• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1017-1034
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• 2023

In this paper, we work two different problems. First, we investigate a new class of fractional differential equations involving Caputo sequential derivative with some (e₁, e₂, θ)-periodic conditions. The existence and uniqueness of solutions are proven. The stability of solutions is also discussed. The second part includes studying traveling wave solutions of a conformable fractional Korteweg-de Vries-Burger (KdV Burger) equation through the Tanh method. Graphs of some of the waves are plotted and discussed, and a conclusion follows.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.501-515
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• 2009

A second order nonlinear ordinary differential equation is obtained by solving the initial-boundary value problem of a class of elas-todynamics equations, which models the radially symmetric motion of a incompressible hyper-elastic solid sphere under a suddenly applied surface tensile load. Some new conclusions are presented. All existence conditions of nonzero solutions of the ordinary differential equation, which describes cavity formation and motion in the interior of the sphere, are presented. It is proved that the differential equation has singular periodic solutions only when the surface tensile load exceeds a critical value, in this case, a cavity would form in the interior of the sphere and the motion of the cavity with time would present a class of singular periodic oscillations, otherwise, the sphere remains a solid one. To better understand the results obtained in this paper, the modified Varga material is considered simultaneously as an example, and numerical simulations are given.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.2
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• pp.222-235
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• 2017

In this study, finite element modeling was used to predict the material properties of tri-axially braided textile composite. The model was made based on an experimental test specimen which was also used to compare the final results. The full interlacing of tows was geometrically modelled, from which repeating parts that make up the whole braid called unit cells were identified based on the geometric and mechanical property periodicity. In order to simulate the repeating nature of the unit cell, periodic boundary conditions were applied. For validation of the method, a reference model was analyzed for which a very good agreement was obtained. Material property calculation was done by simulating uniaxial and pure shear tests on the unit cell. The comparison of these results with that of experimental test results showed an excellent agreement. Finally, parametric study on the effect of number of plies, stacking type (symmetric/anti-symmetric) and stacking phase shift was conducted.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.205-230
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• 2015

A class of periodic type boundary value problems of coupled impulsive fractional differential equations are proposed. Sufficient conditions are given for the existence of solutions of these problems. We allow the nonlinearities p(t)f(t, x, y) and q(t)g(t, x, y) in fractional differential equations to be singular at t = 0, 1 and be involved a sup-multiplicative-like function. So both f and g may be super-linear and sub-linear. The analysis relies on a well known fixed point theorem. An example is given to illustrate the efficiency of the theorems.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.2
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• pp.79-88
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• 2005

Evaluating the effective properties of materials containing various types of in-homogeneities is an important issue in the analysis of structures composed of those materials. A simple and effective method for the purpose is to impose the periodic displacement boundary conditions on the finite element model of a unit cell. Their theoretical background is explained based on the purely kinematical relations in the regularly spaced in-homogeneity problems, and the strategies to implement them into the analysis and to evaluate the homogenized material constants are introduced. The creep behavior of a thin sheet with square arrayed rectangular voids is characterized, where the orthotropy is induced by the presence of the voids. The homogenization method is validated through the comparison of the analysis of detailed model with that of the simplified one with the effective parameters.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.571-579
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• 2007

Finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with a periodic boundary condition, which is of the type $ut+\frac{{\partial}^2} {{\partial}x^2}\;g\;(u,\;u_x,\;u_{xx})=f(u,\;u_x,\;u_{xx})$. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Bulletin of the Korean Chemical Society
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• v.13 no.6
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• pp.665-669
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• 1992

We consider the problem of a random walker on a one-dimensional lattice (N sites) confronting a centrally-located deep trap (trapping probability, T=1) and N-1 adjacent sites at each of which there is a nonzero probability s(0 < s < 1) of the walker being trapped. Exact analytic expressions for < n > and the average number of steps required for trapping for arbitrary s are obtained for two types of finite boundary conditions (confining and reflecting) and for the infinite periodic chain. For the latter case of boundary condition, Montroll's exact result is recovered when s is set to zero.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1150-1155
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• 1990

This paper proposes an optimal redundancy resolution of a kinematically redundant manipulator while considering homotopy classes. The necessary condition derived by minimizing an integral cost criterion results in a second-order differential equation. Also boundary conditions as well as the necessary condition are required to uniquely specify the solution. In the case of a cyclic task, we reformulate the periodic boundary value problem as a two point boundary value problem to find an initial joint velocity as many dimensions as the degrees of redundancy for given initial configuration. Initial conditions which provide desirable solutions are obtained by using the basis of the null projection operator. Finally, we show that the method can be used as a topological lifting method of nonhomotopic extremal solutions and also show the optimal solution with considering the manipulator dynamics.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.6 s.261
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• pp.694-700
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• 2007

Recently, a new cellular metal, WBK(Wire woven Bulk Kagome) has been introduced. WBK is fabricated by assembling metal wires in six directions into a Kagome-like truss structure and by brazing it at all the crossings. Wires as the raw material are easy to handle and to attain high strength with minimum defect. And the strength and energy absorption are superior to previous cellular metals. Therefore, WBK seems to be promising once the fabrication process for mass production is developed. In this paper, an upper bound solution for the mechanical properties of the bulk WBK under compression is presented. In order to simulate uniform behavior of WBK consisted of perfectly uniform cells, a unit cell of WBK with periodic boundary conditions is analyzed by the finite element method. In comparison with experimental test results, it is found that the solution provides a good approximation of the mechanical properties of bulk WBK cellular metals except for Young's modulus. And also, the brazing joint size does not have any significant effect on the properties with an exception of an idealized thin joint.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1418-1423
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• 2004

Optimization of a heat exchanger with internally finned circular tubes has been performed for three-dimensional periodically fully developed turbulent flow and heat transfer. The design variables of fin number N, fin width ($d_1,d_2$) and fin height(H), are numerically optimized for the limiting conditions of $N=22{\sim}37$, $d_1=0.5{\sim}1.5$ mm, $d_2=0.5{\sim}1.5$ mm, $H=0.1{\sim}1.5$. Due to the periodic boundary conditions along main flow direction, the three layers of meshes are considered. The CFD and the mathematical optimization are coupled to optimize the heat exchanger. The flow and thermal fields are predicted using the finite volume method and the optimization is carried out by using the sequential quadratic programming (SQP) method which is widely used in the constrained nonlinear optimization problem.