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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 2015年第Sep.1期294卷 359-383页

作者： Zhang, Weihong Zhao, Linying Cai, Shouyu Northwestern Polytech Univ Sch Mech Engn Engn Simulat & Aerosp Comp Xian 710072 Shaanxi Peoples R China

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. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Shape optimization of support boundary Dirichlet boundary condition Finite cell method Weighting function Fixed grid level-set function

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A topology optimization algorithm based on topological derivative and level-set function for designing phononic crystals

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ENGINEERING COMPUTATIONS 2022年第1期39卷 354-379页

作者： Yera, Rolando Forzani, Luisina Gustavo Mendez, Carlos Huespe, Alfredo E. Consejo Nacl Invest Cient & Tecn Cimec Santa Fe Argentina UNL Cimec Santa Fe Argentina

Purpose This work presents a topology optimization methodology for designing microarchitectures of phononic crystals. The objective is to get microstructures having, as a consequence of wave propagation phenomena in these media, bandgaps between two specified bands. An additional target is to enlarge the range of frequencies of these bandgaps. Design/methodology/approach The resulting optimization problem is solved employing an augmented Lagrangian technique based on the proximal point methods. The main primal variable of the Lagrangian function is the characteristic function determining the spatial geometrical arrangement of different phases within the unit cell of the phononic crystal. This characteristic function is defined in terms of a level-set function. Descent directions of the Lagrangian function are evaluated by using the topological derivatives of the eigenvalues obtained through the dispersion relation of the phononic crystal. Findings The description of the optimization algorithm is emphasized, and its intrinsic properties to attain adequate phononic crystal topologies are discussed. Particular attention is addressed to validate the analytical expressions of the topological derivative. Application examples for several cases are presented, and the numerical performance of the optimization algorithm for attaining the corresponding solutions is discussed. Originality/value The original contribution results in the description and numerical assessment of a topology optimization algorithm using the joint concepts of the level-set function and topological derivative to design phononic crystals.

关键词： Phononic crystal design Topology optimization technique Topological derivative of eigenvalues Bandgaps level-set function

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Topology optimization method for interior flow based on transient information of the lattice Boltzmann method with a level-set function

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JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2017年第2期34卷 611-632页

作者： Yonekura, Kazuo Kanno, Yoshihiro IHI Corp Isogo Ku 1 Shin Nakahara Cho Yokohama Kanagawa 2358501 Japan Tokyo Inst Technol Midori Ku 4259 Nagatsuta Cho Yokohama Kanagawa 2268503 Japan

We propose a topology optimization method for a flow field using transient information. The optimization algorithm of many conventional methods use the fully converged information of a flow field. In contrast, our approach uses the transient information of an unsteady flow field and update the design domain while solving the unsteady flow field, thereby greatly reducing the computational cost. The fluid and solid regions are clearly distinguished by a level-set function. Consequently, the boundary is concretely represented, and precise boundary conditions are applied on the wall boundary. The lattice Boltzmann method is employed as a fluid computation method. To implement the non-slip boundary conditions at the fluid-solid boundary, we apply bounce-back conditions. We update the domain according to a sensitivity analysis. A sensitivity is formulated based on the lattice Boltzmann equations without adjoint equations for self-adjoint flow. We approximately use the sensitivity for non-self-adjoint equations, i.e. lattice Boltzmann equations, and discuss the optimality and limitations. The approximated sensitivity also considers the bounce-back boundary conditions at the wall separating the fluid and solid regions.

关键词： Flow optimization Lattice Boltzmann method Multiple relaxation time level-set function Sensitivity analysis

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Exact imposition of inhomogeneous Dirichlet boundary conditions based on weighted finite cell method and level-set function

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2016年第Aug.1期307卷 316-338页

作者： Zhang, Weihong Zhao, Linying Northwestern Polytech Univ Sch Mech Engn Engn Simulat & Aerosp Comp Xian 710072 Shaanxi Peoples R China

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. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Inhomogeneous Dirichlet boundary conditions Finite cell method Weighted interpolation level-set function

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Topology Optimization Based on Regularized level-set function for Solving 3-D Nonlinear Magnetic Field System With Spatial Symmetric Condition

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IEEE TRANSACTIONS ON MAGNETICS 2016年第3期52卷 1-4页

作者： Okamoto, Yoshifumi Wakao, Shinji Sato, Shuji Hosei Univ Dept Elect & Elect Engn Tokyo 1848584 Japan Waseda Univ Dept Elect Engn & Biosci Tokyo 1698555 Japan Utsunomiya Univ Dept Elect & Elect Syst Engn Utsunomiya Tochigi 3218585 Japan

Topology optimization (TO) is an effective method for producing practical design of electrical machines. TO is conventionally implemented based on the material density;however, this approach can yield a large number of grayscale areas and unfeasible shapes. On the other hand, when the level-set function is applied to the TO of the magnetic field problem, the potential for obtaining a feasible solution improves. This paper implemented a TO method that uses the regularized level-set function to solve the 3-D nonlinear magnetic field problem. Furthermore, a spatial symmetry condition (SSC), which can introduce the mirror and periodic symmetry of the level-set function from the viewpoint of the electromagnetism, is proposed. To achieve symmetry in the electromagnetic field distribution, the validity of the SSC is investigated and confirmed in a 3-D magnetic shielding problem.

关键词： level-set function regularization spatial symmetry condition (SSC) topology optimization (TO)

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Fast free-surface detection and level-set function definition in SPH solvers

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JOURNAL OF COMPUTATIONAL PHYSICS 2010年第10期229卷 3652-3663页

作者： Marrone, S. Colagrossi, A. Le Touze, D. Graziani, G. INSEAN Rome Italy CNRS Ecole Cent Nantes Fluid Mech Lab Nantes France Univ Roma La Sapienza Dept Mech & Aeronaut Rome Italy

The present paper proposes a novel algorithm to detect the free-surface in particle simulations, both in two and three dimensions Since the proposed algorithms are based on SPH interpolations their implementation does not require complex geometrical procedures Thus the free-surface detection can be easily embedded in SPH solvers, without a significant increase of the CPU time. Throughout this procedure accurate normal vectors to the free-surface are made available Then it is possible to define a level-set function algorithm which is presented in detail. The latter allows in-depth analyses of three-dimensional free-surface simulations by using standard visualization tools, including internal features of the flow. The algorithms proposed for detecting free-surface particles and defining the level-set function are validated on simple and complex two- and three-dimensional flow simulations The usefulness of the proposed procedures to post-process and analyze complex flows are illustrated on realistic examples (C) 2010 Elsevier Inc All rights reserved

关键词： Smoothed particle hydrodynamics Free-surface flows Fluid-structure impact flows level-set function Flow visualization

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Topology Optimization Based on Regularized level-set function for Solving 3-D Nonlinear Magnetic Field System With Spatial Symmetric Condition

Topology Optimization Based on Regularized Level-Set Functio...

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20th International Conference on the Computation of Electromagnetic Fields (Compumag)

关键词： level-set function regularization spatial symmetry condition (SSC) topology optimization (TO)

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A study on topology optimization using the level-set function and BEM

A study on topology optimization using the level-set functio...

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34th International Conference on Boundary Elements and Other Mesh Reduction Methods

作者： Matsumoto, T. Yamada, T. Shichi, S. Takahashi, T. Nagoya Univ Nagoya Aichi 4648601 Japan

ISBN: (纸本)9781845646226

A framework to solve topology optimization problems using a level-set based approach and boundary element method (BEM) is presented. The objective functional is assumed to be defined only on the boundary, thus the problem is suitable for handling with BEM. The boundary of the structure is defined as the isosurface of the level-set function. The distribution of the level-set function is obtained by solving an evolution equation defined in a fixed design domain. The evolution equation has a source term related to the topological sensitivity of the objective functional. The sensitivity can be evaluated from BEM analysis results both for the original physical variable and its adjoint variable. The shape of the structure is defined as the isosurface of the level-set function defined in a fixed design domain, and the boundary mesh is generated by extracting the isosurface. Since the fixed design domain has a simple rectangular solid shape and does not change its domain shape through iteration steps, the evolution equation of the level-set function can be solved by FEM more efficiently than by BEM. The effectiveness of the proposed approach is demonstrated through a minimum compliance topology optimization problem.

关键词： topology optimization level-set function adjoint method boundary element method

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Adjoint-based shape optimization for radiative transfer using level-set function and volume penalization method

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2023年第1期210卷

作者： Liu, Ming Hasegawa, Yosuke Univ Tokyo Inst Ind Sci 4-6-1 KomabaMeguro Ku Tokyo 1538505 Japan

A inverse design of a radiative heat transfer surface is established based on an adjoint analysis com-bined with a level-set function and a volume penalization method. The level-set function is employed to represent an arbitrary complex geometry embedded in a Cartesian grid system, whereas the volume penalization method is applied to simulate a forward radiative transfer problem. Then, the sensitivity of a current shape with respect to a prescribed cost functional is obtained from adjoint analysis, and it is used to update the shape. The entire inverse design procedures including the forward and adjoint anal-yses as well as the shape update based on the adjoint analysis are implemented to an open-source CFD solver, OpenFOAM. Two pure radiation problems from the existing literature are considered for verifying the proposed method. The resultant optimal geometries in both problems show good agreement with the reference data. Finally, the present method is applied to a more complex three-dimensional problem to validate the strength of its applicability to complex geometries.(c) 2023 Elsevier Ltd. All rights reserved.

关键词： Radiative transfer Inverse design Adjoint method level-set function Volume penalization method

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An Approach to Generate level set function from STL File for Fluid-Structure Interaction Computations 6th

An Approach to Generate Level Set Function from STL File for...

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6th International Conference on Geotechnics, Civil Engineering and Structures (CIGOS)

作者： Son Tung Dang Johansen, Stein Tore Akhatov, Iskander SINTEF Ind SP Andersens Veg 15B N-7031 Trondheim Norway NTNU Dept Energy & Proc Engn N-7041 Trondheim Norway Skolkovo Inst Sci & Technol Moscow 121205 Russia Viettel High Technol Ind Corp Da Nang Vietnam

ISBN: (纸本)9789811671609;9789811671593

In this paper, we will present an approach to compute the signed distance or level set function from the Standard Triangle Language (STL) file format. Then the level set is used to represent the surface of a given object inside the computational domain. The continuity and Navier-Stokes equations are solved numerically to study the fluid flows over the solid body. The finite-volume method (FVM) is applied to approximate all terms in the governing equations to conserve mass and momentum. The cut-cell method is employed to avoid recomputing the mesh points when the body moves around. The transport equation for the level set function is solved accordingly to update the position of the object.

关键词： Fluid-structure interaction Computational fluid dynamics level-set function Cut-cell method

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