The Experts below are selected from a list of 114420 Experts worldwide ranked by ideXlab platform
Shinji Nishiwaki - One of the best experts on this subject based on the ideXlab platform.
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matlab code for a Level Set based topology optimization method using a reaction diffusion equation
Structural and Multidisciplinary Optimization, 2015Co-Authors: Masaki Otomori, Kazuhiro Izui, Takayuki Yamada, Shinji NishiwakiAbstract:This paper presents a simple Matlab implementation for a Level Set-based topology optimization method in which the Level Set Function is updated using a reaction diffusion equation, which is different from conventional Level Set-based approaches (Allaire et al. 2002, 2004; Wang et al. 2003) that use the Hamilton-Jacobi equation to update the Level Set Function. With this method, the geometrical complexity of optimized configurations can be easily controlled by appropriately Setting a regularization parameter. We explain the code in detail, and also the derivation of the topological derivative that is used in the Level Set-based topology optimization. Numerical results for stiffness maximization problems are provided to facilitate the reader's understanding. The presented code is intended for educational purposes only. This paper was inspired by previously published papers presenting Matlab code for a SIMP method (Sigmund 2001; Andreassen et al. 2011), a Level Set-based method (Challis 2010), and FreeFem ++ code for a structural optimization method (Allaire and Pantz 2006). Readers can investigate results provided by these different methods and discover the prominent aspects of each particular method. The code presented here can be downloaded from http://www.osdel.me.kyoto-u.ac.jp/members/yamada/codes.html.
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a Level Set based topology optimization method targeting metallic waveguide design problems
International Journal for Numerical Methods in Engineering, 2011Co-Authors: Shintaro Yamasaki, Tsuyoshi Nomura, Atsushi Kawamoto, Kazuo Sato, Shinji NishiwakiAbstract:In this paper, we propose a Level Set-based topology optimization method targeting metallic waveguide design problems, where the skin effect must be taken into account since the metallic waveguides are generally used in the high-frequency range where this effect critically affects performance. One of the most reasonable approaches to represent the skin effect is to impose an electric field constraint condition on the surface of the metal. To implement this approach, we develop a boundary-tracking scheme for the arbitrary Lagrangian Eulerian (ALE) mesh pertaining to the zero iso-contour of the Level Set Function that is given in an Eulerian mesh, and impose Dirichlet boundary conditions at the nodes on the zero iso-contour in the ALE mesh to compute the electric field. Since the ALE mesh accurately tracks the zero iso-contour at every optimization iteration, the electric field is always appropriately computed during optimization. For the sensitivity analysis, we compute the nodal coordinate sensitivities in the ALE mesh and smooth them by solving a Helmholtz-type partial differential equation. The obtained smoothed sensitivities are used to compute the normal velocity in the Level Set equation that is solved using the Eulerian mesh, and the Level Set Function is updated based on the computed normal velocity. Finally, the utility of the proposed method is discussed through several numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.
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design optimization of h plane waveguide component by Level Set method
IEICE Transactions on Electronics, 2011Co-Authors: Koichi Hirayama, Shintaro Yamasaki, Yasuhide Tsuji, Shinji NishiwakiAbstract:We present a design optimization method of H-plane waveguide components, based on the Level Set method with the finite element method. In this paper, we propose a new formulation for the improvement of a Level Set Function, which describes shape, location, and connectivity of dielectric in a design region. Employing the optimization procedure, we demonstrate that optimized structures of an H-plane waveguide filter and T-junction are obtained from an initial structure composed of several circular blocks of dielectric.
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a structural optimization method incorporating Level Set boundary expressions based on the concept of the phase field method
Journal of Environment and Engineering, 2011Co-Authors: Takayuki Yamada, Kazuhiro Izui, Shinji Nishiwaki, Masataka Yoshimura, Akihiro TakezawaAbstract:Topology optimization has been successfully used in many industries, especially those engaged in the design and manufacturing of mechanical devices, but numerical problems are often encountered, such as grayscale representations of obtained composites. A type of structural optimization method using the Level Set theory for boundary expressions has been proposed, in which the outlines of target structures are implicitly represented using the Level Set Function, and optimal configurations are obtained by updating this Function based on the shape sensitivities. Level Set-based methods typically have a drawback, however, in that topological changes that increase the number of holes in the material domain are not allowed. To overcome the above numerical and topological problems, this paper proposes a new topology optimization method incorporating Level Set boundary expressions based on the concept of the phase field method, which we apply to a minimum mean compliance problem. First, a structural optimization problem is formulated based on a boundary expression, using the Level Set Function. Next, a time evolutionary equation for updating the Level Set Function is formulated based on the concept of the phase field method, and the minimum mean compliance problem is formulated using a Level Set boundary expression. An optimization algorithm for the topology optimization incorporating the Level Set boundary expression based on the concept of the phase field method is then derived. Several examples are provided to confirm the usefulness of the proposed structural topology optimization method.
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a topology optimization method based on the Level Set method incorporating a fictitious interface energy
Computer Methods in Applied Mechanics and Engineering, 2010Co-Authors: Takayuki Yamada, Kazuhiro Izui, Shinji Nishiwaki, Akihiro TakezawaAbstract:This paper proposes a new topology optimization method, which can adjust the geometrical complexity of optimal configurations, using the Level Set method and incorporating a fictitious interface energy derived from the phase field method. First, a topology optimization problem is formulated based on the Level Set method, and the method of regularizing the optimization problem by introducing fictitious interface energy is explained. Next, the reaction–diffusion equation that updates the Level Set Function is derived and an optimization algorithm is then constructed, which uses the finite element method to solve the equilibrium equations and the reaction–diffusion equation when updating the Level Set Function. Finally, several optimum design examples are shown to confirm the validity and utility of the proposed topology optimization method.
Christophe Josset - One of the best experts on this subject based on the ideXlab platform.
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Reactive fluid flow topology optimization with the multi-relaxation time lattice Boltzmann method and a Level-Set Function
Journal of Computational Physics, 2020Co-Authors: Florian Dugast, Yann Favennec, Christophe JossetAbstract:This paper presents a topology optimization algorithm based on the lattice Boltzmann method coupled with a Level-Set method for increasing the eciency of reactive uid ows. The multi-relaxation time model is considered for the lattice Boltzmann collision operator, allowing higher Reynolds numbers ow simulations compared to the ordinary single-relaxation time model. The cost Function gradient is obtained with the derivation of the adjoint-state formulation for the fully coupled problem. The proposed method is tested successfully on several numerical applications involving Reynolds numbers from 10 up to 1,000, as well as with dierent Damkohler and Peclet numbers. A limitation of the maximal pressure drop is also applied. The obtained results demonstrate that the proposed numerical method is robust and efcient for solving topology optimization problems of reactive uid ows, in dierent operating conditions.
Shouyu Cai - One of the best experts on this subject based on the ideXlab platform.
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shape optimization of dirichlet boundaries based on weighted b spline finite cell method and Level Set Function
Computer Methods in Applied Mechanics and Engineering, 2015Co-Authors: Weihong Zhang, Linying Zhao, Shouyu CaiAbstract:Abstract This paper addresses extended shape optimization problems where structural supports, i.e., Dirichlet boundaries and free boundaries are simultaneously optimized. Unlike traditional FEM, the weighted B-spline finite cell method (FCM) is applied as structural analysis tool and combined with the Level-Set Function (LSF) to take into account Dirichlet boundary condition (DBC) automatically through penalization of the displacement field. The proposed shape optimization method achieves a comprehensive integration of fixed grid, B-spline shape Function and Level-Set Function. As both the structure and Dirichlet boundaries are described in the form of LSF, any modification of Dirichlet boundaries can be made in a straightforward way as easily as free boundaries by changing continuous design variables. Meanwhile, the computing accuracy is ensured within the framework of fixed grid owing to the quadtree refinements of boundary cells. Stress related shape optimization problems are finally solved to demonstrate the merit and validity of the proposed optimization method in dealing with shape optimization of Dirichlet boundaries.
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stress constrained shape and topology optimization with fixed mesh a b spline finite cell method combined with Level Set Function
Computer Methods in Applied Mechanics and Engineering, 2014Co-Authors: Shouyu Cai, Weihong Zhang, Jihong Zhu, Tong GaoAbstract:Abstract In this paper, we develop an efficient and flexible design method that integrates the B-spline finite cell method (B-spline FCM) and the Level Set Function (LSF) for stress constrained shape and topology optimization. Any structure of complex geometry is embedded within an extended, regular and fixed Eulerian mesh no matter how the structure is optimized. High-order B-spline shape Functions are further implemented to ensure precisions of stress analysis and sensitivity analysis. Meanwhile, Level Set Functions, i.e., implicit Functions are used to enable topological changes of the considered structure through smooth boundary variations. Involved parameters rather than the conventional discrete form of LSF are directly taken as design variables to facilitate the numerical computing process. To be specific, the LSF is constructed by means of R-Functions that incorporate cubic splines as implicit Functions to offer flexibilities for shape optimization within the framework of fixed mesh, while the compactly supported radial basis Functions (CS-RBFs) are employed as implicit Functions for stress constrained topology optimization. It is shown the proposed FCM/LSF method is a convenient approach that makes it possible to calculate stress and stress sensitivities with high precision. Representative examples of shape and topology optimization with and without stress constraints are solved with success demonstrating the advantages of the FCM/LSF method.
Weihong Zhang - One of the best experts on this subject based on the ideXlab platform.
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exact imposition of inhomogeneous dirichlet boundary conditions based on weighted finite cell method and Level Set Function
Computer Methods in Applied Mechanics and Engineering, 2016Co-Authors: Weihong Zhang, Linying ZhaoAbstract:Abstract The imposition of inhomogeneous Dirichlet boundary conditions (IDBCs) is essential in numerical analysis of a structure. It is especially difficult and no longer straightforward whenever non-conformal mesh is used to discretize a structure. The original contribution of this paper is to develop a weighted finite cell method (FCM) with high computing accuracy. The commonly used transfinite interpolation in the computer-aided design (CAD) community is now extended to define boundary value Function so that the IDBCs are imposed exactly. Unlike existing weak imposition forms and weighted interpolation methods, it is shown that the weighting Function and boundary value Function involved in the weighted FCM can directly be applied to the physical field independently of the mesh discretization. Besides, Level-Set Function (LSF) is used to represent the geometry of the considered physical domain. To verify the effectiveness, convergence performance and the generality of the proposed method, numerical examples ranging from purely elastic to thermoelastic problems are illustrated. Computing results are compared with analytical and FEA solutions.
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shape optimization of dirichlet boundaries based on weighted b spline finite cell method and Level Set Function
Computer Methods in Applied Mechanics and Engineering, 2015Co-Authors: Weihong Zhang, Linying Zhao, Shouyu CaiAbstract:Abstract This paper addresses extended shape optimization problems where structural supports, i.e., Dirichlet boundaries and free boundaries are simultaneously optimized. Unlike traditional FEM, the weighted B-spline finite cell method (FCM) is applied as structural analysis tool and combined with the Level-Set Function (LSF) to take into account Dirichlet boundary condition (DBC) automatically through penalization of the displacement field. The proposed shape optimization method achieves a comprehensive integration of fixed grid, B-spline shape Function and Level-Set Function. As both the structure and Dirichlet boundaries are described in the form of LSF, any modification of Dirichlet boundaries can be made in a straightforward way as easily as free boundaries by changing continuous design variables. Meanwhile, the computing accuracy is ensured within the framework of fixed grid owing to the quadtree refinements of boundary cells. Stress related shape optimization problems are finally solved to demonstrate the merit and validity of the proposed optimization method in dealing with shape optimization of Dirichlet boundaries.
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stress constrained shape and topology optimization with fixed mesh a b spline finite cell method combined with Level Set Function
Computer Methods in Applied Mechanics and Engineering, 2014Co-Authors: Shouyu Cai, Weihong Zhang, Jihong Zhu, Tong GaoAbstract:Abstract In this paper, we develop an efficient and flexible design method that integrates the B-spline finite cell method (B-spline FCM) and the Level Set Function (LSF) for stress constrained shape and topology optimization. Any structure of complex geometry is embedded within an extended, regular and fixed Eulerian mesh no matter how the structure is optimized. High-order B-spline shape Functions are further implemented to ensure precisions of stress analysis and sensitivity analysis. Meanwhile, Level Set Functions, i.e., implicit Functions are used to enable topological changes of the considered structure through smooth boundary variations. Involved parameters rather than the conventional discrete form of LSF are directly taken as design variables to facilitate the numerical computing process. To be specific, the LSF is constructed by means of R-Functions that incorporate cubic splines as implicit Functions to offer flexibilities for shape optimization within the framework of fixed mesh, while the compactly supported radial basis Functions (CS-RBFs) are employed as implicit Functions for stress constrained topology optimization. It is shown the proposed FCM/LSF method is a convenient approach that makes it possible to calculate stress and stress sensitivities with high precision. Representative examples of shape and topology optimization with and without stress constraints are solved with success demonstrating the advantages of the FCM/LSF method.
Takayuki Yamada - One of the best experts on this subject based on the ideXlab platform.
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matlab code for a Level Set based topology optimization method using a reaction diffusion equation
Structural and Multidisciplinary Optimization, 2015Co-Authors: Masaki Otomori, Kazuhiro Izui, Takayuki Yamada, Shinji NishiwakiAbstract:This paper presents a simple Matlab implementation for a Level Set-based topology optimization method in which the Level Set Function is updated using a reaction diffusion equation, which is different from conventional Level Set-based approaches (Allaire et al. 2002, 2004; Wang et al. 2003) that use the Hamilton-Jacobi equation to update the Level Set Function. With this method, the geometrical complexity of optimized configurations can be easily controlled by appropriately Setting a regularization parameter. We explain the code in detail, and also the derivation of the topological derivative that is used in the Level Set-based topology optimization. Numerical results for stiffness maximization problems are provided to facilitate the reader's understanding. The presented code is intended for educational purposes only. This paper was inspired by previously published papers presenting Matlab code for a SIMP method (Sigmund 2001; Andreassen et al. 2011), a Level Set-based method (Challis 2010), and FreeFem ++ code for a structural optimization method (Allaire and Pantz 2006). Readers can investigate results provided by these different methods and discover the prominent aspects of each particular method. The code presented here can be downloaded from http://www.osdel.me.kyoto-u.ac.jp/members/yamada/codes.html.
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a structural optimization method incorporating Level Set boundary expressions based on the concept of the phase field method
Journal of Environment and Engineering, 2011Co-Authors: Takayuki Yamada, Kazuhiro Izui, Shinji Nishiwaki, Masataka Yoshimura, Akihiro TakezawaAbstract:Topology optimization has been successfully used in many industries, especially those engaged in the design and manufacturing of mechanical devices, but numerical problems are often encountered, such as grayscale representations of obtained composites. A type of structural optimization method using the Level Set theory for boundary expressions has been proposed, in which the outlines of target structures are implicitly represented using the Level Set Function, and optimal configurations are obtained by updating this Function based on the shape sensitivities. Level Set-based methods typically have a drawback, however, in that topological changes that increase the number of holes in the material domain are not allowed. To overcome the above numerical and topological problems, this paper proposes a new topology optimization method incorporating Level Set boundary expressions based on the concept of the phase field method, which we apply to a minimum mean compliance problem. First, a structural optimization problem is formulated based on a boundary expression, using the Level Set Function. Next, a time evolutionary equation for updating the Level Set Function is formulated based on the concept of the phase field method, and the minimum mean compliance problem is formulated using a Level Set boundary expression. An optimization algorithm for the topology optimization incorporating the Level Set boundary expression based on the concept of the phase field method is then derived. Several examples are provided to confirm the usefulness of the proposed structural topology optimization method.
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a topology optimization method based on the Level Set method incorporating a fictitious interface energy
Computer Methods in Applied Mechanics and Engineering, 2010Co-Authors: Takayuki Yamada, Kazuhiro Izui, Shinji Nishiwaki, Akihiro TakezawaAbstract:This paper proposes a new topology optimization method, which can adjust the geometrical complexity of optimal configurations, using the Level Set method and incorporating a fictitious interface energy derived from the phase field method. First, a topology optimization problem is formulated based on the Level Set method, and the method of regularizing the optimization problem by introducing fictitious interface energy is explained. Next, the reaction–diffusion equation that updates the Level Set Function is derived and an optimization algorithm is then constructed, which uses the finite element method to solve the equilibrium equations and the reaction–diffusion equation when updating the Level Set Function. Finally, several optimum design examples are shown to confirm the validity and utility of the proposed topology optimization method.
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a structural optimization method based on the Level Set method using a new geometry based re initialization scheme
International Journal for Numerical Methods in Engineering, 2010Co-Authors: Shintaro Yamasaki, Kazuhiro Izui, Shinji Nishiwaki, Takayuki Yamada, Masataka YoshimuraAbstract:Structural optimization methods based on the Level Set method are a new type of structural optimization method where the outlines of target structures can be implicitly represented using the Level Set Function, and updated by solving the so-called Hamilton–Jacobi equation based on a Eulerian coordinate system. These new methods can allow topological alterations, such as the number of holes, during the optimization process whereas the boundaries of the target structure are clearly defined. However, the re-initialization scheme used when updating the Level Set Function is a critical problem when seeking to obtain appropriately updated outlines of target structures. In this paper, we propose a new structural optimization method based on the Level Set method using a new geometry-based re-initialization scheme where both the numerical analysis used when solving the equilibrium equations and the updating process of the Level Set Function are performed using the Finite Element Method. The stiffness maximization, eigenfrequency maximization, and eigenfrequency matching problems are considered as optimization problems. Several design examples are presented to confirm the usefulness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.