computational processes,potentially reducing the time and resources required compared to traditional optimization methods.
基金supported by the National Natural Science Foundation of China (Grant No. 51179061)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100094110014)
文摘The multi-objective optimization method was used for shape optimization of cement sand and gravel （CSG） dams in this study. The economic efficiency, the sensitivities of maximum horizontal displacement and maximum settlement of the dam to water level changes, the overall stability, and the overall strength security were taken into account during the optimization process. Three weight coefficient selection schemes were adopted to conduct shape optimization of a dam, and the case studies lead to the conclusion that both the upstream-and downstream dam slope ratios for the optimal cross-section equal 1：0.7, which is consistent with the empirically observed range of 1：0.6 to 1;0.8 for the upstream and downstream dam slope ratios of CSG dams. Therefore, the present study is of certain reference value for designing CSG dams.
基金Project supported by the National Natural Science Foundation of China (Nos.200112023 and 10032030).
文摘A new approach for the solution of truss shape and topology optimization problems under local and global stability constraints is proposed.By employing the cross sectional areas of each bar and some shape parameters as topology design variables,the difficulty arising from the jumping of buckling length phenomenon can be easily overcome without the necessity of introduc- ing the overlapping bars into the initial ground structure.Therefore computational efforts can be saved for the solution of this kind of problem.By modifying the elements of the stiffness matrix using Sigmoid function,the continuity of the objective and constraint functions with respect to shape design parameters can be restored to some extent.Some numerical examples demonstrate the effectiveness of the proposed method.
基金financially supported by the National Natural Science Foundation of China(Grant No.51308012)the Key Laboratory of Transportation Tunnel Engineering+1 种基金Ministry of EducationSouthwest Jiaotong University(Grant No.TTE2014-06)
文摘Subsea tunnel lining structures should be designed to sustain the loads transmitted from surrounding ground and groundwater during excavation. Extremely high pore-water pressure reduces the effective strength of the country rock that surrounds a tunnel, thereby lowering the arching effect and stratum stability of the structure. In this paper, the mechanical behavior and shape optimization of the lining structure for the Xiang＇an tunnel excavated in weathered slots are examined. Eight cross sections with different geometric parameters are adopted to study the mechanical behavior and shape optimization of the lining structure. The hyperstatic reaction method is used through finite element analysis software ANSYS. The mechanical behavior of the lining structure is evidently affected by the geometric parameters of crosssectional shape. The minimum safety factor of the lining structure elements is set to be the objective function. The efficient tunnel shape to maximize the minimum safety factor is identified. The minimum safety factor increases significantly after optimization. The optimized cross section significantly improves the mechanical characteristics of the lining structure and effectively reduces its deformation. Force analyses of optimization process and program are conducted parametrically so that the method can be applied to the optimization design of other similar structures. The results obtained from this study enhance our understanding of the mechanical behavior of the lining structure for subsea tunnels. These results are also beneficial to the optimal design of lining structures in general.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51875466 and 51805436)the Fundamental Research Funds for the Central Universities(Grant No.3102020HHZY030003)。
文摘As a type of autonomous underwater vehicle(AUV),underwater gliders(UG)are getting increasing attention in ocean exploration.To save energy and satisfy the mission requirements of a longer voyage,shape optimization for UGs has become a key technique and research focus.In this paper,a conventional UG,including its fuselage and hydrofoil,is optimized,which aims to decrease the average resistance in one motion cycle.To operate the optimization progress for the complex object,multiple free form deformation(FFD)volumes are established for geometric parameterization.High-fidelity simulation models are employed for objective function evaluation and gradients calculation.And sequential quadratic programming(SQP)method is adopted as an optimization algorithm.The optimization results show that there exists a UG with symmetrical and non-horizontal hydrofoils that has lower resistance.
基金Item Sponsored by National Science and Technology Support Program of China(2011BAF15B02)Natural Science Foundation of Hebei Province of China(E2012203108)+2 种基金Science and Technology Research Program of the Colleges and Universities in Hebei of China(ZD2014034)Independent Research Project of Yanshan University of China(14LGA003)Open Project of National Engineering Research Center for Equipment and Technology of Cold Rolling Strip of China(NECSR-201206)
文摘Tailor rolled blank （TRB） is a type of emerging material to produce lightweight vehicle parts. Transitional zoners shape is an important parameter for tailor rolled blank. It not only affects mold design and the local carrying capacity of the stamping parts, but also determines the maximum value and variation characteristics of rolling force. How to get the best transitional zone＇s shape is a key problem for production of tailor rolled blank. A double power function is put forward using for transitional curve, which is continuous and smooth at all connection points inde- pendent of its parameters, so the sudden change of mechanical parameters during rolling and forming process can be avoided. At the same time, the velocity formula and restriction for arbitrary transitional curve are derived to preset vertical velocity of the roller and judge whether the curve can be rolled successfully or not. Then, the finite element method （FEM） is used to verify the precision of velocity formula and study the mechanical characteristics of different curves. Finally, a method to obtain the optimal curve equation is put forward and verified.
基金This research was financially supported by the National Natural Science Foundation of China(Grant Nos.51875466 and 51805436)the China Postdoctoral Science Foundation(Grant No.2019T120941)the China Scholarships Council(Grant No.201806290133).
文摘In this paper,a Double-stage Surrogate-based Shape Optimization(DSSO)strategy for Blended-Wing-Body Underwater Gliders(BWBUGs)is proposed to reduce the computational cost.In this strategy,a double-stage surrogate model is developed to replace the high-dimensional objective in shape optimization.Specifically,several First-stage Surrogate Models(FSMs)are built for the sectional airfoils,and the second-stage surrogate model is constructed with respect to the outputs of FSMs.Besides,a Multi-start Space Reduction surrogate-based global optimization method is applied to search for the optimum.In order to validate the efficiency of the proposed method,DSSO is first compared with an ordinary One-stage Surrogate-based Optimization strategy by using the same optimization method.Then,the other three popular surrogate-based optimization methods and three heuristic algorithms are utilized to make comparisons.Results indicate that the lift-to-drag ratio of the BWBUG is improved by 9.35%with DSSO,which outperforms the comparison methods.Besides,DSSO reduces more than 50%of the time that other methods used when obtaining the same level of results.Furthermore,some considerations of the proposed strategy are further discussed and some characteristics of DSSO are identified.
基金the National Natural Science Foundation of China(No.51009087)
文摘The hull form optimization concerns one of the most important applications of wave-making resistance theories.In recent years,scholars can determine the hull form by using the optimization method based on the computational fluid dynamics(CFD)and other mathematical techniques.In this paper,the hull form optimization method based on the Rankine source method and nonlinear programming(NLP)is discussed;in the optimization process,a hull form modification function is introduced to represent an improved hull surface and to generate a new smooth hull surface by changing its frame lines and bow stem profiles under the prescribed design constraints. Numerical example is given for a practical container hull form.Finally,shape optimization of bow bulls is shown for non-protruding and protruding bow bulls.This study presents a simplified and practical design method to the select frame lines of bow bulls.
基金supported by National Natural Science Foundation of China (Grant No.50575098)
文摘Smoothly stitching multiple surfaces mainly represented by B-spline or NURBS together is an extremely important issue in complex surfaces modeling and reverse engineering. In recent years, a lot of progress has been made in smooth join of non-trimmed surface patches, while there has been seldom research on smoothly stitching trimmed surface patches together. This paper studies the problem of global continuity adjustment, damaged hole repair and local shape optimization for complex trimmed surface model, and presents a uniform scheme to deal with continuity adjustment of trimmed surfaces and geometric repair of local broken region. Constrained B-spline surface refitting technique and trim calculation are first utilized to achieve global G^1 continuity, and then local shape optimization functional is adopted to reduce fitting error and improve local quality of refitted surface patch. The proposed approach is applied to a discontinuity ship hull surface model with an irregular hole, and the result demonstrates the validation of our method. Furthermore, on the premise of global continuity, the proposed locally repairing damaged surface model provides a better foundation for following research work, such as topology recovery technique for complex surface model after geometric repair.
