• Steel and Composite Structures
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• v.24 no.3
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• pp.359-367
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• 2017

In this work, transient heat transfer analysis of functionally graded (FG) carbon nanotube reinforced nanocomposite (CNTRC) cylinders with various essential and natural boundary conditions is investigated by a mesh-free method. The cylinders are subjected to thermal flux, convection environments and constant temperature faces. The material properties of the nanocomposite are estimated by an extended micro mechanical model in volume fraction form. The distribution of carbon nanotube (CNT) has a linear variation along the radial direction of axisymmetric cylinder. In the mesh-free analysis, moving least squares shape functions are used for approximation of temperature field in the weak form of heat transform equation and the transformation method is used for the imposition of essential boundary conditions. Newmark method is applied for solution time depended problem. The effects of CNT distribution pattern and volume fraction, cylinder thickness and boundary conditions are investigated on the transient temperature field of the nanocomposite cylinders.

• Proceedings of the Korea Contents Association Conference
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• 2010.05a
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• pp.381-383
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• 2010

In order to solve electromagnetic boundary value problems efficiently, we prove the equivalence of tangential and normal boundary conditions. Using four Maxwell's equations simultaneously, we deduce the conditions to satisfy the equivalence of tangential and normal boundary conditions for electromagnetic waves. The conditions proposed in this work can be used to obtain the simultaneous equations of electromagnetic boundary value problems.

• Structural Engineering and Mechanics
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• v.27 no.3
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• pp.333-345
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• 2007

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms were also included in the equations. The dimensionless equations were solved for six different set of boundary conditions. A perturbation method was applied to the equations of motions. The first terms of the perturbation series lead to the linear problem. Natural frequencies for the linear problem were calculated exactly for different boundary conditions. Second order non-linear terms of the perturbation series behave as corrections to the linear problem. Amplitude and phase modulation equations were obtained. Non-linear free and forced vibrations were investigated in detail. The effects of the position and magnitude of the step, as well as effects of different boundary conditions on the vibrations, were determined.

• Advances in nano research
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• v.13 no.5
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• pp.453-463
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• 2022

This paper aims to investigate the vibration analysis of functionally graded porous (FGP) beams using State-space approach with several classical and non-classical boundary conditions. The materials properties of the porous FG beams are considered to have even and uneven distributions profiles along the thickness direction. The equation of motion for FGP beams with various boundary conditions is obtained through Hamilton's principle. State-space approach is used to obtain the governing equation of porous FG beam. The comparison of the results of this study with those in the literature validates the present analysis. The effects of span-to-depth ratio (L/h), of distribution shape of porosity and others parameters on the dynamic behavior of the beams are described. The results show that the boundary conditions, the geometry of the beams and the distribution shape of porosity affect the fundamental frequencies of the beams.

• Journal of Mechanical Science and Technology
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• v.20 no.12
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• pp.2230-2241
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• 2006

This paper presents a sole application of boundary element method to the conjugate heat transfer problem of thermally developing laminar flow in a thick walled pipe when the fluid velocities are fully developed. Due to the coupled mechanism of heat conduction in the solid region and heat convection in the fluid region, two separate solutions in the solid and fluid regions are sought to match the solid-fluid interface continuity condition. In this method, the dual reciprocity boundary element method (DRBEM) with the axial direction marching scheme is used to solve the heat convection problem and the conventional boundary element method (BEM) of axisymmetric model is applied to solve the heat conduction problem. An iterative and numerically stable BEM solution algorithm is presented, which uses the coupled interface conditions explicitly instead of uncoupled conditions. Both the local convective heat transfer coefficient at solid-fluid interface and the local mean fluid temperature are initially guessed and updated as the unknown interface thermal conditions in the iterative solution procedure. Two examples imposing uniform temperature and heat flux boundary conditions are tested in thermally developing region and compared with analytic solutions where available. The benchmark test results are shown to be in good agreement with the analytic solutions for both examples with different boundary conditions.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.267-277
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• 2011

This paper is concerned with eigenvalues of second-order vector equations on time scales with boundary value conditions. Properties of eigenvalues and matrix-valued solutions are studied. Relationships between eigenvalues of different boundary value problems are discussed.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.497-502
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• 2022

Existence and uniqueness for fractional differential equations satisfying a general nonlocal initial or boundary condition are proven by means of Schauder's fixed point theorem. The nonlocal condition is given as an integral with respect to a signed measure, and includes the standard initial value condition and multi-point boundary value condition.

• Geomechanics and Engineering
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• v.16 no.1
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• pp.1-9
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• 2018

In this paper an efficient and simple refined shear deformation theory is presented for the free vibration of Functionally Graded Plates Under Various Boundary Conditions. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. The plates are considered of the type having two opposite sides simply-supported, and the two other sides having combinations of simply-supported, clamped, and free boundary conditions. The mechanical properties of functionally graded material are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion are derived using Hamilton's principle. The results of this theory are compared with those of other shear deformation theories. Various numerical results including the effect of boundary conditions, power-law index, plate aspect ratio, and side-to-thickness ratio on the free vibration of FGM plates are presented.

• Steel and Composite Structures
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• v.50 no.2
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• pp.149-158
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• 2024

Considering that different boundary conditions can have an important impact on structural vibration characteristics. In this paper, the nonlinear forced vibration behavior of functionally graded material (FGM) doubly curved shells with initial geometric imperfections under different boundary conditions is studied. Considering initial geometric imperfections and von Karman geometric nonlinearity, the nonlinear governing equations of FGM doubly curved shells are derived using Reissner's first order shear deformation (FOSD) theory. Three different boundary conditions of four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS) were studied, and a system of nonlinear ordinary differential equations was obtained with the help of Galerkin principle. The nonlinear forced vibration response of the FGM doubly curved shell is obtained by using the modified Lindstedt Poincare (MLP) method. The accuracy of this method was verified by comparing it with published literature. Finally, the effects of curvature ratio, power law index, void coefficient, prestress, and initial geometric imperfections on the resonance of FGM doubly curved shells under different boundary conditions are fully discussed. The relevant research results can provide certain guidance for the design and application of doubly curved shell.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1817-1828
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• 2017

We give a simple and direct proof of the characterization of positivity preserving semi-flows for ordinary differential systems. The same method provides an abstract result on a class of evolution systems containing reaction-diffusion systems in a bounded domain of ${\mathbb{R}}^n$ with either Neumann or Dirichlet homogeneous boundary conditions. The conditions are exactly the same with or without diffusion. A similar approach gives the optimal result for invariant rectangles in the case of Neumann conditions.