• Journal of the Korean Geophysical Society
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• v.8 no.1
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• pp.23-33
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• 2005

The digital surface model (DSM) is used for several purposes in photogrammetry, remote sensing and laser scanned data such as orthoimage production, contours erivation, extraction of height information. Creation of a surface model from point-clouds (3-D sparse points) that can be derived from stereo imagery and range data (e.g. laser scanned data) can be done with several mathematical interpolation models. In this paper, thin-plate-spline (TPS) is used for digital surface modeling. Determination of suitable weight is an important problem in thin-plate function for a surface. The Voronoi algorithm has been proposed as a method for determination of the weight in thin-plate-spline. In this paper, methods has been tested for different surfaces. The results show that thin-plate-spline can be independent of weight.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.321-332
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• 2010

In this paper, we experiment image warping and morphing. In image warping, we use radial basis functions : Thin Plate Spline, Multi-quadratic and Gaussian. Then we obtain the fact that Thin Plate Spline interpolation of the displacement with reverse mapping is the efficient means of image warping. Reflecting the result of image warping, we generate two examples of image morphing.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.4
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• pp.409-416
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• 2015

In many practical applications, we face the problem of reconstruction of an unknown function sampled at some data points. Among infinitely many possible reconstructions, the thin plate spline interpolation is known to be the least oscillatory one in the Beppo-Levi semi norm, when the data points are sampled in $\mathbb{R}^2$. The traditional proofs supporting the argument are quite lengthy and complicated, keeping students and researchers off its understanding. In this article, we introduce a simple and short proof for the optimal reconstruction. Our proof is unique and reguires only elementary mathematical background.

• Structural Engineering and Mechanics
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• v.25 no.5
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• pp.613-629
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• 2007

A finite element method (FEM) of B-spline wavelet on the interval (BSWI) is used in this paper to solve the static and vibration problems of thin plate. Instead of traditional polynomial interpolation, the scaling functions of two-dimensional tensor product BSWI are employed to construct the transverse displacements field. The method combines the accuracy of B-spline functions approximation and various basis functions for structural analysis. Some numerical examples are studied to demonstrate the proposed method and the numerical results presented are in good agreement with the solutions of other methods.

• Steel and Composite Structures
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• v.44 no.5
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• pp.633-649
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• 2022

This paper is first implemented with the bending behavior of three-dimensional functionally graded (3DFG) plates in the framework of level set-based topology optimization (LS-based TO). Besides, due to the suitable properties of the current design domain, the thin-plate spline (TPS) is recognized as a RBF to construct the LS function. The overall mechanical properties of the 3DFG plate are assessed using a power-law distribution scheme via Mori-Tanaka micromechanical material model. The bending response is obtained using the first-order shear deformation theory (FSDT). The mixed interpolation of four elements of tensorial components (MITC4) is also implemented to overcome a well-known shear locking problem when the thickness becomes thinner. The Hamilton-Jacobi method is utilized in each iteration to enforce the necessary boundary conditions. The mathematical formulas are expressed in great detail for the LS-based TO using 3DFG materials. Several numerical examples are exhibited to verify the efficiency and reliability of the current methodology with the previously reported literature. Finally, the influences of FG materials in the optimized design are explained in detail to illustrate the behaviors of optimized structures.

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.893-907
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• 2014

Meshless local collocation method produces much better conditioned matrices than meshless global collocation methods. In this paper, the meshless local collocation method based on thin plate spline radial basis function and first-order shear deformation theory are used to calculate the natural frequencies and mode shapes of laminated composite shells. Through numerical experiments, the accuracy and efficiency of present method are demonstrated.

• 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.

• Journal of Korean Society of Steel Construction
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• v.10 no.3 s.36
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• pp.407-421
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• 1998

The purpose of this paper is to provide and verify an analytical method, based on the spline finite strip method, which can be used to investigate the buckling mode and stress of thin-walled steel sections. Geometric imperfection and initial stress of plates and plate assemblies, which are resulted from various preloadings and may cause prebuckling deformations before buckling, are included in the analysis. Material nonlinearity and residual stress are also considered. It can be applied to sections with simple or non-simple boundary conditions and arbitrary loading. The method has been applied to investigate the buckling behavior of plates and plate assemblies which are subjected to compression with initial imperfections and residual stresses.

• Architectural research
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• v.16 no.2
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• pp.67-74
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• 2014

Free vibration analysis of thin shells is carried out by using isogeometric approach. For this purpose, a thin shell element based on Kirchhoff-Love shell theory is developed. Non-uniform rational B-spline surface (NURBS) definition is introduced to represent the geometry of shell and also used to derive all terms required in the isogeometric element formulation. Gauss integration rule is used for stiffness and mass matrices. The present shell element is then applied to examine vibrational behaviours of thin plate and shell structures. From numerical results, it is found be that reliable natural frequencies and associated mode shapes of thin shell structures can be predicted by the present isogeometric shell element.

• Journal of computational fluids engineering
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• v.13 no.1
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• pp.41-48
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• 2008

The fluid-structure interaction analysis such as a static aeroelastic analysis requires the result of each analysis as an input to the other analysis. Usually the grids for the fluid analysis and the structural analysis are different, so the results should be transformed properly for each other. The Infinite Plate Spline(IPS) and the Thin Plate Spline(TPS) are used in interpolating the displacement and the pressure. In this study, such interpolation methods are compared with kriging which provides a precise response surface. The static aeroelastic analysis is performed for the supersonic flow field with shock waves and the pressure field is interpolated by the TPS and kriging. The TPS shows tendency to weaken the shock strength, whereas kriging preserves the shock strength.