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Michael Yu Wang - One of the best experts on this subject based on the ideXlab platform.
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Shape equilibrium constraint: a strategy for stress-constrained Structural topology optimization
Structural and Multidisciplinary Optimization, 2013Co-Authors: Michael Yu WangAbstract:In topology optimization of a continuum, it is important to consider stress-related objective or constraints, from both theoretical and application perspectives. It is known that the problem is challenging. Although remarkable achievements have been made with the SIMP (Solid Isotropic Material with Penalization) framework, a number of critical issues are yet to be fully resolved. In the paper, we present an approach of a shape equilibrium constraint strategy with the level-set/X-FEM framework. We formulate the topology optimization problem under (spatially-distributed) stress constraints into a shape equilibrium problem of active stress constraint. This formulation allows us to effectively handle the stress constraint, and the intrinsic non-differentiability introduced by local stress constraints is removed. The optimization problem is made into one of continuous shape-sensitivity and it is solved by evolving a coherent interface of the shape equilibrium concurrently with shape variation in the Structural Boundary during a level-set evolution process. Several numerical examples in two dimensions are provided as a benchmark test of the proposed shape equilibrium constraint strategy for minimum-weight and fully-stressed designs and for designs with stress constraint satisfaction.
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Shape equilibrium constraint: a strategy for stress-constrained Structural topology optimization
Structural and Multidisciplinary Optimization, 2013Co-Authors: Michael Yu Wang, Li LiAbstract:In topology optimization of a continuum, it is important to consider stress-related objective or constraints, from both theoretical and application perspectives. It is known that the problem is challenging. Although remarkable achievements have been made with the SIMP (Solid Isotropic Material with Penalization) framework, a number of critical issues are yet to be fully resolved. In the paper, we present an approach of a shape equilibrium constraint strategy with the level-set/X-FEM framework. We formulate the topology optimization problem under (spatially-distributed) stress constraints into a shape equilibrium problem of active stress constraint. This formulation allows us to effectively handle the stress constraint, and the intrinsic non-differentiability introduced by local stress constraints is removed. The optimization problem is made into one of continuous shape-sensitivity and it is solved by evolving a coherent interface of the shape equilibrium concurrently with shape variation in the Structural Boundary during a level-set evolution process. Several numerical examples in two dimensions are provided as a benchmark test of the proposed shape equilibrium constraint strategy for minimum-weight and fully-stressed designs and for designs with stress constraint satisfaction.
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a semi implicit level set method for Structural shape and topology optimization
Journal of Computational Physics, 2008Co-Authors: Liping Chen, Liyong Tong, Michael Yu WangAbstract:This paper proposes a new level set method for Structural shape and topology optimization using a semi-implicit scheme. Structural Boundary is represented implicitly as the zero level set of a higher-dimensional scalar function and an appropriate time-marching scheme is included to enable the discrete level set processing. In the present study, the Hamilton-Jacobi partial differential equation (PDE) is solved numerically using a semi-implicit additive operator splitting (AOS) scheme rather than explicit schemes in conventional level set methods. The main feature of the present method is it does not suffer from any time step size restriction, as all terms relevant to stability are discretized in an implicit manner. The semi-implicit scheme with additive operator splitting treats all coordinate axes equally in arbitrary dimensions with good rotational invariance. Hence, the present scheme for the level set equations is stable for any practical time steps and numerically easy to implement with high efficiency. Resultantly, it allows enhanced relaxation on the time step size originally limited by the Courant-Friedrichs-Lewy (CFL) condition of the explicit schemes. The stability and computational efficiency can therefore be greatly improved in advancing the level set evolvements. Furthermore, the present method avoids additional cost to globally reinitialize the level set function for regularization purpose. It is noted that the periodically applied reinitializations are time-consuming procedures. In particular, the proposed method is capable of creating new holes freely inside the design domain via Boundary incorporating, splitting and merging processes, which makes the final design independent of initial guess, and helps reduce the probability of converging to a local minimum. The availability of the present method is demonstrated with two widely studied examples in the framework of the Structural stiffness designs.
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a level set method for Structural topology optimization
Computer Methods in Applied Mechanics and Engineering, 2003Co-Authors: Michael Yu Wang, Xiaoming WangAbstract:This paper presents a new approach to Structural topology optimization. We represent the Structural Boundary by a level set model that is embedded in a scalar function of a higher dimension. Such level set models are flexible in handling complex topological changes and are concise in describing the Boundary shape of the structure. Furthermore, a well-founded mathematical procedure leads to a numerical algorithm that describes a Structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints. The result is a 3D topology optimization technique that demonstrates outstanding flexibility of handling topological changes, fidelity of Boundary representation and degree of automation. We have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods. The benefit and the advantages of the proposed method are illustrated with several 2D examples that are widely used in the recent literature of topology optimization, especially in the homogenization based methods.
Tim Dumslaff - One of the best experts on this subject based on the ideXlab platform.
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On-surface synthesis of graphene nanoribbons with zigzag edge topology
Nature, 2016Co-Authors: Pascal Ruffieux, Leopold Talirz, Prashant Shinde, Carlos Sánchez-sánchez, Carlo A Pignedoli, Daniele Passerone, Shiyong Wang, Thomas Dienel, Bo Yang, Tim DumslaffAbstract:Synthesis of atomically precise zigzag edges in graphene nanoribbons is demonstrated using a bottom-up strategy based on surface-assisted arrangement and reaction of precursor monomers; these nanoribbons have edge-localized states with large energy splittings. Graphene-based nanostructures exhibit electronic properties that are not present in extended graphene. For example, quantum confinement in carbon nanotubes and armchair graphene nanoribbons leads to the opening of substantial electronic bandgaps that are directly linked to their Structural Boundary conditions^ 1 , 2 . Nanostructures with zigzag edges are expected to host spin-polarized electronic edge states and can thus serve as key elements for graphene-based spintronics^ 3 . The edge states of zigzag graphene nanoribbons (ZGNRs) are predicted to couple ferromagnetically along the edge and antiferromagnetically between the edges^ 4 , but direct observation of spin-polarized edge states for zigzag edge topologies—including ZGNRs—has not yet been achieved owing to the limited precision of current top-down approaches^ 5 , 6 , 7 , 8 , 9 , 10 . Here we describe the bottom-up synthesis of ZGNRs through surface-assisted polymerization and cyclodehydrogenation of specifically designed precursor monomers to yield atomically precise zigzag edges. Using scanning tunnelling spectroscopy we show the existence of edge-localized states with large energy splittings. We expect that the availability of ZGNRs will enable the characterization of their predicted spin-related properties, such as spin confinement^ 11 and filtering^ 12 , 13 , and will ultimately add the spin degree of freedom to graphene-based circuitry. Graphene nanoribbons with zigzag edges are predicted to host spin-polarized electronic edge states that would make them suitable as elements for graphene-based spintronics applications. The production of nanoribbons with 'zigzag', rather than the more familiar 'armchair' edges, remains a major challenge, in part because of the instability of such edge configurations. This paper reports an elegant bottom-up strategy for the production of zigzag-edged graphene nanoribbons, based on the surface-assisted arrangement and reaction of precursor monomers. The authors also present evidence of the predicted spin-polarized edge states obtained using scanning tunnelling microscopy.
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on surface synthesis of graphene nanoribbons with zigzag edge topology
Nature, 2016Co-Authors: Pascal Ruffieux, Leopold Talirz, Prashant Shinde, Carlo A Pignedoli, Daniele Passerone, Shiyong Wang, Thomas Dienel, Bo Yang, Carlos Sanchezsanchez, Tim DumslaffAbstract:Graphene-based nanostructures exhibit electronic properties that are not present in extended graphene. For example, quantum confinement in carbon nanotubes and armchair graphene nanoribbons leads to the opening of substantial electronic bandgaps that are directly linked to their Structural Boundary conditions1, 2. Nanostructures with zigzag edges are expected to host spin-polarized electronic edge states and can thus serve as key elements for graphene-based spintronics3. The edge states of zigzag graphene nanoribbons (ZGNRs) are predicted to couple ferromagnetically along the edge and antiferromagnetically between the edges4, but direct observation of spin-polarized edge states for zigzag edge topologies—including ZGNRs—has not yet been achieved owing to the limited precision of current top-down approaches5, 6, 7, 8, 9, 10. Here we describe the bottom-up synthesis of ZGNRs through surface-assisted polymerization and cyclodehydrogenation of specifically designed precursor monomers to yield atomically precise zigzag edges. Using scanning tunnelling spectroscopy we show the existence of edge-localized states with large energy splittings. We expect that the availability of ZGNRs will enable the characterization of their predicted spin-related properties, such as spin confinement11 and filtering12, 13, and will ultimately add the spin degree of freedom to graphene-based circuitry.
Pascal Ruffieux - One of the best experts on this subject based on the ideXlab platform.
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On-surface synthesis of graphene nanoribbons with zigzag edge topology
Nature, 2016Co-Authors: Pascal Ruffieux, Leopold Talirz, Prashant Shinde, Carlos Sánchez-sánchez, Carlo A Pignedoli, Daniele Passerone, Shiyong Wang, Thomas Dienel, Bo Yang, Tim DumslaffAbstract:Synthesis of atomically precise zigzag edges in graphene nanoribbons is demonstrated using a bottom-up strategy based on surface-assisted arrangement and reaction of precursor monomers; these nanoribbons have edge-localized states with large energy splittings. Graphene-based nanostructures exhibit electronic properties that are not present in extended graphene. For example, quantum confinement in carbon nanotubes and armchair graphene nanoribbons leads to the opening of substantial electronic bandgaps that are directly linked to their Structural Boundary conditions^ 1 , 2 . Nanostructures with zigzag edges are expected to host spin-polarized electronic edge states and can thus serve as key elements for graphene-based spintronics^ 3 . The edge states of zigzag graphene nanoribbons (ZGNRs) are predicted to couple ferromagnetically along the edge and antiferromagnetically between the edges^ 4 , but direct observation of spin-polarized edge states for zigzag edge topologies—including ZGNRs—has not yet been achieved owing to the limited precision of current top-down approaches^ 5 , 6 , 7 , 8 , 9 , 10 . Here we describe the bottom-up synthesis of ZGNRs through surface-assisted polymerization and cyclodehydrogenation of specifically designed precursor monomers to yield atomically precise zigzag edges. Using scanning tunnelling spectroscopy we show the existence of edge-localized states with large energy splittings. We expect that the availability of ZGNRs will enable the characterization of their predicted spin-related properties, such as spin confinement^ 11 and filtering^ 12 , 13 , and will ultimately add the spin degree of freedom to graphene-based circuitry. Graphene nanoribbons with zigzag edges are predicted to host spin-polarized electronic edge states that would make them suitable as elements for graphene-based spintronics applications. The production of nanoribbons with 'zigzag', rather than the more familiar 'armchair' edges, remains a major challenge, in part because of the instability of such edge configurations. This paper reports an elegant bottom-up strategy for the production of zigzag-edged graphene nanoribbons, based on the surface-assisted arrangement and reaction of precursor monomers. The authors also present evidence of the predicted spin-polarized edge states obtained using scanning tunnelling microscopy.
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on surface synthesis of graphene nanoribbons with zigzag edge topology
Nature, 2016Co-Authors: Pascal Ruffieux, Leopold Talirz, Prashant Shinde, Carlo A Pignedoli, Daniele Passerone, Shiyong Wang, Thomas Dienel, Bo Yang, Carlos Sanchezsanchez, Tim DumslaffAbstract:Graphene-based nanostructures exhibit electronic properties that are not present in extended graphene. For example, quantum confinement in carbon nanotubes and armchair graphene nanoribbons leads to the opening of substantial electronic bandgaps that are directly linked to their Structural Boundary conditions1, 2. Nanostructures with zigzag edges are expected to host spin-polarized electronic edge states and can thus serve as key elements for graphene-based spintronics3. The edge states of zigzag graphene nanoribbons (ZGNRs) are predicted to couple ferromagnetically along the edge and antiferromagnetically between the edges4, but direct observation of spin-polarized edge states for zigzag edge topologies—including ZGNRs—has not yet been achieved owing to the limited precision of current top-down approaches5, 6, 7, 8, 9, 10. Here we describe the bottom-up synthesis of ZGNRs through surface-assisted polymerization and cyclodehydrogenation of specifically designed precursor monomers to yield atomically precise zigzag edges. Using scanning tunnelling spectroscopy we show the existence of edge-localized states with large energy splittings. We expect that the availability of ZGNRs will enable the characterization of their predicted spin-related properties, such as spin confinement11 and filtering12, 13, and will ultimately add the spin degree of freedom to graphene-based circuitry.
Zhan Kang - One of the best experts on this subject based on the ideXlab platform.
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multi material topology optimization considering interface behavior via xfem and level set method
Computer Methods in Applied Mechanics and Engineering, 2016Co-Authors: Zhan KangAbstract:Abstract In most of the existing topology optimization studies of multi-material structures, the interface of different materials was assumed to be perfectly bonded. Optimal design based on the perfect-interface assumption may introduce the risk of failure caused by interface debonding. This paper presents an efficient multi-material topology optimization strategy for seeking the optimal layout of structures considering the cohesive constitutive relationship of the interface. Based on the color level set method to describe the topology and the interface, the interface behavior is simulated by combining the extended finite element method (XFEM) and the cohesive model on fixed mesh. This enables modeling of possible separation of material interfaces, and thus provides a more realistic model of multi-material structures. Furthermore, this interface modeling technique avoids the difficulty of re-meshing when tracking the moving cohesive interface positions during the optimization process. In the topology optimization model, the normal velocities defined on the level set points are considered as design variables. In conjunction with the adjoint-variable sensitivity analysis, these design variables are updated by using the mathematical programming approach and then used to interpolate the Boundary velocities. These Boundary velocities are extrapolated to the whole domain with the fast marching method and used to advance the Structural Boundary through the Hamilton–Jacobi equation. This topology optimization technique can handle multiple constraints easily in the framework of level set method and at the same time preserve the signed distance property of the level set functions. Two numerical examples are given to demonstrate the effectiveness of the present method. It is also revealed that the optimal design considering interface behavior may exhibit tension/compression non-symmetric topology, in which material interfaces mainly undergo compression.
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a level set method for Structural shape and topology optimization using radial basis functions
Computers & Structures, 2009Co-Authors: Liyong Tong, Zhan KangAbstract:This paper presents an alternative level set method for shape and topology optimization of continuum structures. An implicit free Boundary representation model is established by embedding Structural Boundary into the zero level set of a higher-dimensional level set function. An explicit parameterization scheme for the level set surface is proposed by using radial basis functions with compact support. In doing so, the originally more difficult shape and topology optimization, driven by the temporal and spatial Hamilton-Jacobi partial differential equation (PDE), is transformed into a relatively easier size optimization of the expansion coefficients of the basis functions. The design optimization is converted to an iterative numerical process that combines the parameterization with a derivation of the shape sensitivity of the design functions, so as to allow using mathematical programming algorithms to solve the level set-based design problem and avoid directly solving the Hamilton-Jacobi PDE. Furthermore, a numerically more stable and efficient volume integration scheme is proposed to implement calculations of the shape derivatives, leading to the creation of new holes which are generated initially along the Boundary and then propagated to the interior of the design domain. Two widely studied examples are used to demonstrate the effectiveness of the proposed optimization method.
Liyong Tong - One of the best experts on this subject based on the ideXlab platform.
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a level set method for Structural shape and topology optimization using radial basis functions
Computers & Structures, 2009Co-Authors: Liyong Tong, Zhan KangAbstract:This paper presents an alternative level set method for shape and topology optimization of continuum structures. An implicit free Boundary representation model is established by embedding Structural Boundary into the zero level set of a higher-dimensional level set function. An explicit parameterization scheme for the level set surface is proposed by using radial basis functions with compact support. In doing so, the originally more difficult shape and topology optimization, driven by the temporal and spatial Hamilton-Jacobi partial differential equation (PDE), is transformed into a relatively easier size optimization of the expansion coefficients of the basis functions. The design optimization is converted to an iterative numerical process that combines the parameterization with a derivation of the shape sensitivity of the design functions, so as to allow using mathematical programming algorithms to solve the level set-based design problem and avoid directly solving the Hamilton-Jacobi PDE. Furthermore, a numerically more stable and efficient volume integration scheme is proposed to implement calculations of the shape derivatives, leading to the creation of new holes which are generated initially along the Boundary and then propagated to the interior of the design domain. Two widely studied examples are used to demonstrate the effectiveness of the proposed optimization method.
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a semi implicit level set method for Structural shape and topology optimization
Journal of Computational Physics, 2008Co-Authors: Liping Chen, Liyong Tong, Michael Yu WangAbstract:This paper proposes a new level set method for Structural shape and topology optimization using a semi-implicit scheme. Structural Boundary is represented implicitly as the zero level set of a higher-dimensional scalar function and an appropriate time-marching scheme is included to enable the discrete level set processing. In the present study, the Hamilton-Jacobi partial differential equation (PDE) is solved numerically using a semi-implicit additive operator splitting (AOS) scheme rather than explicit schemes in conventional level set methods. The main feature of the present method is it does not suffer from any time step size restriction, as all terms relevant to stability are discretized in an implicit manner. The semi-implicit scheme with additive operator splitting treats all coordinate axes equally in arbitrary dimensions with good rotational invariance. Hence, the present scheme for the level set equations is stable for any practical time steps and numerically easy to implement with high efficiency. Resultantly, it allows enhanced relaxation on the time step size originally limited by the Courant-Friedrichs-Lewy (CFL) condition of the explicit schemes. The stability and computational efficiency can therefore be greatly improved in advancing the level set evolvements. Furthermore, the present method avoids additional cost to globally reinitialize the level set function for regularization purpose. It is noted that the periodically applied reinitializations are time-consuming procedures. In particular, the proposed method is capable of creating new holes freely inside the design domain via Boundary incorporating, splitting and merging processes, which makes the final design independent of initial guess, and helps reduce the probability of converging to a local minimum. The availability of the present method is demonstrated with two widely studied examples in the framework of the Structural stiffness designs.
