• Journal of Information Processing Systems
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• v.10 no.1
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• pp.23-35
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• 2014

Recently, novel application areas in digital geometry processing, such as simulation, dynamics, and medical surgery simulations, have necessitated the representation of not only the surface data but also the interior volume data of a given 3D object. In this paper, we present an efficient framework for the shape approximations of spherical solid objects based on trivariate B-splines. To do this, we first constructed a smooth correspondence between a given object and a unit solid cube by computing their harmonic mapping. We set the unit solid cube as a rectilinear parametric domain for trivariate B-splines and utilized the mapping to approximate the given object with B-splines in a coarse-to-fine manner. Specifically, our framework provides user-controllability of shape approximations, based on the control of the boundary condition of the harmonic parameterization and the level of B-spline fitting. Experimental results showed that our method is efficient enough to compute trivariate B-splines for several models, each of whose topology is identical to a solid sphere.

• Journal of Mechanical Science and Technology
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• v.19 no.7
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• pp.1432-1440
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• 2005

High-temperature rupture behavior of 5083-Al alloy was tested for failure at 548K under multiaxial stress conditions: uniaxial tension using smooth bar specimens, biaxial shearing using double shear bar specimens, and triaxial tension using notched bar specimens. Rupture times were compared for uniaxial, biaxial, and triaxial stress conditions with respect to the maximum principal stress, the von Mises effective stress, and the principal facet stress. The results indicate that the von Mises effective and principal facet stresses give good correlation for the material investigated, and these parameters can predict creep life data under the multiaxial stress states with the rupture data obtained from specimens under the uniaxial stress. The results suggest that the creep rupture of this alloy under the testing condition is controlled by cavitation coupled with highly localized deformation process, such as grain boundary sliding. It is also conceivable that strain softening controls the highly localized deformation modes which result in cavitation damage in controlling rupture time of this alloy.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.2
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• pp.78-85
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• 1994

Impact forces are acting on the fore part of a body entering water and those are function o the shape of the fore part and entrance angle. In this paper, impact forces are computed for the flat faced body with arbitrary entrance angle The geometric characteristics of the wetted surface of the body are complicated. The surface is divided into several smooth parts and each of them is represented by a bi-cubic B-spline. The free surface condition, $\phi=0$, is applied at the undisturbed free surface and he boundary value problem is analized by using Green's function.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.2
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• pp.15-21
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• 1994

In the previous researches on mesh curve fairing method, a set of discrete data points in a mesh can be selected as variables. End tangent vectors can not be variables. This restriction makes some problems in preparing the end tangent vectors at the bow or stern parts, because their slopes are not infinites or zeros. In this paper end tangent vectors are included as variables and the more smooth results are obtained. Also two methods of constructing ship hull surface from mesh curves are examined. It is shown that the skinning method is better than non-uniform B-spline fitting method in representing the area near boundary. The generation of a ship surface is given as an example.

• Proceedings of the SAREK Conference
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• 2006.06a
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• pp.1113-1118
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• 2006

A numerical investigation of single phase heat and flow characteristics in circular tubes with a single set of spiral micro fins was performed with varying geometrical parameters like fin height, spiral angle, and number of fins. The properties of $40^{\circ}C$ water was used as a working fluid to simulate a condenser and the RNG $k-{\epsilon}$ turbulence model was adopted. Calculation results were obtained in fully developed turbulent flow with constant surface heat flux boundary condition. Relative terms were introduced to investigate the substitution effect of conventional smooth tubes. The dimensionless terms were the heat transfer enhancement factor, the pressure drop penalty factor, and the efficiency index. Additionally, a numerical optimization was carried out to maximize thermal performance with the concept of the robust design. A statistical analysis showed that fin height interacts with number of fins and spiral angle.

• Journal of the Semiconductor & Display Technology
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• v.8 no.3
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• pp.31-37
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• 2009

This paper presents one and two dimensional simulation results with discontinuous features (shocks) of capacitively coupled rf plasmas. The model consists of the first two and three moments of the Boltzmann equation for the ion and electron fluids respectively, coupled to Poisson's equation for the self-consistent electric field. The local field and drift-diffusion approximations are not employed, and as a result the charged species conservation equations are hyperbolic in nature. Hyperbolic equations may develop discontinuous solutions even if their initial conditions are smooth. Indeed, in this work, secondary electron emission is shown to produce transient electron shock waves. These shocks form at the boundary between the cathodic sheath (CS) and the quasi-neutral (QN) bulk region. In the CS, the electrons emitted from the electrode are accelerated to supersonic velocities due to the large electric field. On the other hand, in the QN the electric field is not significant and electrons have small directed velocities. Therefore, at the transition between these regions, the electron fluid decelerates from a supersonic to a subsonic velocity in the direction of flow and a jump in the electron velocity develops. The presented numerical results are consistent with both experimental observations and kinetic simulations.

• Journal of Korea Foundry Society
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• v.43 no.2
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• pp.55-63
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• 2023

Due to the importance of the surface on the final slab quality, it is essential to maintain a smooth segment roll surface that is in touch with the thin solid shell during solidification. In this paper, the surface of the used continuous casting guide roll was analyzed to realize the mechanism of its surface deterioration. Surface analysis has revealed severe corrosion at two distinct areas leading to deep roughness occurring on the guide roll. Firstly, the severe corrosion follows prior austenite grain boundary due to exposure with acidic environment. Also, in heat affected zone (HAZ) where two cladding beads overlap, more severe corrosion takes place. The overheat input results in local ferritization without full melting which increases retained δ-ferrite content almost 10 times higher than surrounding area. Corrosion was observed to happen at the δ-γ interface where Cr depletion takes place.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.565-586
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• 2023

We study the Dirichlet problem for the degenerate nonlocal parabolic equation u_t - a(||∇u||²_L²(Ω))∆u = C_b ||u||^β_L²(Ω) |u|^q(x,t)-2 u log |u| + f in Q_T, where Q_T := Ω × (0, T), T > 0, Ω ⊂ ℝ^N, N ≥ 2, is a bounded domain with a sufficiently smooth boundary, q(x, t) is a measurable function in Q_T with values in an interval [q^-, q⁺] ⊂ (1, ∞) and the diffusion coefficient a(·) is a continuous function defined on ℝ₊. It is assumed that a(s) → 0 or a(s) → ∞ as s → 0⁺, therefore the equation degenerates or becomes singular as ||∇u(t)||2 → 0. For both cases, we show that under appropriate conditions on a, β, q, f the problem has a global in time strong solution which possesses the following global regularity property: ∆u ∈ L²(Q_T) and a(||∇u||²_L²(Ω))∆u ∈ L²(Q_T ).

• Steel and Composite Structures
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• v.47 no.5
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• pp.569-585
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• 2023

This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.

• Advances in nano research
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• v.17 no.1
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• pp.19-32
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• 2024

Functionally graded-carbon nanotube (FG-CNT) is expected to be a new generation of materials with a wide range of potential applications in technological fields such as aerospace, defense, energy, and structural industries. In this paper, an exact finite strip method for functionally graded-carbon nanotube sandwich plates is developed using first-order shear deformation theory to get the exact natural frequencies of the plates. The face sheets of the plates are made of FG-CNT with continuous and smooth grading based on the power law index. The equations of motion have been generated based on the Hamilton principle. By extracting the exact stiffness matrix for any strip of the sandwich plate as a non-algebraic function of natural frequencies, it is possible to calculate the exact free vibration frequencies. The accuracy and efficiency of the current method is established by comparing its findings to the results of the literature works. Examples are presented to prove the efficiency of the generated method to deal with various problems, such as the influence of the length-to-height ratio, the power law index, and a core-to-face sheet thickness of the single and multi-span sandwich plates with various boundary conditions on the natural frequencies. The exact results obtained from this analysis can check the validity and accuracy of other numerical methods.