Combining the vector level set model,the shape sensitivity analysis theory with the gradient projection technique,a level set method for topology optimization with multi-constraints and multi-materials is presented in...Combining the vector level set model,the shape sensitivity analysis theory with the gradient projection technique,a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper.The method implicitly describes structural material in- terfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure.In order to increase computational efficiency for a fast convergence,an appropriate nonlinear speed mapping is established in the tangential space of the active constraints.Meanwhile,in order to overcome the numerical instability of general topology opti- mization problems,the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process.The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity,compared with other methods based on explicit boundary variations in the literature.展开更多
A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier-Stokes equation in the liquid r...A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier-Stokes equation in the liquid region is solved by MAC projection algorithm combined with second-order ENO scheme for the advection terms. The moving inter-face is captured by the level set function, and the interface velocity is resolved by "one-side" velocity extension from the liquid region to the bubble region, complementing the second-order weighted least squares method across the interface and projection inside bubble. The use of non-uniform grid overcomes the difficulty caused by the large computational domain and very small bubble size. The computation is very stable without suffering from large flow-field gradients, and the results are in good agreements with other studies. The bubble interface kinematics, dynamics and its effect on the wall are highlighted, which shows that the code can effectively capture the "shock wave"-like pressure and velocity at jet impact, toroidal bubble, and complicated pressure structure with peak, plateau and valley in the later stage of bubble oscillating.展开更多
Knowledge-Based Engineering (KBE) is introduced into the ship structural design in this paper. From the implementation of KBE, the design solutions for both Rules Design Method (RDM) and Interpolation Design Meth...Knowledge-Based Engineering (KBE) is introduced into the ship structural design in this paper. From the implementation of KBE, the design solutions for both Rules Design Method (RDM) and Interpolation Design Method (IDM) are generated. The corresponding Finite Element (FE) models are generated. Topological design of the longitudinal structures is studied where the Gaussian Process (GP) is employed to build the surrogate model for FE analysis. Multi-objective optimization methods inspired by Pareto Front are used to reduce the design tank weight and outer surface area simultaneously. Additionally, an enhanced Level Set Method (LSM) which employs implicit algorithm is applied to the topological design of typical bracket plate which is used extensively in ship structures. Two different sets of boundary conditions are considered. The proposed methods show satisfactory efficiency and accuracy.展开更多
Based on a level set model, a topology optimization method has been suggestedrecently. It uses a level set to express the moving structural boundary, which can flexibly handlecomplex topological changes. By combining ...Based on a level set model, a topology optimization method has been suggestedrecently. It uses a level set to express the moving structural boundary, which can flexibly handlecomplex topological changes. By combining vector level set models with gradient projectiontechnology, the level set method for topological optimization is extended to a topologicaloptimization problem with multi-constraints, multi-materials and multi-load cases. Meanwhile, anappropriate nonlinear speed, mapping is established in the tangential space of the activeconstraints for a fast convergence. Then the method is applied to structure designs, mechanism andmaterial designs by a number of benchmark examples. Finally, in order to further improvecomputational efficiency and overcome the difficulty that the level set method cannot generate newmaterial interfaces during the optimization process, the topological derivative analysis isincorporated into the level set method for topological optimization, and a topological derivativeand level set algorithm for topological optimization is proposed.展开更多
This article introduces a new normalized nonlocal hybrid level set method for image segmentation.Due to intensity overlapping,blurred edges with complex backgrounds,simple intensity and texture information,such kind o...This article introduces a new normalized nonlocal hybrid level set method for image segmentation.Due to intensity overlapping,blurred edges with complex backgrounds,simple intensity and texture information,such kind of image segmentation is still a challenging task.The proposed method uses both the region and boundary information to achieve accurate segmentation results.The region information can help to identify rough region of interest and prevent the boundary leakage problem.It makes use of normalized nonlocal comparisons between pairs of patches in each region,and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation.The boundary information can help to detect the precise location of the target object,it makes use of the geodesic active contour model to obtain the target boundary.The corresponding variational segmentation problem is implemented by a level set formulation.We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function.At last,experimental results on synthetic images and real images are shown in the paper with promising results.展开更多
The goal of the arterial graft design problem is to find an optimal graft built on an occluded artery, which can be mathematically modeled by a fluid based shape optimization problem. The smoothness of the graft is on...The goal of the arterial graft design problem is to find an optimal graft built on an occluded artery, which can be mathematically modeled by a fluid based shape optimization problem. The smoothness of the graft is one of the important aspects in the arterial graft design problem since it affects the flow of the blood significantly. As an attractive design tool for this problem, level set methods are quite efficient for obtaining better shape of the graft. In this paper, a cubic spline level set method and a radial basis function level set method are designed to solve the arterial graft design problem. In both approaches, the shape of the arterial graft is implicitly tracked by the zero-level contour of a level set function and a high level of smoothness of the graft is achieved. Numerical results show the efficiency of the algorithms in the arterial graft 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
A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method.It is inspired by the procedure of determining the threshold of sensitivity numb...A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method.It is inspired by the procedure of determining the threshold of sensitivity number in the BESO method.It first computes the difference between the volume of current design and the upper bound of volume.Then,the Lagrange multiplier is regarded as the threshold of sensitivity number to remove the redundant material.Numerical examples proved that this approach is effective to constrain the volume.More importantly,there is no parameter in the proposed approach,which makes it convenient to use.In addition,the convergence is stable,and there is no big oscillation.展开更多
2-D and 3-D micro-architectured multiphase thermoelastic metamaterials are designed and analyzed using a parametric level set method for topology optimization and the finite element method.An asymptotic homogenization...2-D and 3-D micro-architectured multiphase thermoelastic metamaterials are designed and analyzed using a parametric level set method for topology optimization and the finite element method.An asymptotic homogenization approach is employed to obtain the effective thermoelastic properties of the multiphase metamaterials.Theε-constraint multi-objective optimization method is adopted in the formulation.The coefficient of thermal expansion(CTE)and Poisson’s ratio(PR)are chosen as two objective functions,with the CTE optimized and the PR treated as a constraint.The optimization problems are solved by using the method of moving asymptotes.Effective isotropic and anisotropic CTEs and stiffness constants are obtained for the topologically optimized metamaterials with prescribed values of PR under the constraints of specified effective bulk modulus,volume fractions and material symmetry.Two solid materials along with one additional void phase are involved in each of the 2-D and 3-D optimal design examples.The numerical results reveal that the newly proposed approach can integrate shape and topology optimizations and lead to optimal microstructures with distinct topological boundaries.The current method can topologically optimize metamaterials with a positive,negative or zero CTE and a positive,negative or zero Poisson’s ratio.展开更多
As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been invest...As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been investigated. By using the Level Set method, the transformation of a solitary wave over a front step was simulated. The results were in good agreement with laboratory experiments.展开更多
Some basic problems on the level set methods were discussed, such as the method used to preserve the distance junction , the existence and uniqueness of solution for the level set equations. The main contribution is t...Some basic problems on the level set methods were discussed, such as the method used to preserve the distance junction , the existence and uniqueness of solution for the level set equations. The main contribution is to prove that in a neighborhood of the initial zero level set, the level set equations with the restriction of the distance function have a unique solution, which must be the signed distance function with respect to the evolving surface. Some skillful approaches were used: Noticing that any solution for the original equation was a distance function, the original level set equations were transformed into a simpler alternative form. Moreover, since the new system was not a classical one, the system was transformed into an ordinary one, for which the implicit function method was adopted.展开更多
Air entrapped in liquid metal during the mold filling process seriously affects the casting quality, thus it is important to track its behavior in the mold cavity. A liquid-gas two-phase flow model is developed to des...Air entrapped in liquid metal during the mold filling process seriously affects the casting quality, thus it is important to track its behavior in the mold cavity. A liquid-gas two-phase flow model is developed to describe the mold filling process and predict the air entrapment defect. The model is based on the combination of SOLA and Level Set Method. The pressure and velocity fields are calculated by SOLA,and the interface movement is simulated by Level Set method as the most common interface tracking method in recent years.In order to validate the feasibility of the model,the liquid-gas two-phase simulation results were tested by the broken dam problem and the S-shaped experiment. Comparison between the experiments and simulation results show that Level Set method might be a very promising tool in two-phase flow simulation during the mold filling process.展开更多
The salt intrusion phenomenon is caused by </span><u><span style="font-family:Verdana;">overexploitation</span></u><span style="font-family:Verdana;"> of aquifer...The salt intrusion phenomenon is caused by </span><u><span style="font-family:Verdana;">overexploitation</span></u><span style="font-family:Verdana;"> of aquifers in coastal areas. This physical phenomenon has been the subject of numerous </span><span style="font-family:Verdana;">studies and numerous methods have been proposed, with the aim of protecting the quality of the water in these aquifers. This work proposes a two-dimensional</span><span style="font-family:Verdana;"> saline intrusion model using the sharp interface approach and the level set method. It consists of a parabolic equation modeling the underground flow and a hyperbolic Equation (the level set equation) which makes it possible to track the evolution of the interface. High</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">order numerical schemes such as the space scheme </span><u><span style="font-family:Verdana;">WENO5</span></u><span style="font-family:Verdana;"> and the third</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">order time scheme </span><u><span style="font-family:Verdana;">TVD</span></u><span style="font-family:Verdana;">-</span><u><span style="font-family:Verdana;">RK</span></u><span style="font-family:Verdana;"> were used for the numerical resolution of the hyperbolic equation. To limit the tightening of the contour curves of the level set function, the </span><u><span style="font-family:Verdana;">redistanciation</span></u><span style="font-family:Verdana;"> or </span><u><span style="font-family:Verdana;">reinitialization</span></u><span style="font-family:Verdana;"> algorithm proposed by </span><u><span style="font-family:Verdana;">Sussma </span><i><span style="font-family:Verdana;">et al.</span></i></u><span style="font-family:Verdana;"> (1994) was used. To ensure the effectiveness and reliability of the proposed method, two tests relating to the standard Henry problem and the modified Henry problem were performed. Recall that Henry’s problem uses the variable density modeling approach in a confined and homogeneous aquifer. By comparing the results obtained by the level set method with </span><u><span style="font-family:Verdana;">reinitialization</span></u><span style="font-family:Verdana;"> (</span><u><span style="font-family:Verdana;">LSMR</span></u><span style="font-family:Verdana;">) and those obtained by Henry (1964), and by Simpson and Clement (2004), we see in the two test cases that the level set method reproduces well the toe, the tip and the </span><u><span style="font-family:Verdana;">behaviour</span></u><span style="font-family:Verdana;"> of the interface. These results correspond to the results obtained by </span><u><span style="font-family:Verdana;">Abarca</span></u><span style="font-family:Verdana;"> for Henry’s problem with constant dispersion coefficients. The results obtained with </span><u><span style="font-family:Verdana;">LSMR</span></u><span style="font-family:Verdana;">, reproduced the interface with a slight spacing compared to those obtained by Henry. According to </span><u><span style="font-family:Verdana;">Abarca</span></u><span style="font-family:Verdana;"> (2006), this spacing is due to the absence of the longitudinal and </span><u><span style="font-family:Verdana;">transversal</span></u><span style="font-family:Verdana;"> dispersion coefficients in the model.展开更多
A flexure hinge is a major component in designing compliant mechanisms that o ers unique possibilities in a wide range of application fields in which high positioning accuracy is required. Although various flexure hin...A flexure hinge is a major component in designing compliant mechanisms that o ers unique possibilities in a wide range of application fields in which high positioning accuracy is required. Although various flexure hinges with di erent configurations have been successively proposed, they are often designed based on designers' experiences and inspirations. This study presents a systematic method for topological optimization of flexure hinges by using the level set method. Optimization formulations are developed by considering the functional requirements and geometrical constraints of flexure hinges. The functional requirements are first constructed by maximizing the compliance in the desired direction while minimizing the compliances in the other directions. The weighting sum method is used to construct an objective function in which a self-adjust method is used to set the weighting factors. A constraint on the symmetry of the obtained configuration is developed. Several numerical examples are presented to demonstrate the validity of the proposed method. The obtained results reveal that the design of a flexure hinge starting from the topology level can yield more choices for compliant mechanism design and obtain better designs that achieve higher performance.展开更多
A non-isothermal injection molding process for a non-Newtonian viscous pseudoplastic fluid is simulated.A conservative interface capturing technique and the flow field solving method are coupled to perform a dynamic s...A non-isothermal injection molding process for a non-Newtonian viscous pseudoplastic fluid is simulated.A conservative interface capturing technique and the flow field solving method are coupled to perform a dynamic simulation.The validity of the numerical method is verified by a benchmark problem.The melt interface evolution versus time is captured and the physical quantities such as temperature,velocity and pressure at each time step are obtained with corresponding analysis.A"frozen skin"layer with the thickness increasing versus time during the injection process is found.The fact that the"frozen skin"layer can be reduced by increasing the injection velocity is numerically verified.The fountain flow phenomenon near the melt interface is also captured.Moreover,comparisons with the non-isothermal Newtonian case show that the curvatures of the interface arcs and the pressure contours near the horizontal mid-line of the cavity for the non-Newtonian pseudoplastic case is larger than that for the Newtonian case.The velocity profiles are different at different positions for the non-Newtonian pseudoplastic case,while in the case of Newtonian flow the velocity profiles are parabolic and almost the same at different positions.展开更多
The behavior of single bubble rising in quiescent shear-thinning fluids was investigated numerically by level set method. A number of bubbles in a large range of Reynolds number and Eotvos number were investigated inc...The behavior of single bubble rising in quiescent shear-thinning fluids was investigated numerically by level set method. A number of bubbles in a large range of Reynolds number and Eotvos number were investigated including spherical, oblate and spherical. The bubble shape and drag coefficient were compared with experimental results. It is observed that the simulated results show good conformity to experimental results over a wide range of Reynolds number. In addition, the detailed flow field based on the reference coordinate system moving with the bubble is obtained, and the relationship among flow field, bubble shape and velocity is discussed.展开更多
The simulation of three-dimensional(3D) non-isothermal, non-Newtonian fluid filling process is an extremely difficult task and remains a challenging problem, which includes polymer melt flow with free surface coupled ...The simulation of three-dimensional(3D) non-isothermal, non-Newtonian fluid filling process is an extremely difficult task and remains a challenging problem, which includes polymer melt flow with free surface coupled with transient heat transfer. This paper presents a full 3D non-isothermal two-phase flow model to predict the complex flow in melt filling process, where the Cross-WLF model is applied to characterize the rheological behavior of polymer melt. The governing equations are solved using finite volume method with SIMPLEC algorithm on collocated grids and the melt front is accurately captured by a high resolution level set method. A domain extension technique is adopted to deal with the complex cavities, which greatly reduces the computational burden. To verify the validity of the developed 3D approach, the melts filling processes in two thin rectangular cavities(one of them with a cylindrical insert) are simulated. The predicted melt front interfaces are in good agreement with the experiment and commercial software prediction. For a case with a rather complex cavity, the dynamic filling process in a hemispherical shell is successfully simulated. All of the numerical results show that the developed numerical procedure can provide a reasonable prediction for injection molding process.展开更多
Segmentation of three-dimensional(3D) complicated structures is of great importance for many real applications.In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmenta...Segmentation of three-dimensional(3D) complicated structures is of great importance for many real applications.In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model.Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations.Instead,the minimum cut on a special designed graph need to be computed.The method is tested on data with complicated structures.It is rather stable with respect to initial value and the algorithm is nearly parameter free.Experiments show that it can solve large problems much faster than traditional approaches.展开更多
In biology ferment engineering,accurate statistics of the quantity of bacteria is one of the most important subjects. In this paper,the quantity of bacteria which was observed traditionally manuauy can be detected aut...In biology ferment engineering,accurate statistics of the quantity of bacteria is one of the most important subjects. In this paper,the quantity of bacteria which was observed traditionally manuauy can be detected automatically. Image acquisition and processing system is designed to accomplish image preprocessing,image segmentation and statistics of the quantity of bacteria. Segmentation of bacteria images is successfully realized by means of a region-based level set method and then the quantity of bacteria is computed precisely,which plays an important role in optimizing the growth conditions of bacteria.展开更多
基金The project supported by the National Natural Science Foundation of China (59805001,10332010) and Key Science and Technology Research Project of Ministry of Education of China (No.104060)
文摘Combining the vector level set model,the shape sensitivity analysis theory with the gradient projection technique,a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper.The method implicitly describes structural material in- terfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure.In order to increase computational efficiency for a fast convergence,an appropriate nonlinear speed mapping is established in the tangential space of the active constraints.Meanwhile,in order to overcome the numerical instability of general topology opti- mization problems,the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process.The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity,compared with other methods based on explicit boundary variations in the literature.
基金the National Natural Science Foundation of China(10272032 and 10672043).
文摘A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier-Stokes equation in the liquid region is solved by MAC projection algorithm combined with second-order ENO scheme for the advection terms. The moving inter-face is captured by the level set function, and the interface velocity is resolved by "one-side" velocity extension from the liquid region to the bubble region, complementing the second-order weighted least squares method across the interface and projection inside bubble. The use of non-uniform grid overcomes the difficulty caused by the large computational domain and very small bubble size. The computation is very stable without suffering from large flow-field gradients, and the results are in good agreements with other studies. The bubble interface kinematics, dynamics and its effect on the wall are highlighted, which shows that the code can effectively capture the "shock wave"-like pressure and velocity at jet impact, toroidal bubble, and complicated pressure structure with peak, plateau and valley in the later stage of bubble oscillating.
基金financially supported by the Project of Ministry of Education and Finance of China(Grant Nos.200512 and 201335)the Project of the State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University(Grant No.GKZD010053-10)
文摘Knowledge-Based Engineering (KBE) is introduced into the ship structural design in this paper. From the implementation of KBE, the design solutions for both Rules Design Method (RDM) and Interpolation Design Method (IDM) are generated. The corresponding Finite Element (FE) models are generated. Topological design of the longitudinal structures is studied where the Gaussian Process (GP) is employed to build the surrogate model for FE analysis. Multi-objective optimization methods inspired by Pareto Front are used to reduce the design tank weight and outer surface area simultaneously. Additionally, an enhanced Level Set Method (LSM) which employs implicit algorithm is applied to the topological design of typical bracket plate which is used extensively in ship structures. Two different sets of boundary conditions are considered. The proposed methods show satisfactory efficiency and accuracy.
基金This project is supported by National Natural Science Foundation of China(No.598005001, No.10332010) and Key Science and Technology Research Project of Ministry of Education (No.104060).
文摘Based on a level set model, a topology optimization method has been suggestedrecently. It uses a level set to express the moving structural boundary, which can flexibly handlecomplex topological changes. By combining vector level set models with gradient projectiontechnology, the level set method for topological optimization is extended to a topologicaloptimization problem with multi-constraints, multi-materials and multi-load cases. Meanwhile, anappropriate nonlinear speed, mapping is established in the tangential space of the activeconstraints for a fast convergence. Then the method is applied to structure designs, mechanism andmaterial designs by a number of benchmark examples. Finally, in order to further improvecomputational efficiency and overcome the difficulty that the level set method cannot generate newmaterial interfaces during the optimization process, the topological derivative analysis isincorporated into the level set method for topological optimization, and a topological derivativeand level set algorithm for topological optimization is proposed.
基金supported in part by the National Natural Science Foundation of China(11626214,11571309)the General Research Project of Zhejiang Provincial Department of Education(Y201635378)+3 种基金the Zhejiang Provincial Natural Science Foundation of China(LY17F020011)J.Peng is supported by the National Natural Science Foundation of China(11771160)the Research Promotion Program of Huaqiao University(ZQN-PY411)Natural Science Foundation of Fujian Province(2015J01254)
文摘This article introduces a new normalized nonlocal hybrid level set method for image segmentation.Due to intensity overlapping,blurred edges with complex backgrounds,simple intensity and texture information,such kind of image segmentation is still a challenging task.The proposed method uses both the region and boundary information to achieve accurate segmentation results.The region information can help to identify rough region of interest and prevent the boundary leakage problem.It makes use of normalized nonlocal comparisons between pairs of patches in each region,and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation.The boundary information can help to detect the precise location of the target object,it makes use of the geodesic active contour model to obtain the target boundary.The corresponding variational segmentation problem is implemented by a level set formulation.We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function.At last,experimental results on synthetic images and real images are shown in the paper with promising results.
基金Supported by National Foundation of Natural Science(11471092)Natural Science Foundation of Zhejiang Province(LZ13A010003)Foundation of Zhejiang Educational Committee(Y201121891)
文摘The goal of the arterial graft design problem is to find an optimal graft built on an occluded artery, which can be mathematically modeled by a fluid based shape optimization problem. The smoothness of the graft is one of the important aspects in the arterial graft design problem since it affects the flow of the blood significantly. As an attractive design tool for this problem, level set methods are quite efficient for obtaining better shape of the graft. In this paper, a cubic spline level set method and a radial basis function level set method are designed to solve the arterial graft design problem. In both approaches, the shape of the arterial graft is implicitly tracked by the zero-level contour of a level set function and a high level of smoothness of the graft is achieved. Numerical results show the efficiency of the algorithms in the arterial graft 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This research work is supported by the National Natural Science Foundation of China(Grant No.51975227).
文摘A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method.It is inspired by the procedure of determining the threshold of sensitivity number in the BESO method.It first computes the difference between the volume of current design and the upper bound of volume.Then,the Lagrange multiplier is regarded as the threshold of sensitivity number to remove the redundant material.Numerical examples proved that this approach is effective to constrain the volume.More importantly,there is no parameter in the proposed approach,which makes it convenient to use.In addition,the convergence is stable,and there is no big oscillation.
文摘2-D and 3-D micro-architectured multiphase thermoelastic metamaterials are designed and analyzed using a parametric level set method for topology optimization and the finite element method.An asymptotic homogenization approach is employed to obtain the effective thermoelastic properties of the multiphase metamaterials.Theε-constraint multi-objective optimization method is adopted in the formulation.The coefficient of thermal expansion(CTE)and Poisson’s ratio(PR)are chosen as two objective functions,with the CTE optimized and the PR treated as a constraint.The optimization problems are solved by using the method of moving asymptotes.Effective isotropic and anisotropic CTEs and stiffness constants are obtained for the topologically optimized metamaterials with prescribed values of PR under the constraints of specified effective bulk modulus,volume fractions and material symmetry.Two solid materials along with one additional void phase are involved in each of the 2-D and 3-D optimal design examples.The numerical results reveal that the newly proposed approach can integrate shape and topology optimizations and lead to optimal microstructures with distinct topological boundaries.The current method can topologically optimize metamaterials with a positive,negative or zero CTE and a positive,negative or zero Poisson’s ratio.
文摘As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been investigated. By using the Level Set method, the transformation of a solitary wave over a front step was simulated. The results were in good agreement with laboratory experiments.
基金the National Natural Science Foundation of China (6001161942, 60203003)
文摘Some basic problems on the level set methods were discussed, such as the method used to preserve the distance junction , the existence and uniqueness of solution for the level set equations. The main contribution is to prove that in a neighborhood of the initial zero level set, the level set equations with the restriction of the distance function have a unique solution, which must be the signed distance function with respect to the evolving surface. Some skillful approaches were used: Noticing that any solution for the original equation was a distance function, the original level set equations were transformed into a simpler alternative form. Moreover, since the new system was not a classical one, the system was transformed into an ordinary one, for which the implicit function method was adopted.
基金National High Technology Research and Development Program of China (863program) (2006AA04Z140)National Natural Science Foundation of China (NSFC) (50605024)
文摘Air entrapped in liquid metal during the mold filling process seriously affects the casting quality, thus it is important to track its behavior in the mold cavity. A liquid-gas two-phase flow model is developed to describe the mold filling process and predict the air entrapment defect. The model is based on the combination of SOLA and Level Set Method. The pressure and velocity fields are calculated by SOLA,and the interface movement is simulated by Level Set method as the most common interface tracking method in recent years.In order to validate the feasibility of the model,the liquid-gas two-phase simulation results were tested by the broken dam problem and the S-shaped experiment. Comparison between the experiments and simulation results show that Level Set method might be a very promising tool in two-phase flow simulation during the mold filling process.
文摘The salt intrusion phenomenon is caused by </span><u><span style="font-family:Verdana;">overexploitation</span></u><span style="font-family:Verdana;"> of aquifers in coastal areas. This physical phenomenon has been the subject of numerous </span><span style="font-family:Verdana;">studies and numerous methods have been proposed, with the aim of protecting the quality of the water in these aquifers. This work proposes a two-dimensional</span><span style="font-family:Verdana;"> saline intrusion model using the sharp interface approach and the level set method. It consists of a parabolic equation modeling the underground flow and a hyperbolic Equation (the level set equation) which makes it possible to track the evolution of the interface. High</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">order numerical schemes such as the space scheme </span><u><span style="font-family:Verdana;">WENO5</span></u><span style="font-family:Verdana;"> and the third</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">order time scheme </span><u><span style="font-family:Verdana;">TVD</span></u><span style="font-family:Verdana;">-</span><u><span style="font-family:Verdana;">RK</span></u><span style="font-family:Verdana;"> were used for the numerical resolution of the hyperbolic equation. To limit the tightening of the contour curves of the level set function, the </span><u><span style="font-family:Verdana;">redistanciation</span></u><span style="font-family:Verdana;"> or </span><u><span style="font-family:Verdana;">reinitialization</span></u><span style="font-family:Verdana;"> algorithm proposed by </span><u><span style="font-family:Verdana;">Sussma </span><i><span style="font-family:Verdana;">et al.</span></i></u><span style="font-family:Verdana;"> (1994) was used. To ensure the effectiveness and reliability of the proposed method, two tests relating to the standard Henry problem and the modified Henry problem were performed. Recall that Henry’s problem uses the variable density modeling approach in a confined and homogeneous aquifer. By comparing the results obtained by the level set method with </span><u><span style="font-family:Verdana;">reinitialization</span></u><span style="font-family:Verdana;"> (</span><u><span style="font-family:Verdana;">LSMR</span></u><span style="font-family:Verdana;">) and those obtained by Henry (1964), and by Simpson and Clement (2004), we see in the two test cases that the level set method reproduces well the toe, the tip and the </span><u><span style="font-family:Verdana;">behaviour</span></u><span style="font-family:Verdana;"> of the interface. These results correspond to the results obtained by </span><u><span style="font-family:Verdana;">Abarca</span></u><span style="font-family:Verdana;"> for Henry’s problem with constant dispersion coefficients. The results obtained with </span><u><span style="font-family:Verdana;">LSMR</span></u><span style="font-family:Verdana;">, reproduced the interface with a slight spacing compared to those obtained by Henry. According to </span><u><span style="font-family:Verdana;">Abarca</span></u><span style="font-family:Verdana;"> (2006), this spacing is due to the absence of the longitudinal and </span><u><span style="font-family:Verdana;">transversal</span></u><span style="font-family:Verdana;"> dispersion coefficients in the model.
基金Supported by National Natural Science Foundation of China(Grant Nos.51605166,51820105007)Fundamental Research Funds for the Central Universities of China
文摘A flexure hinge is a major component in designing compliant mechanisms that o ers unique possibilities in a wide range of application fields in which high positioning accuracy is required. Although various flexure hinges with di erent configurations have been successively proposed, they are often designed based on designers' experiences and inspirations. This study presents a systematic method for topological optimization of flexure hinges by using the level set method. Optimization formulations are developed by considering the functional requirements and geometrical constraints of flexure hinges. The functional requirements are first constructed by maximizing the compliance in the desired direction while minimizing the compliances in the other directions. The weighting sum method is used to construct an objective function in which a self-adjust method is used to set the weighting factors. A constraint on the symmetry of the obtained configuration is developed. Several numerical examples are presented to demonstrate the validity of the proposed method. The obtained results reveal that the design of a flexure hinge starting from the topology level can yield more choices for compliant mechanism design and obtain better designs that achieve higher performance.
基金Supported by the National Natural Science Foundation of China(10871159) the National Basic Research Program of China(2005CB321704)
文摘A non-isothermal injection molding process for a non-Newtonian viscous pseudoplastic fluid is simulated.A conservative interface capturing technique and the flow field solving method are coupled to perform a dynamic simulation.The validity of the numerical method is verified by a benchmark problem.The melt interface evolution versus time is captured and the physical quantities such as temperature,velocity and pressure at each time step are obtained with corresponding analysis.A"frozen skin"layer with the thickness increasing versus time during the injection process is found.The fact that the"frozen skin"layer can be reduced by increasing the injection velocity is numerically verified.The fountain flow phenomenon near the melt interface is also captured.Moreover,comparisons with the non-isothermal Newtonian case show that the curvatures of the interface arcs and the pressure contours near the horizontal mid-line of the cavity for the non-Newtonian pseudoplastic case is larger than that for the Newtonian case.The velocity profiles are different at different positions for the non-Newtonian pseudoplastic case,while in the case of Newtonian flow the velocity profiles are parabolic and almost the same at different positions.
基金Project(21406141)supported by the National Natural Science Foundation of ChinaProject(20141078)supported by the Scientific Research Starting Foundation for Doctors of Liaoning Province,China+1 种基金Project(L2014060)supported by the Foundation of Department of Education of Liaoning Province,ChinaProject(157B21)supported by the Scientific Research Starting Foundation for Doctors of Shenyang Aerospace University,China
文摘The behavior of single bubble rising in quiescent shear-thinning fluids was investigated numerically by level set method. A number of bubbles in a large range of Reynolds number and Eotvos number were investigated including spherical, oblate and spherical. The bubble shape and drag coefficient were compared with experimental results. It is observed that the simulated results show good conformity to experimental results over a wide range of Reynolds number. In addition, the detailed flow field based on the reference coordinate system moving with the bubble is obtained, and the relationship among flow field, bubble shape and velocity is discussed.
基金Supported by the National Basic Research Program of China(2012CB025903)the National Natural Science Foundation of China(91434201,11402210)
文摘The simulation of three-dimensional(3D) non-isothermal, non-Newtonian fluid filling process is an extremely difficult task and remains a challenging problem, which includes polymer melt flow with free surface coupled with transient heat transfer. This paper presents a full 3D non-isothermal two-phase flow model to predict the complex flow in melt filling process, where the Cross-WLF model is applied to characterize the rheological behavior of polymer melt. The governing equations are solved using finite volume method with SIMPLEC algorithm on collocated grids and the melt front is accurately captured by a high resolution level set method. A domain extension technique is adopted to deal with the complex cavities, which greatly reduces the computational burden. To verify the validity of the developed 3D approach, the melts filling processes in two thin rectangular cavities(one of them with a cylindrical insert) are simulated. The predicted melt front interfaces are in good agreement with the experiment and commercial software prediction. For a case with a rather complex cavity, the dynamic filling process in a hemispherical shell is successfully simulated. All of the numerical results show that the developed numerical procedure can provide a reasonable prediction for injection molding process.
基金support from the Centre for Integrated Petroleum Research(CIPR),University of Bergen, Norway,and Singapore MOE Grant T207B2202NRF2007IDMIDM002-010
文摘Segmentation of three-dimensional(3D) complicated structures is of great importance for many real applications.In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model.Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations.Instead,the minimum cut on a special designed graph need to be computed.The method is tested on data with complicated structures.It is rather stable with respect to initial value and the algorithm is nearly parameter free.Experiments show that it can solve large problems much faster than traditional approaches.
基金Supported by National Natural Science Committee and Chinese Engineering Physics Institute Foundation(10576013)Natural Science Foundation of Henan Province(0611053200)Natural Science Study Foundation of Henan University(06YBZR028)
基金863 Programgrant number:2007AA02Z211+3 种基金Jiangsu Science and Technology Departmentgrant number:BE2008399Education of Jiangsu Provincegrant number:08KJA530002
文摘In biology ferment engineering,accurate statistics of the quantity of bacteria is one of the most important subjects. In this paper,the quantity of bacteria which was observed traditionally manuauy can be detected automatically. Image acquisition and processing system is designed to accomplish image preprocessing,image segmentation and statistics of the quantity of bacteria. Segmentation of bacteria images is successfully realized by means of a region-based level set method and then the quantity of bacteria is computed precisely,which plays an important role in optimizing the growth conditions of bacteria.