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Evolutionary topology optimization of continuum structures with smooth boundary representation

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2018年第6期57卷 2143-2159页

作者： Da, Daicong Xia, Liang Li, Guangyao Huang, Xiaodong Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha Hunan Peoples R China Collaborat Innovat Ctr Intelligent New Energy Veh Shanghai 200092 Peoples R China Huazhong Univ Sci & Technol State Key Lab Digital Mfg Equipment & Technol Wuhan Hubei Peoples R China Swinburne Univ Technol Fac Sci Engn & Technol Melbourne Vic 3122 Australia

This paper develops an extended bi-directional evolutionary structural optimization (BESO) method for topology optimization of continuum structures with smoothed boundary representation. In contrast to conventional zigzag BESO designs and removal/addition of elements, the newly proposed evolutionary topology optimization (ETO) method, determines implicitly the smooth structural topology by a level-set function (LSF) constructed by nodal sensitivity numbers. The projection relationship between the design model and the finite element analysis (FEA) model is established. The analysis of the design model is replaced by the FEA model with various elemental volume fractions, which are determined by the auxiliary LSF. The introduction of sensitivity LSF results in intermediate volume elements along the solid-void interface of the FEA model, thus contributing to the better convergence of the optimized topology for the design model. The effectiveness and robustness of the proposed method are verified by a series of 2D and 3D topology optimization design problems including compliance minimization and natural frequency maximization. It has been shown that the developed ETO method is capable of generating a clear and smooth boundary representation;meanwhile the resultant designs are less dependent on the initial guess design and the finite element mesh resolution.

关键词： Topology optimization Evolutionary topology optimization (ETO) level-set function Smooth boundary representation

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Integral vorticity transport method on an overset grid

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2012年第3期69卷 567-589页

作者： Renjitham, S. Marshall, J. S. Univ Vermont Sch Engn Burlington VT 05405 USA

We present an overset grid method for solution of the integro-differential vorticityvelocity formulation of the NavierStokes equations for two-dimensional, incompressible flow. The method uses a body-fitted inner grid, on which vorticity is evolved semi-implicitly, and a Cartesian outer grid with explicit vorticity evolution. The BiotSavart integral is solved using an adaptive, optimized multipole acceleration method. The BiotSavart integration is performed over all inner grid cells, over all active cells of the outer grid that lie entirely outside of the inner grid, and over sub-elements of a set of overhanging cells of the outer grid that overlap part of the inner grid. A novel method is developed using a level-set distance function to rapidly and easily partition the overhanging grid cells, which is essential for the BiotSavart integration in order to avoid double-counting vorticity in the overhanging region. A similar decomposition into outer, inner and overhanging cells is used in solving for pressure using a boundary-element formulation, which requires evaluation of an integral over the vorticity field using a method similar to that used for the BiotSavart integral. The new overset grid method is applied to flow past stationary and moving bodies in two dimensions and found to agree well with prior experimental and numerical results. Copyright (C) 2011 John Wiley & Sons, Ltd.

关键词： vorticity transport overset grids level-set function

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Numerical scheme solving the temperature of the interface between gas and heterogeneous solid with phase change

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2022年第4期123卷 1036-1056页

作者： Cang, Yu Hu, Yue Wang, Lipo Shen, Yongxing Shanghai Jiao Tong Univ UM SJTU Joint Inst Room 524Longbin BldgMinhang Campus Shanghai Peoples R China

To solve the temperature at the fluid-solid interface in conjugate heat transfer simulations, a partitioned yet non-iterative scheme with desirable accuracy has been developed. It takes into account the involved complex effects, for example, heterogeneous solid structure, moving interface, and phase change. The fluid and solid phases are discretized by standard Cartesian and unstructured tetrahedron meshes, respectively. At each time step the moving fluid-solid interface is tracked with the level-set function. The non-iterative solution is achieved by formulating a linear system formed from the discretized interface elements, each of which, either triangular or quadrilateral, is assigned with a respective control volume constructed from adjacent grid points in both fluid and solid phases. The temperature gradient operator is treated by the node-based Green-Gauss formula for better robustness if the interface geometry (or mesh) is highly skewed. Numerical results demonstrate the second-order accuracy with satisfactory robustness even on highly skewed interfaces.

关键词： conjugate heat transfer fluid-solid interface heterogeneous solid level-set function phase change

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Efficient level-set segmentation model driven by the local GMM and split Bregman method

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IET IMAGE PROCESSING 2019年第5期13卷 761-770页

作者： Wang, Dengwei Univ Elect Sci & Technol China Sch Aeronaut & Astronaut 2006 Xiyuan Ave Chengdu 611731 Sichuan Peoples R China

An efficient level-set model driven by the local Gaussian mixture model (GMM) and split Bregman method is proposed for image segmentation. Firstly, the two intensity fitting functions in the original local binary fitting (LBF) model are pre-estimated by using a local GMM-based intensity distribution estimator before curve evolution. The benefit of this pre-computation strategy is to avoid updating the fitting functions at each step of the curve evolution, and it also overcomes the initialisation problem of common gradient descent-based active contour models, i.e. the level-set function can be initialised as an arbitrary random matrix instead of a signed distance function in the proposed processing framework. Secondly, two processing ideas named global convex segmentation (GCS) method and split Bregman are introduced into the numerical implementation, where the role of GCS is to transform the proposed model into a simplified convex segmentation model, and the purpose of the split Bregman is to quickly output a convergent solution of the newly derived convex segmentation model in an alternate iterative format. Experimental results for synthetic and real images of different modalities with inhomogeneity or homogeneity validate the desired performances of the proposed method in terms of accuracy, robustness, and rapidity.

关键词： gradient methods iterative methods image segmentation Gaussian processes medical image processing original local binary fitting model local GMM-based intensity distribution estimator curve evolution pre-computation strategy common gradient descent-based active contour models level-set function signed distance function global convex segmentation method split Bregman modified LBF model simplified convex segmentation model global convex optimisation newly derived convex segmentation model level-set model shows excellent processing performance segmentation applications efficient level-set segmentation model efficient level-set model local Gaussian mixture model image segmentation intensity fitting functions

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A constitutive level-set model for ferromagnetic shape-memory alloys

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CONTINUUM MECHANICS AND THERMODYNAMICS 2020年第6期32卷 1763-1778页

作者： Arvanitakis, Antonios I. Univ Ioannina Dept Mat Sci & Engn Lab Math Modeling & Sci Comp GR-45110 Ioannina Greece

This work proposes a phenomenological level-set model for ferromagnetic shape-memory alloys (FSMAs), developed under consistent thermodynamic analysis. A set of adequate internal and external variables is chosen so as to describe the rate-independent magneto-mechanical response of a FSMA single crystal. Almost every phenomenological model in bibliography adopts martensitic volume fractions as internal variables. The novelty of this work is the introduction of a continuous level-set function as an internal variable of state, which accounts implicitly for the dissipative twin boundary motion in the evolution of inelastic reorientation of martensitic variants. Following the usual internal variable formalism within the framework of standard magnetomechanics, the evolution equations for the level-set function are derived for the forward and reverse variant reorientation processes. The model is implemented in a two-dimensional special case, where the reduced equations are numerically solved capturing the important effects of stress-induced and magnetic field-induced martensitic variant reorientation, such as magnetization hysteresis, pseudoelastic/partial pseudoelastic behavior and magnetic shape-memory effect. The proposed constitutive model is capable of explaining the constitutive response caused by the reorientation of martensitic variants in FSMAs and may be further improved so as to be implemented in even more complicated situations, such as dynamic and rate-dependent analysis.

关键词： Constitutive model Magnetic shape-memory alloys level-set function Twin boundary motion Magnetic shape-memory effect Magnetization hysteresis Pseudoelasticity

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Adjoint-based shape optimization for compressible flow based on volume penalization method

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ENGINEERING WITH COMPUTERS 2024年第2期41卷 989-1010页

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

Reducing the resistance of compressible flow around a blunt body is of great interest in engineering applications, while an efficient shape optimization method for compressible flows remains far from well established, especially for high Mach numbers. To this end, a volume penalization method for simulating compressible flows past a no-slip and isothermal solid is established by introducing an artificial body force and a heat sink into the governing equations. The level-set functions are introduced as design variables, and the cost functional is defined as the total drag acting on the solid. Then, a continuous adjoint-based shape optimization algorithm for drag reduction is developed by deriving the adjoint equations, the adjoint boundary conditions, and the shape update formula. Both the forward and adjoint simulations are verified by existing studies. The results show that the relative deviations of the drag coefficients obtained in the present study from those reported in the reference studies are around 5% at most, and also a comparable drag reduction rate and also optimal shapes can be reproduced by the present optimization scheme for benchmark problems at relatively low Mach numbers considered in previous studies. Finally, the present method is applied to shape optimization of an initially two-dimensional cylinder and also a three-dimensional sphere in the transonic regime of Ma infinity = 1.2. The drag reduction of over 20% is achieved for both two-dimensional and three-dimensional cases.

关键词： Compressible flow Adjoint method Volume penalization method level-set function

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Microstructure optimization of porous mixed ionic and electronic conducting cathode for solid oxide fuel cells

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JOURNAL OF POWER SOURCES 2020年 478卷 228771-228771页

作者： He, An Onishi, Junya Gong, Jiaming Shikazono, Naoki Univ Tokyo Inst Ind Sci Meguro Ku 4-6-1 Komaba Tokyo 1538505 Japan

In the present study, a numerical method is proposed to optimize the porous mixed ionic and electronic conducting (MIEC) cathode microstructure of the solid oxide fuel cell (SOFC). During the optimization, the local nonuniform three-dimensional distributions of solid and pore phases are deformed so that the total amount of reaction current is maximized. Computational results show that the total reaction current in the optimal La0.6Sr0.4Co0.2Fe0.8O3 (LSCF) cathode microstructure increased by 40% compared with that of the original real structure reconstructed from the focused ion beam scanning electronic microscope (FIB-SEM). Different initial structures are applied for the optimization, where the difference in the optimized total reaction currents between different initial microstructures are less than 4%. Universal optimal geometric features are extracted from these optimizations, i.e. the microstructures are composed of small particles, and the solid volume fraction reduces monotonically from the electrolyte along the thickness direction. Then, the influence of the grid size on the optimization is analyzed. Finally, the influence of the bulk ionic conductivity on the optimization is investigated. For the cathode with higher bulk ionic conductivity, the reactive thickness is thinner and the solid volume fraction is smaller, which results in more pronounced performance improvement.

关键词： Solid oxide fuel cell Numerical optimization Porous microstructure Cathode level-set function

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Unification of parametric and implicit methods for shape sensitivity analysis and optimization with fixed mesh

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2017年第3期109卷 326-344页

作者： Zhang, Weihong Huang, Qiangqiang Northwestern Polytech Univ Sch Mech Engn ESAC Xian 710072 Shaanxi Peoples R China

Parametric and implicit methods are traditionally thought to be two irrelevant approaches in structural shape optimization. Parametric method works as a Lagrangian approach and often uses the parametric boundary representation (B-rep) of curves/surfaces, for example, Bezier and B-splines in combination with the conformal mesh of a finite element model, while implicit method relies upon level-set functions, that is, implicit functions for B-rep, and works as an Eulerian approach in combination with the fixed mesh within the scope of extended finite element method or finite cell method. The original contribution of this work is the unification of both methods. First, a new shape optimization method is proposed by combining the features of the parametric and implicit B-reps. Shape changes of the structural boundary are governed by parametric B-rep on the fixed mesh to maintain the merit in computer-aided design modeling and avoid laborious remeshing. Second, analytical shape design sensitivity is formulated for the parametric B-rep in the framework of fixed mesh of finite cell method by means of the Hamilton-Jacobi equation. Numerical examples are solved to illustrate the unified methodology. Copyright (C) 2016 John Wiley & Sons, Ltd.

关键词： shape optimization implicit and parametric method fixed mesh level-set function

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Numerical simulation of multiphase flows of CO₂ storage in saline aquifers in Daqingzijing oilfield, China

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CLEAN TECHNOLOGIES AND ENVIRONMENTAL POLICY 2012年第4期14卷 609-618页

作者： Yang, Duo X. Zeng, Rong S. Zhang, Y. Wang, Zhong Q. Wang, S. Jin, C. Chinese Earthquake Adm Inst Crustal Dynam Beijing 100085 Peoples R China Res Inst Innovat Technol Earth Kyoto 6190292 Japan Chinese Acad Sci Inst Geol & Geophys Beijing 100029 Peoples R China State Intellectual Property Off Beijing 100088 Peoples R China

In this article, according to in situ geological and geophysical data archived of Daqingzijing oilfield, a 3D multiphase flow model based on hydrodynamic trapping mechanism is set up, with the phase interface mechanism considered. A high-order CE/SE (space-time conservation element and solution element) method coupled with (HPLS) Hybrid level-set method is updated to simulate migration and build-up of CO2 in saline aquifers for short-term time scales. Results revealed that both the lateral variation of stratigraphic thickness and the heterogeneity of permeability control migration and accumulation of CO2 plume. After 20 years of injection, CO2 front propagates 8-9 km away from injection wells. The saline aquifer formation with high permeability is the dominant channel for CO2 migration. The present work provides a novel approach for simulation of hydrodynamic trapping mechanism for CO2 geological storage in saline aquifers of Songliao Basin of China, which could be a suitable location for a CO2 storage demonstration project.

关键词： CO2 storage Multiphase flow CE/SE method Heterogeneity Saline aquifer level-set function

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Precise generation of complex statistical Representative Volume Elements (RVEs) in a finite element context

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COMPUTATIONAL MATERIALS SCIENCE 2012年 61卷 224-238页

作者： Hitti, K. Laure, P. Coupez, T. Silva, L. Bernacki, M. CNRS MINES ParisTech Ctr Mat Forming CEMEF UMR 7635 F-06904 Sophia Antipolis France Univ Nice Sophia Antipolis CNRS Lab JA Dieudonne UMR 6621 F-06108 Nice 02 France

A precise procedure to generate complex 2D and 3D statistical virtual microstructures in a finite element (FE) context is described. This technique, based on Laguerre tessellations and advancing front method, level-set description of interfaces and anisotropic meshing adaptation, is detailed for equiaxial polycrystal and powder RVEs defined by a size distribution law. The capability of the procedure to respect statistical data could be insured by the advancing front method coupled with an optimization procedure depending on the nature of the considered RVE. Moreover, by applying a graph coloration technique, the number of level-set functions used to represent the cells and also in anisotropic mesh adaptation is greatly reduced. (c) 2012 Elsevier B.V. All rights reserved.

关键词： Laguerre-Voronoi Tessellation Advancing front method level-set function Polycrystal RVE Powder RVE Anisotropic meshing adaptation

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