Hokyung Shim¹, Vinh Thuy Tran Ho^1,,Semyung Wang^1,2, 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 >

S.Y. Wang^1,2, M.Y. Wang³

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 119-148, 2006, DOI:10.3970/cmes.2006.013.119

Abstract In this paper, an implicit free boundary parametrization method is presented as an effective approach for simultaneous shape and topology optimization of structures. The moving free boundary of a structure is embedded as a zero level set of a higher dimensional implicit level set function. The radial basis functions (RBFs) are introduced to parametrize the implicit function with a high level of accuracy and smoothness. The motion of the free boundary is thus governed by a mathematically more convenient ordinary differential equation (ODE). Eigenvalue stability can be guaranteed due to the use of inverse multiquadric RBF splines. To perform both… More >

Zhen Luo¹, Nong Zhang¹, Tao Wu^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.4, pp. 299-328, 2012, DOI:10.3970/cmes.2012.085.299

Abstract This paper presents a meshless Galerkin level-set method (MGLSM) for shape and topology optimization of compliant mechanisms of geometrically nonlinear structures. The design boundary of the mechanism is implicitly described as the zero level set of a Lipschitz continuous level set function of higher dimension. The moving least square (MLS) approximation is used to construct the meshless shape functions with the global Galerkin weak-form in terms of a set of arbitrarily distributed nodes. The MLS shape function is first employed to parameterize the level set function via the surface fitting rather than interpolation, and then used to implement the meshless… More >

Ashraf Balabel

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 599-638, 2012, DOI:10.3970/cmes.2012.083.599

Abstract In the present paper, a new generalized level set numerical method based on the Fast Marching Method is developed for predicting the moving interface thermo-fluid dynamics in turbulent free surface flows. The numerical method is devoted to predict the turbulent interfacial dynamics resulting from either aerodynamic force or thermocapillary effects. The unsteady Reynolds averaged Navier-Stokes equations (RANS) and energy equation are coupled with the level set method and solved separately in each phase using the finite volume method on a non-staggered grid system. The application of the fast marching technique enables the fast as well as the accurate transport of… More >

Zhen Luo^1,2, Nong Zhang^1,3, Yu Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.1, pp. 73-96, 2012, DOI:10.3970/cmes.2012.083.073

Abstract This paper aims to present a physically meaningful level set method for shape and topology optimization of structures. Compared to the conventional level set method which represents the design boundary as the zero level set, in this study the boundary is embedded into non-zero constant level sets of the level set function, to implicitly implement shape fidelity and topology changes in time via the propagation of the discrete level set function. A point-wise nodal density field, non-negative and value-bounded, is used to parameterize the level set function via the compactly supported radial basis functions (CSRBFs) at a uniformly defined set… More >

Binxin Yang¹, Jie Ouyang¹, Tao Jiang¹, Chuntai Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.3, pp. 191-222, 2010, DOI:10.3970/cmes.2010.063.191

Abstract A gas-solid-liquid three-phase model is proposed for fiber reinforced composites mold filling process. The fluid flow is described in Eulerian coordinate while the dynamics of fibers is described in Langrangian coordinate. The interaction of fluid flow and fibers are enclosed in the model. The influence of fluid flow on fibers is described by the resultant forces imposed on fibers and the influence of fibers on fluid flow is described by the momentum exchange source term in the model. A finite volume method coupled with a level set method for viscoelastic-Newtonian fluid flow is used to solve the model. The direct… More >

L. Mai-Cao¹, T. Tran-Cong²

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.3, pp. 157-188, 2008, DOI:10.3970/cmes.2008.031.157

Abstract This paper presents a new meshless numerical approach to solving a special class of moving interface problems known as the passive transport where an ambient flow characterized by its velocity field causes the interfaces to move and deform without any influences back on the flow. In the present approach, the moving interface is captured by the level set method at all time as the zero contour of a smooth function known as the level set function whereas one of the two new meshless schemes, namely the SL-IRBFN based on the semi-Lagrangian method and the Taylor-IRBFN scheme based on Taylor series… More >

S.Y. Wang^1,2, K.M. Lim^2,3, B.C. Khoo^2,3, M.Y. Wang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.3, pp. 219-238, 2007, DOI:10.3970/cmes.2007.021.219

Abstract Hole nucleation is an important issue not yet fully addressed in structural topology optimization using the level set methods. In this paper, a consistent and robust nucleation method is proposed to overcome the inconsistencies in the existing implementations and to allow for smooth hole nucleation in the conventional shape derivatives-based level set methods to avoid getting stuck at a premature local optimum. The extension velocity field is constructed to be consistent with the mutual energy density and favorable for hole nucleation. A negative extension velocity driven nucleation mechanism is established due to the physically meaningful driving force. An extension velocity… More >

S.Y. Wang^1,2, K.M. Lim^2,3, B.C. Khoo^2,3, M.Y. Wang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 1-40, 2007, DOI:10.3970/cmes.2007.021.001

Abstract The level set method is a numerical technique for simulating moving interfaces. In this paper, an unconditionally BIBO (Bounded-Input-Bounded-Output) time-stable consistent meshfree level set method is proposed and applied as a more effective approach to simultaneous shape and topology optimization. In the present level set method, the meshfree infinitely smooth inverse multiquadric Radial Basis Functions (RBFs) are employed to discretize the implicit level set function. A high level of smoothness of the level set function and accuracy of the solution to the Hamilton-Jacobi partial differential equation (PDE) can be achieved. The resulting dynamic system of coupled Ordinary Differential Equations (ODEs)… More >

S.Y. Wang^1,2, K.M. Lim^2,3, B.C. Khoo^2,3, M.Y. Wang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.3, pp. 155-182, 2007, DOI:10.3970/cmes.2007.018.155

Abstract In this paper, a geometric deformation constrained level set method is presented as an effective approach for structural shape and topology optimization. A level set method is used to capture the motion of the free boundary of a structure. Furthermore, the geometric deformation of the free boundary is constrained to preserve the structural connectivity and/or topology during the level set evolution. An image-processing-based structural connectivity and topology preserving approach is proposed. A connected components labeling technique based on the 4-neighborhood connectivity measure and a binary image is used for the present region identification. The corresponding binary image after an exploratory… More >