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  • Open Access


    Topology Optimization for Steady-State Navier-Stokes Flow Based on Parameterized Level Set Based Method

    Peng Wei1, Zirun Jiang1, Weipeng Xu1, Zhenyu Liu2, Yongbo Deng2,3, Minqiang Pan4,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 593-619, 2023, DOI:10.32604/cmes.2023.023978

    Abstract In this paper, we consider solving the topology optimization for steady-state incompressible Navier-Stokes problems via a new topology optimization method called parameterized level set method, which can maintain a relatively smooth level set function with a local optimality condition. The objective of topology optimization is to find an optimal configuration of the fluid and solid materials that minimizes power dissipation under a prescribed fluid volume fraction constraint. An artificial friction force is added to the Navier-Stokes equations to apply the no-slip boundary condition. Although a great deal of work has been carried out for topology optimization of fluid flow in… More >

  • Open Access


    Functionally Graded Cellular Structure Design Using the Subdomain Level Set Method with Local Volume Constraints

    Lianxiong Chen1, Hui Liu1,*, Xihua Chu1,2, Jiao Wang3

    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 1197-1218, 2021, DOI:10.32604/cmes.2021.016894

    Abstract Functional graded cellular structure (FGCS) usually shows superior mechanical behavior with low density and high stiffness. With the development of additive manufacturing, functional graded cellular structure gains its popularity in industries. In this paper, a novel approach for designing functionally graded cellular structure is proposed based on a subdomain parameterized level set method (PLSM) under local volume constraints (LVC). In this method, a subdomain level set function is defined, parameterized and updated on each subdomain independently making the proposed approach much faster and more cost-effective. Additionally, the microstructures on arbitrary two adjacent subdomains can be connected perfectly without any additional… More >

  • Open Access


    A Parameter-Free Approach to Determine the Lagrange Multiplier in the Level Set Method by Using the BESO

    Zihao Zong, Tielin Shi, Qi Xia*

    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.1, pp. 283-295, 2021, DOI:10.32604/cmes.2021.015975

    Abstract 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.… More >

  • Open Access


    Topology and Shape Optimization of 2-D and 3-D Micro-Architectured Thermoelastic Metamaterials Using a Parametric Level Set Method

    Ellie Vineyard1, Xin-Lin Gao2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.3, pp. 819-854, 2021, DOI:10.32604/cmes.2021.015688

    Abstract 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. The -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… More >

  • Open Access


    Numerical Simulation of Multi-Layer Penetration Process of Binder Droplet in 3DP Technique

    Xiangyu Gao, Weidong Yang*, Hongxuan Xian, Xiyuan Tu, Yuanyuang Wang*

    CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.1, pp. 227-241, 2020, DOI:10.32604/cmes.2020.09923

    Abstract This paper studies the binder droplet injection process in the 3DP technique. The mathematical model of the binder penetration process for multi-nozzle and multi-layer in 3DP technique is established, by using the conservation Level set method. According to the two-dimensional plane model of three-dimensional spatial structure of sand bed, the construction method of an equivalent cylindrical mapping infiltration model is proposed to represent the porosity of the model in the two-dimensional plane, which is exactly the same as that in the three-dimensional space, as well as closer to the arrangement of the three-dimensional space, and to realize the differentiation between… More >

  • Open Access


    Multiscale Isogeometric Topology Optimization with Unified Structural Skeleton

    Chen Yu1, Qifu Wang1, ∗, Chao Mei1, Zhaohui Xia1

    CMES-Computer Modeling in Engineering & Sciences, Vol.122, No.3, pp. 779-803, 2020, DOI:10.32604/cmes.2020.09363

    Abstract This paper proposes a multiscale isogeometric topology optimization (ITO) method where the configuration and layout of microstructures are optimized simultaneously. At micro scale, a shape deformation method is presented to transform a prototype microstructure (PM) for obtaining a series of graded microstructures (GMs), where microstructural skeleton based on the level set framework is applied to retain more topology features and improve the connectability. For the macro scale calculation, the effective mechanical properties can be estimated by means of the numerical homogenization method. By adopting identical non-uniform rational basis splines (NURBS) as basis functions for both parameterized level set model and… More >

  • Open Access


    Structural Topology Optimization Based on the Level Set Method Using COMSOL

    Shaohua Zhang1,2, Pei Li1, Yongteng Zhong1, Jiawei Xiang1,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.1, pp. 17-31, 2014, DOI:10.3970/cmes.2014.101.017

    Abstract In order to obtain smooth boundary and improve computational efficiency, a new topology optimization scheme based on the level set method is presented. Using the level set function as design variable and the volume ratio of the solid material as volume constraint, respectively, this scheme can easily implement compliance minimization structure topology optimization in associated with the reaction-diffusion equation in commercial software COMSOL. Compared with the results of solid isotropic material with penalization (SIMP) and traditional level set method, this scheme obtained a smooth geometry boundary. In the present computational scheme, the computational cost could be enormously saved without solving… More >

  • Open Access


    Numerical Modelling of Liquid Jet Breakup by Different Liquid Jet/Air Flow Orientations Using the Level Set Method

    Ashraf Balabel1

    CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.4, pp. 283-302, 2013, DOI:10.3970/cmes.2013.095.283

    Abstract This paper presents the numerical results obtained from the numerical simulation of turbulent liquid jet atomization due to three distinctly different types of liquid jets/air orientations; namely, coflow jet, coaxial jet and the combined coflow-coaxial jet. The applied numerical method, developed by the present authors, is based on the solution of the Reynolds-Averaged Navier Stokes (RANS) equations for time-dependent, axisymmetric and incompressible two-phase flow in both phases separately and on regular and structured cell-centered collocated grids using the control volume approach. The transition from one phase to another is performed through a consistent balance of the interfacial dynamic and kinematic… More >

  • Open Access


    Numerical Modelling of Turbulence Effects on Droplet Collision Dynamics using the Level Set Method

    Ashraf Balabel1,

    CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.4, pp. 283-301, 2012, DOI:10.3970/cmes.2012.089.283

    Abstract This paper presents a novel numerical method for solving the twophase flow problems with moving interfaces in either laminar or turbulent flow regimes. The developed numerical method is based on the solution of the Reynolds- Averaged Navier Stokes equations in both phases separately with appropriate boundary conditions located at the interface separating the two fluids. The solution algorithm is performed on a regular and structured two-dimensional computational grid using the control volume approach. The complex shapes as well as the geometrical quantities of the interface are determined via the level set method. The numerical method is firstly validated against the… More >

  • Open Access


    Topological Shape Optimization of Electromagnetic Problems using Level Set Method and Radial Basis Function

    Hokyung Shim1, Vinh Thuy Tran Ho1,,Semyung Wang1,2, Daniel A. Tortorelli3

    CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.2, pp. 175-202, 2008, DOI:10.3970/cmes.2008.037.175

    Abstract This paper presents a topological shape optimization technique for electromagnetic problems using a level set method and radial basis functions. The proposed technique is a level set (LS) based optimization dealing with geometrical shape derivatives and topological design. The shape derivative is computed by an adjoint variable method to avoid numerous sensitivity evaluations. A level set model embedded into the scalar function of higher dimensions is propagated to represent the design boundary of a domain. The level set function interpolated into a fixed initial domain is evolved by using the Hamilton-Jacobi equation. The moving free boundaries (dynamic interfaces) represented in… More >

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