• Steel and Composite Structures
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• v.37 no.6
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• pp.663-678
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• 2020

This paper proposes a novel topology optimization method generating multiple materials for external linear plane crack structures based on the combination of IsoGeometric Analysis (IGA) and eXtended Finite Element Method (X-FEM). A so-called eXtended IsoGeometric Analysis (X-IGA) is derived for a mechanical description of a strong discontinuity state's continuous boundaries through the inherited special properties of X-FEM. In X-IGA, control points and patches play the same role with nodes and sub-domains in the finite element method. While being similar to X-FEM, enrichment functions are added to finite element approximation without any mesh generation. The geometry of structures based on basic functions of Non-Uniform Rational B-Splines (NURBS) provides accurate and reliable results. Moreover, the basis function to define the geometry becomes a systematic p-refinement to control the field approximation order without altering the geometry or its parameterization. The accuracy of analytical solutions of X-IGA for the crack problem, which is superior to a conventional X-FEM, guarantees the reliability of the optimal multi-material retrofitting against external cracks through using topology optimization. Topology optimization is applied to the minimal compliance design of two-dimensional plane linear cracked structures retrofitted by multiple distinct materials to prevent the propagation of the present crack pattern. The alternating active-phase algorithm with optimality criteria-based algorithms is employed to update design variables of element densities. Numerical results under different lengths, positions, and angles of given cracks verify the proposed method's efficiency and feasibility in using X-IGA compared to a conventional X-FEM.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.577-582
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• 2007

A variational formulation for plane elasticity problems is derived based on an isogeometric approach. The isogeometric analysis is an emerging methodology such that the basis functions in analysis domain arc generated directly from NURBS (Non-Uniform Rational B-Splines) geometry. Thus. the solution space can be represented in terms of the same functions to represent the geometry. The coefficients of basis functions or the control variables play the role of degrees-of-freedom. Furthermore, due to h-. p-, and k-refinement schemes, the high order geometric features can be described exactly and easily without tedious re-meshing process. The isogeometric sensitivity analysis method enables us to analyze arbitrarily shaped structures without re-meshing. Also, it provides a precise construction method of finite element model to exactly represent geometry using B-spline base functions in CAD geometric modeling. To obtain precise shape sensitivity, the normal and curvature of boundary should be taken into account in the shape sensitivity expressions. However, in conventional finite element methods, the normal information is inaccurate and the curvature is generally missing due to the use of linear interpolation functions. A continuum-based adjoint sensitivity analysis method using the isogeometric approach is derived for the plane elasticity problems. The conventional shape optimization using the finite element method has some difficulties in the parameterization of boundary. In isogeometric analysis, however, the geometric properties arc already embedded in the B-spline shape functions and control points. The perturbation of control points in isogeometric analysis automatically results in shape changes. Using the conventional finite clement method, the inter-element continuity of the design space is not guaranteed so that the normal vector and curvature arc not accurate enough. On tile other hand, in isogeometric analysis, these values arc continuous over the whole design space so that accurate shape sensitivity can be obtained. Through numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.

• Journal of the Society of Naval Architects of Korea
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• v.43 no.5 s.149
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• pp.550-559
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• 2006

A design procedure for a ship with minimum total resistance was developed using a numerical optimization method called SQP(Sequential Quadratic Programming) and a CFD technique based on the Rankine source panel method with the nonlinear free surface boundary conditions. During the whole optimization process the geometry of the hull shape was represented based on the NURBS(Non-uniform rational B-spline) technique and the modification of the hull shape was controlled using the Bell-shaped distribution function to keep the fairness of the hull shape before and after the hull modification. The numerical analysis was carried out using 4000TEU container ship in the towing tank facility installed in the Pusan national university to know the validity of the developed algorithm for this study. As the results of the numerical analysis it proved that the resistance of the optimized hull is conspicuously reduced in comparison with the original hull in a wave-making resistance point of view.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.4
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• pp.97-103
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• 2001

Accuracy of a machined part is determined by the relative motion between the cutting tool and the workpiece. One of the important factors which affects the relative motion is the geometric errors of a machine tool. In this study, firstly, geometric errors are measured by laser interferometer, and the positioning error of each control point selected uniformly on the control surface CAD model can be estimated from th oirm shaping model and geometric error data base. Where a form shaping function is derived from the link of homogeneous transformation matrix. Secondly, control points are shifted to the estimated amount of positioning errors. A new control surface is modeled with NURBS(Non Uniform Rational B-Spline) surface approximation to the shifted control points. By generating tool paths to the redesigned control surface, we reduce the machining error quite.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.3
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• pp.548-558
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• 2009

This paper attempts to develop an algorithm which optimizes the electric field through the so-called NURB(Non-Uniform Rational B-spline) curve in order to improve the insulation capacity. In particular, the NURB curve is a kind of interpolation curve that can be expressed by a few variables. The electric field of a conductor is computed by Charge Simulation Method(CSM) while that of a spacer by Surface Charge Method(SCM); this mixed calculation method is adopted for the electric field optimization. For calculation of the initial and optimal shapes, the Gauss-Newton method, which is quite easy to formulate and has slightly faster convergence rate than other optimization techniques, was used. The tangential electric field, the total electric field, and the product of the tangential electric field and area (Area Effect) were chosen as the optimization objective function by the average value of electric field for the determined initial shape.

• Journal of the Korean Society for Precision Engineering
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• v.29 no.6
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• pp.640-647
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• 2012

Current electronic products are dominated by the laser processing and the application will be extended this time. Especially, demands for high precision laser processing with a large area has been increasing for a number of applications such as in solar cell battery, display parts, electronic component and automobile industry. In this paper we designed an on-the-fly system for ultrafast/high precision/large area laser processing. In addition, we have developed the path algorithm for large area. Expansion of the area in which laser processing is an important factor to handle the ultrafast/wide area processing, it will require a processing path. Processing path is path of 2- axis stage and stage of change in velocity can be smooth as possible. We proposed a path of the user concept using NURBS(Non-Uniform Rational B-Spline)method. Through our experiment with the chopper, was to prove the continuity of edge parts. Through basic shape experiments, we proved that large area can be processed using laser. We developed a simulation tool using Visual C++.

• Journal of KIISE:Software and Applications
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• v.33 no.10
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• pp.868-876
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• 2006

2D input data have to be converted into 3D data by means of some functions and menu system in 2D input modeling system. But data in 3D input system for virtual spatial design can be directly connected to the 3D modeling data. Nevertheless, efficient surface modeling and deformation algorithm for the 3D input modeling system are not proposed yet. In this paper, problems of conventional NURBS surface deformation methods which can occur when applied in the 3D input modeling system are introduced. And NURBS surface deformation by 3D target curves, in which the designer can easily approach, are suggested. Designer can efficiently implement the virtual spatial sketching and design by using the proposed deformation algorithm.

• Journal of the Society of Naval Architects of Korea
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• v.36 no.2
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• pp.121-134
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• 1999

In this paper, a ship calculation program is developed, which prof[nuts hydrostatics and volume calculation intact and damage stability and hull variation. Hull form and compartment geometry are expressed with NURBS curve wire-frame model. Hydrostatics and volume calculation are performed directly with the intersection method between section geometry and 3D planar surface. Equilibrium ship position is calculated with hydrostatic equilibrium equation which is linearized by 1st order Taylor series expansion sequentially. The developed program shows more accurate results and easy uses than the latter.

• Journal of Ocean Engineering and Technology
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• v.20 no.3 s.70
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• pp.82-87
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• 2006

An approach to model a high-speed monohull vessel is introduced. The high-speed monohull form belonging to the category of multihull is drawing new attention, due to the rapidly growing trend of fast passenger ships and military purpose. Multihull forms are much thinner in their overall shape, compared to those of the conventional commercial vessels. Moreover, the parent hull forms are not readily obtainable when a new design is intended, which makes it hard to perform various technical calculations in terms of hull optimization, hydrodynamic computation, structural design, and so forth. In this paper, a parametric technique is used to design a high-speed hull form. To model a hull form, NURBS (Non Uniform Rational B-Spline) representation is used. The goal of research is to provide a fast and convenient tool to design an initial hull form with fewer parameters available in the early design stage. The technique employed in this paper will be applied to the design of multihull forms, such as catamaran, trimaran, and semi-swath.

• Journal of Ocean Engineering and Technology
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• v.22 no.2
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• pp.78-84
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• 2008

As a preliminary step to build a complete superyacht hull design program, the development of superyacht profile design system is introduced. The two-dimensional hull profile is decomposed into four local zones depending upon the functionality and connecting continuity of the profile. Characteristics of each zone are investigated and used to generate the model describing the geometric shape of zone using freeform curves. A set of design parameters is derived from the established geometric model. Generation and modification of a model are is by manipulating the chosen parameters. Four zones designed are integrated to form a final profile. An interactive design system performing all the modeling and modification processes is implemented using the graphic user interface system based an Microsoft Foundation Class and OpenCASCADE, a open graphic library. The shapes of the profiles generated by the developed design system are verified with those of built superyachts. The developed design system will be used for the construction of three-dimensional superyacht hull modeling system.