• Structural Engineering and Mechanics
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• v.45 no.3
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• pp.355-371
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• 2013

Single- and multi-span orthotropic functionally graded hollow cylinders subjected to axisymmetrical bending are investigated on the basis of a unified shear deformable shell theory, in which the transverse displacement is expressed by means of a general shape function. To approach the through-thickness inhomogeneity of the hollow cylinder, a laminated model is employed. The shape function therefore shall be determined for each fictitious layer. To improve the computational efficiency, we resort to a transfer matrix method. Based on the principle of minimum potential energy, equilibrium equations are established, which are then solved analytically using the transfer matrix method for arbitrary boundary conditions. Numerical comparisons among a third-order shear deformable shell theory, an exact elastic theory and the present theory are provided for a simply supported hollow cylinder, from which the present theory turns out to be superior in stress estimation. Distributions of displacements and stresses in single- and three-span hollow cylinders with different boundary conditions are also illustrated in numerical examples.

• Journal of Ocean Engineering and Technology
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• v.15 no.3
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• pp.107-113
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• 2001

This study is focused on the wave control by economical multi-rowed impermeable submerged breakwaters which need less materials than a one-rowed submerged breakwater. A boundary element method and eigenfunction expansion method based on the Green\`s theorem are appled to analyze the characteristics of wave transformation. Submerged breakwaters are consisted of one and two-row with rectangular section. Wave transformation characteristics are investigated by the various combinations of placement distance and crown water depth.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.383-395
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• 2016

The convergence rate of a numerical procedure based on Schwarz Alternating Method (SAM) for solving elliptic boundary value problems depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It has been observed that the Robin condition (mixed interface condition), controlled by a parameter, can optimize SAM's convergence rate. In [8], one formulated the twolayer multi-parameterized SAM and determined the optimal values of the multi-parameters to produce the best convergence rate for one-dimensional elliptic boundary value problems. Two-dimensional implementation was presented in [10]. In this paper, we present an implementation for threedimensional problem.

• Tribology and Lubricants
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• v.21 no.6
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• pp.263-267
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• 2005

The tribological performance of multi-walled carbon nanotubes (MWNT) in mineral oils is investigated at ambient temperature. The frictional forces, wear amounts and cycles to scuffing of the oils with nanotubes and without those were measured using the ball-on-disk tester. It was found that there were little differences in the frictional forces and wear amounts of two oils. However, the scuffing times of oils with nanotubes were much longer than those of oils without nanotubes in sliding tests. The nanotubes were very effective on maintaining the oil gap and protecting the surfaces in boundary lubricated sliding.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.33-44
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• 2015

The convergence rate of a numerical procedure based on Schwarz Alternating Method(SAM) for solving elliptic boundary value problems depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It has been observed that the Robin condition (mixed interface condition), controlled by a parameter, can optimize SAM's convergence rate. In [7], one formulated the multi-parameterized SAM and determined the optimal values of the multi-parameters to produce the best convergence rate for one-dimensional elliptic boundary value problems. Two-dimensional implementation was presented in [8]. In this paper, we present an implementation for three-dimensional problem.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.32 no.9
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• pp.713-719
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• 2008

Most of the MEMS parts are made of multi-grain silicon wafer, which is the orthotropic material and its material direction is arbitrary. The reliability of the parts must be guaranteed in order to use for the commercial usage. The need of the structural analysis of its parts emerges an important factor. The material properties of the MEMS parts are calculated by the numerical method in order to reduce a material test. In this study, the effective elastic modulus and its Poisson's ratio are calculated by the boundary element method(BEM) and are compared with the results by the finite element method(FEM).

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.10
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• pp.967-974
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• 2011

The direct and indirect PFBEM(power flow boundary element method) for the treatment of the 3 dimensional multi-domain problems are proposed to predict the acoustic energy density in medium to high frequency ranges. In the proposed method, the equation is derived in a matrix form by considering coupled relationships of the power flow at the interface of given domains. The proposed method can successfully obtain the analytical solutions for the problems of coupled cubes and the small-scale reverberant chamber. Then the experiment is carried out to obtain STL(sound transmission loss) by using small-scale reverberant chamber and the results are compared with analysis results.

• Steel and Composite Structures
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• v.23 no.6
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• pp.657-668
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• 2017

In the most of previous studies, researchers have restricted their own studies to consider the effect of single walled carbon nanotubes as a reinforcement on the vibrational behavior of structures. In the present work, free vibration characteristics of functionally graded annular plates reinforced by multi-walled carbon nanotubes resting on Pasternak foundation are presented. The response of the elastic medium is formulated by the Winkler/Pasternak model. Modified Halpin-Tsai equation was used to evaluate the Young's modulus of the multi-walled carbon nanotube/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the multi-walled carbon nanotubes wt% range considered. The 2-D generalized differential quadrature method as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the plates are investigated. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of annular plates.

• Honam Mathematical Journal
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• v.8 no.1
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• pp.21-49
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• 1986

A class of singular quadratic control problem is considered. The state is governed by a higher order system of ordinary linear differential equations and very general nonstandard boundary conditions. These conditions in many important cases reduce to standard boundary conditions and because of the conditions the usual controllability condition is not needed. In the special case where the coefficient matrix of the control variable in the cost functional is a time-independent singular matrix, the corresponding optimal control law as well as the optimal controller are computed. The method of investigation is based on the theory of least-squares solutions of multi-valued operator equations.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.113-130
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• 2024

In this work, we explore the existence and uniqueness results for a class of boundary value issues for implicit Volterra-Fredholm nonlinear integro-differential equations (IDEs) with Atangana-Baleanu-Riemann fractional (ABR-fractional) that have non-instantaneous multi-point fractional boundary conditions. The findings are supported by Krasnoselskii's fixed point theorem, Gronwall-Bellman inequality, and the Banach contraction principle. Finally, a demonstrative example is provided to support our key findings.