• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.257-270
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• 2014

In this article, we consider a homogeneous function of degree four in quaternionic vector spaces and $S^{4n+3}$ which is invariant under $S^3$ and U(n + 1)-action. We show it is an isoparametric function providing isoparametric hypersurfaces in $S^{4n+3}$ with g = 4 distinct principal curvatures and isoparametric hypersurfaces in quaternionic projective spaces with g = 5. This extends study of Nomizu on isoparametric function on complex vector spaces and complex projective spaces.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.619-623
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• 2002

In this paper, we study transnormal systems on the Euclidean and semi-Euclidean spaces. We classified transnormal systems on Rf" . We also prove that transnormal systems on R$\^$n/$\sub$p/ are algebraic even though there are non-algebraic isoparametric hypersurfaces.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.12
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• pp.1973-1983
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• 1997

Higher order isoparametric elements are usually used in the finite element analysis because they can represent easily the geometric shape of a complex structure ad can improve the solution quality. When these elements are used, the position of internal nodes affects greatly on the solution accuracy. Decreasing of the accuracy related to the position of internal nodes is due to non-conformal mapping often results in an unstable Jacobian value. This paper, in order to remove this difficulty, suggests a modified shape function which can establish conformal mapping between two coordinate systems. Numerical experiments with the proposed shape function show that a stable solution can be obtained without respect to the position of internal nodes, and offer convenience that one can take arbitrarily the position of internal nodes considering only the geometric shape of element boundaries.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.1-15
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• 2021

In the recent papers, S'anchez-Reyes [Appl. Math. Model. 40 (2016), 1676-1682] described the method for finding a minimal surface through a geodesic, and Li et al. [Appl. Math. Model. 37 (2013), 6415-6424] studied the approximation of minimal surfaces with a geodesic from Dirichlet function. In the present article, we consider an isoparametric surface generated by Frenet frame of a curve introduced by Wang et al. [Comput. Aided Des. 36 (2004), 447-459], and give the necessary and sufficient condition to satisfy both geodesic of the curve and minimality of the surface. From this, we construct minimal surfaces in terms of constant curvature and torsion of the curve. As a result, we present a new approach for constructions of the minimal surfaces from a prescribed closed geodesic and unclosed geodesic, and show some new examples of minimal surfaces with a circle and a helix as a geodesic. Our approach can be used in design of minimal surfaces from geodesics.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.5
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• pp.413-420
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• 2012

In this study, the Kernel integration scheme for 2D linear elastic direct boundary element method has been discussed on the basis of subparametric element. Usually, the isoparametric based boundary element uses same polynomial order in the both basis function and mapping function. On the other hand, the order of mapping function is lower than the order of basis function to define displacement field when the subparametric concept is used. While the logarithmic numerical integration is generally used to calculate Kernel integration as well as Cauchy principal value approach, new formulation has been derived to improve the accuracy of numerical solution by algebraic modification. The subparametric based direct boundary element has been applied to 2D elliptical partial differential equation, especially for plane stress/strain problems, to demonstrate whether the proposed algebraic expression for integration of singular Kernel function is robust and accurate. The problems including cantilever beam and square plate with a cutout have been tested since those are typical examples of simple connected and multi connected region cases. It is noted that the number of DOFs has been drastically reduced to keep same degree of accuracy in comparison with the conventional isoparametric based BEM. It is expected that the subparametric based BEM associated with singular Kernel function integration scheme may be extended to not only subparametric high order boundary element but also subparametric high order dual boundary element.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.3A
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• pp.439-445
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• 2006

Analysis problems of tunnels whose geometrical dimensions are very small compared with surrounding media can be treated as infinite region problems. In such cases, even if finite element models can be applied, excessive number of elements is required to obtain satisfactory accuracy. However, inaccurate results may be produced due to assumed artificial boundary conditions. To solve these problems, a hybrid model, which models the region of interest with finite elements and the surrounding infinite media with infinite elements, is introduced for the analysis of infinite region. Three-dimensional isoparametric infinite elements with various decay characteristics are formulated in this paper and the corresponding parameters are presented by means of parametric studies. Three-dimensional tunnel analysis performed on a representative example verifies the applicability of hybrid model using infinite elements.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.109-112
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• 1997

In this paper, we study on a classification of hypersurfaces given by tansnormal functions on $R^{n+1}_1$. If M is a level set of a transnormal function on $R^{n+1}_1$, then it is one of a hyperplane, a cylinder around k-plane, a pseudo-sphere and a pseudo-hyperbolic space.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.19-26
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• 1998

The isoparametric spline finite strip method for degenerated shells is presented. In the formulation, both the geometry and the displacement field are represented by uniform cubic B-spline curves. Spline shell strip is degenerated stress-resultant shell with 6 dof at each node;and the penalty function method is used to incorporated the six dof,

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.5
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• pp.1069-1078
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• 1990

It is shown that the performance of finite element based on energy orthogonal functions may be superior to conventional formulation for plane stress problem. Using this finite element, it is then attempted to show the distribution of stress concentration effect for subsurface under loading point. It turned out that the stress concentration effect for subsurface is not dependent on the width of the member but the loading area. And then it is shown that the solution attained by taking the stress function as a Fourier series is not satisfactory in y<0.1B.

• Journal of Korean Society of Steel Construction
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• v.16 no.6 s.73
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• pp.819-832
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• 2004

This study describes an efficient and facile method for configuration optimum design of structures. One of the ways to achieve numerical shape representation and the selection of design variables is using the design element concept. Using this technique, the number of design variables could be drastically reduced. Isoparametric mapping was utilized to automatically generate the finite element mesh during the optimization process, and this made it possible to easily calculate the derivatives of the coordinates of generated finite element nodes w.r.t. the design variables. For the structural analysis, finite element analysis was adopted in the optimization procedure, and two different techniques(the deterministic method, a modified method of feasible direction; and the stochastic method, a genetic algorithms) were applied to obtain the minimum volumes and section areas for an efficient configuration optimization procedure. Futhermore, spline interpolation was introduced to present a realistic optimum configuration that meet the manufacturing requirements. According to the results of several numerical examples(steel structures), the two techniques suggested in this study simplified the process of configuration optimum design of structures, and yielded improved objective function values with a robust convergence rate. This study's applicability and capability have therefore been demonstrated.