• Journal of computational fluids engineering
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• v.21 no.2
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• pp.1-11
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• 2016

Considerable efforts are required to develop a monotone, robust and stable high-order numerical scheme for solving the hyperbolic system. The discontinuous Galerkin(DG) method is a natural choice, but elimination of the spurious oscillations from the high-order solutions demands a new development of proper limiters for the DG method. There are several available limiters for controlling or removing unphysical oscillations from the high-order approximate solution; however, very few studies were directed to analyze the exact role of the limiters in the hyperbolic systems. In this study, the performance of the several well-known limiters is examined by comparing the high-order($p^1$, $p^2$, and $p^3$) approximate solutions with the exact solutions. It is shown that the accuracy of the limiter is in general problem-dependent, although the Hermite WENO limiter and maximum principle limiter perform better than the TVD and generalized moment limiters for most of the test cases. It is also shown that application of the troubled cell indicators may improve the accuracy of the limiters under some specific conditions.

• Steel and Composite Structures
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• v.26 no.6
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• pp.663-672
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• 2018

This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.63-69
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• 2022

This article is the result of calculating the convolution of Ramanujan's sum and natural number multiplied. Among these results, special values are expressed by Euler and Bernoulli functions.

• Journal of the Korean Recycled Construction Resources Institute
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• v.11 no.4
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• pp.467-475
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• 2023

To ensure the safety of the pipeline against large deformation of the pipeline during lowering construction, the analysis for pipeline becomes emphasized. The FE analysis has a lower efficiency at calculating time, while it could be obtained high accuracy. In this paper, a reasonable analytical model for analysis of pipeline is proposed during lowering-in. This analytical model is partitioned considering the geometrical characteristics and modeled as two parameters Beam On Elastic Foundation and Euler-Bernoulli beam considering the boundary condition. This takes into account the pipeline-soil interaction and the axial forces acting on the pipeline. Previous model can only be applied to standardized conditions, whereas the proposed model defined as Segmented Pipeline Model can be considered for the majority of construction conditions occurred during lowering-in. In addition, minimized assumptions and segmented elements lead to improve the convenience and applicability of modeling. Nevertheless, the model shows accurate results compared to the FE model. Accordingly, it is expected that it will be used efficiently for configuration management as well as safety assessment of pipeline during lowering-in.

• 한국전산유체공학회:학술대회논문집
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• 2008.08a
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• pp.45.3-45.3
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• 2008

• The Mathematical Education
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• v.41 no.1
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• pp.91-100
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• 2002

The purpose of this study is to help the students understand the concepts for the series and calculate the sum of series with diverse methods --- a) High School Algebraic Technique, b) Using Bernoulli Number, c) Integral Method, d) Euler Formular, e) Fourier Series

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.164-169
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• 2001

A comprehensive extension of functions and efficiency of the software system, DS/Block, developed earlier for the purpose of simulation of the motion of a ship block during lifting and turnover operation. A viewpoint change used in 3D-CAD is utilized and saves the time for displays of a series of configurations for the motion. The Euler parameters are adopted to convert 3 rotational degrees of freedom about global coordinate system to those about local coordinate system defined in Pro/ENGINEER. DS/Block provides FEM input data for stress and strain analyses. Several functions are incorporated for user-friendliness. DS/Block is to be tested and installed in a shipyard.

• Structural Engineering and Mechanics
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• v.47 no.3
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• pp.307-329
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• 2013

The bending problem of Euler-Bernoulli discontinuous beams is dealt with, in which the discontinuities are due to the loads and eventually to essential constrains applied along the beam axis. In particular, the loads are modelled as random delta-correlated processes acting along the beam axis, while the ulterior eventual discontinuities are produced by the presence of external rollers applied along the beam axis. This kind of structural model can be considered in the static study of bridge beams. In the present work the exact expression of the response quantities are given in terms of means and variances, thanks to the use of the stochastic analysis rules and to the use of the generalized functions. The knowledge of the means and the variances of the internal forces implies the possibility of applying the reliability ${\beta}$-method for verifying the beam.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1981-1988
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• 2013

We say a positive integer n satisfies the Lehmer property if ${\phi}(n)$ divides n - 1, where ${\phi}(n)$ is the Euler's totient function. Clearly, every prime satisfies the Lehmer property. No composite integer satisfying the Lehmer property is known. In this article, we show that every composite integer of the form $D_{p,n}=np^n+1$, for a prime p and a positive integer n, or of the form ${\alpha}2^{\beta}+1$ for ${\alpha}{\leq}{\beta}$ does not satisfy the Lehmer property.

• Korean Journal of Computational Design and Engineering
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• v.5 no.4
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• pp.293-300
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• 2000

The non-manifold geometric modeling technique is to improve design process and to Integrate design, analysis, and manufacturing by handling mixture of wireframe model, surface model, and solid model in a single data structure. For the non-manifold geometric modeling, Euler operators and other high level modeling methods are necessary. Boolean operation is one of the representative modeling method for the non-manifold geometric modeling. This thesis studies Boolean operations of non-manifold model with the data structure of selective storage. The data structure of selective storage is improved non-manifold data structure in that existing non-manifold data structures using ordered topological representation method always store non-manifold information even if edges and vortices are in the manifold situation. To implement Boolean operations for non-manifold model, intersection algorithm for topological cells of three different dimensions, merging and selection algorithm for three dimensional model, and Open Inventor(tm), a 3D toolkit from SGI, are used.