• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.4
• /
• pp.381-394
• /
• 2019

In this paper, we are extending fractional partial differential equations to fuzzy fractional partial differential equation under Riemann-Liouville and Caputo fractional derivatives, namely Variational iteration methods, and this method have applied to the fuzzy fractional wave equation with initial conditions as in fuzzy. It is explained by one and two-dimensional wave equations with suitable fuzzy initial conditions.

• Journal of The Korean Astronomical Society
• /
• v.31 no.2
• /
• pp.89-93
• /
• 1998

An attempt is made to find the boundary tangential components of potential magnetic fields without constructing solutions in the entire domain. In our procedure, the magnetic energy is expressed as a functional of tangential and normal magnetic fields at the boundary and is minimized by the variational principle. This paper reports a preliminary study on two dimensional potential fields above a plane.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.37 no.11
• /
• pp.36-42
• /
• 2000

We calculate the facet reflectivity as a function of the waveguide width of buried channel waveguides using the angular spectrum method and the field profiles obtained by the effective index method, the variational method and the modified variational method, respectively and discuss the results. As the waveguide width increases, the facet reflectivity of buried channel waveguides approaches to that of slab waveguides. As the waveguide width decreases, the facet reflectivity of quasi-TE mode decreases from that of slab waveguides, while that of quasi-TE mode increases from that of slab waveguides. The variation of the facet reflectivity of quasi-TE mode as a function of waveguide width is much larger than that of quasi-TM mode. When the aspect ratio is one, the difference between the facet reflectivity of quasi-TE mode and that of quasi-TM mode using the variational method and the modified variational method is negligible, while the difference between the facet reflectivity of quasi-TE mode and that of quasi-TM mode using the effective index method is large. In the case of quasi-TE mode, the facet reflectivity using the angular spectrum method and the field profiles obtained by the modified variational method could be more accurate than that obtained by the effective method. In the case of quasi-TM mode, the facet reflectivities obtained by the various methods are almost the same.

• Steel and Composite Structures
• /
• v.17 no.1
• /
• pp.133-143
• /
• 2014

In this paper, we try to prepare an accurate analytical solution for solving nonlinear vibration of thin circular sector cylinder. A new approximate solution called variational approach is presented and correctly applied to the governing equation of thin circular sector cylinder. The effect of important parameters on the response of the problem is considered. Some comparisons have been presented between the numerical solution and the present approach. The results show an excellent agreement between these methods. It has been illustrated that the variational approach can be a useful method to solve nonlinear problems by considering the effects of important parameters.

• East Asian mathematical journal
• /
• v.28 no.5
• /
• pp.597-604
• /
• 2012

Let C be a nonempty closed convex subset of real Hilbert space H and F = $\{S(t):t{\geq}0\}$ a nonexpansive self-mapping semigroup of C, and $f:C{\rightarrow}C$ is a fixed contractive mapping. Consider the process {$x_n$} : $$\{{x_{n+1}={\beta}_nx_n+(1-{\beta}_n)z_n\\z_n={\alpha}_nf(x_n)+(1-{\alpha}_n)S(t_n)P_C(x_n-r_nAx_n)$$. It is shown that {$x_n$} converges strongly to a common element of the set of fixed points of nonexpansive semigroups and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.7 no.1
• /
• pp.52-63
• /
• 1983

The purpose of the study is to find development of contact area, contact pressure and friction forces occurring at joints or connection areas inbetween structural members or mechanical parts. The problem has a pair of difficulties intrinsically; a constraint of displacement due to contact, and presence of work term by nonconservative friction force in the variational principle of the problem. Because of these difficulties, the variational principle remains in the form of inequality. It is resolved by penalty method and perturbation method making the inequality to an equality which is proper for computational purposes. A contact problem without friction is solved to find contact area and contact pressure, which are to be used as data for the analysis of the friction problem using perturbed variational principle. For numerical experiments, a Hertz problem, a rigid punch problem, and the latter one with friction effects are solved using $Q_2$-finite elements.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.6
• /
• pp.1131-1145
• /
• 2012

The purpose of this paper is to use an appropriate variational framework to discuss the boundary value problem with p-Laplacian type operators $$\{({\alpha}(t,x^{\Delta}(t)))^{\Delta}-a(t){\phi}_p(x^{\sigma}(t))+f({\sigma}(t),x^{\sigma}(t))=0,\;{\Delta}-a.e.\;t{\in}I\\x^{\sigma}(0)=0,\\{\beta}_1x^{\sigma}(1)+{\beta}_2x^{\Delta}({\sigma}(1))=0,$$ where ${\beta}_1$, ${\beta}_2$ > 0, $I=[0,1]^{k^2}$, ${\alpha}({\cdot},x({\cdot}))$ is an operator of $p$-Laplacian type, $\mathbb{T}$ is a time scale. Some sufficient conditions for the existence of constant-sign solutions are obtained.

• Journal of the Korean Society for Precision Engineering
• /
• v.15 no.5
• /
• pp.120-127
• /
• 1998

Differential inequalities occurring in problems of obstacle contact problems are recast into variational inequalities and analyzed by finite element methods. A new a posteriori error estimator, which is essential in adaptive finite element method, is introduced to capture the errors in finite element approximations of these variational inequalities. In order to construct a posteriori error estimates, saddle point problems are introduced using Lagrange parameters and upper bounds are provided. The global upper bound is localized by a special mixed formulation, which leads to upper bounds of the element errors. A numerical experiment is performed on an obstacle contact problem to check the effectivity index both in a local and a global sense.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.28 no.8 s.227
• /
• pp.1196-1202
• /
• 2004

A meshfree multi-scale method has been presented for efficient analysis of elasto-plastic problems. From the variational principle, problem is decomposed into a fine scale and a coarse scale problem. In the analysis only the plastic region is discretized using fine scale. Each scale variable is approximated using meshfree method. Adaptivity can easily and nicely be implemented in meshree method. As a method of increasing resolution, partition of unity based extrinsic enrichment is used. Each scale problem is solved iteratively. Iteration procedure is indispensable for the elasto-plastic deformation analysis. Therefore this kind of solution procedure is adequate to that problem. The proposed method is applied to Prandtl's punch test and shear band problem. The results are compared with those of other methods and the validity of the proposed method is demonstrated.

• Steel and Composite Structures
• /
• v.24 no.6
• /
• pp.671-677
• /
• 2017

In this paper, two powerful analytical methods called Variational Approach (VA) and Hamiltonian Approach (HA) are used to solve high nonlinear non-Natural vibration problems. The presented approaches are works well for the whole range of amplitude of the oscillator. The first iteration of the approaches leads us to high accurate solution. Numerical results are also presented by using Runge-Kutta's [RK] algorithm. The full comparison between the presented approaches and the numerical ones are shown in figures. The effects of important parameters on the response of nonlinear behavior of the systems are studied completely. Finally, the results show that the Variational Approach and Hamiltonian approach are strong enough to prepare easy analytical solutions.