• Steel and Composite Structures
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• 제17권1호
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• pp.133-143
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• 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.

• 대한기계학회논문집A
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• 제28권9호
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• pp.1255-1261
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• 2004

A variational approximation procedure is introduced to study the contact stresses between a representative asperity and a feature generally happening in superfinishing processes such as FAM. After a description of the model under consideration is presented, a system of governing equation for the model is derived fullowed by the assumptions made in order to make progress in model development. Final computation is made to evaluate contact stresses on an elastic asperity tip in small scale in size and a computer simulation is performed for detailed surface profile variations on a representative feature. Numerical results are presented along with a discussion of the conclusions that can be drawn from this analysis.

• 한국통신학회논문지
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• 제18권10호
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• pp.1461-1468
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• 1993

본논문은 임의의 유전율 텐서를 포함하는 비등방성 매질에 비스듬하게 입사되는 전파문제를 변분유한 요소법을 통하여 고찰하였다. 먼저, 변분수식은 유기정리, 리액션 이론, 가역정리에 기초한 새로운 접근방법을 통해 유도하였다. 그다음, 유한요소법을 이용하여 구해진 범함수로 부터 전파특성을 해석하였다. 또한, magnetoplasma 슬랩에 입사되는 전파에 대한 수치결과를 나타냈다.

• 대한토목학회논문집
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• 제10권2호
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• pp.1-9
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• 1990

기하학적 비선형구조의 설계민감도 해석을 위해 기준체적과 수반구조개념을 이용한 변분법이 응용되었다. 일반적인 설계민감도식을 사용하였고 이상화된 구조모형에는 비선형 유한요소과정을 이용하였다. 수치예를 통하여 기하학적 비선형 구조거동에 대한 설계민감도 해석에서 변분법의 유용성과 효용성을 확인하였다.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.845-862
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• 2010

In a recent paper, M.A. Noor et al. (Hindawi publishing corporation, Mathematical Problems in Engineering, Volume 2008, Article ID 696734, 11 pages, doi:10.1155/2008/696734) proposed the variational homotopy perturbation method (VHPM) for solving higher dimentional initial boundary value problems. In this paper, we consider the proposed method for analytic treatment of the linear and nonlinear ordinary differential equations, homogeneous or inhomogeneous. The results reveal that the proposed method is very effective and simple and can be applied for other linear and nonlinear problems in mathematical.

• 한국전자파학회논문지
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• 제13권2호
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• pp.170-175
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• 2002

등각사상이 결합된 변분적 유한요소법을 이용하여 대칭 스트립 전송선의 고차모드 차단주파수를 계산한다. 등각사상은 스트립 전송선의 무한영역을 적절한 유한영역으로 변환하는데 사용된다. 변환된 유한영역에 대한 변분 방정식을 유도하고 유한요소법으로 그 해를 구하여 차단주파수를 계산한다. 다른 해석법에 의한 결과와 비교하여 이 해석법이 무한영역이 포함된 전송선의 고차모드 차단주파수 계산에 적합함을 확인한다.

• Korean Journal of Mathematics
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• 제19권4호
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• pp.481-493
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• 2011

We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.

• 대한수학회지
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• 제57권4호
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• pp.825-844
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• 2020

We obtain infinitely many solutions for a class of fractional Schrödinger equation, where the nonlinearity is superquadratic or involves a combination of superquadratic and subquadratic terms at infinity. By using some weaker conditions, our results extend and improve some existing results in the literature.

• 호남수학학술지
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• 제41권2호
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• pp.369-380
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• 2019

Inspired by the problem of finding hyperelastic curves in a Riemannian manifold, we present a study on the variational problem of a hyperelastic curve in Lie group. In a Riemannian manifold, we reorganize the characterization of the hyperelastic curve with appropriate constraints. By using this equilibrium equation, we derive an Euler-Lagrange equation for the hyperelastic energy functional defined in a Lie group G equipped with bi-invariant Riemannian metric. Then, we give a solution of this equation for a null hyperelastic Lie quadratic when Lie group G is SO(3).

• 대한수학회보
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• 제59권4호
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• pp.961-977
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• 2022

In this paper, we consider the following Kirchhoff type equation on the whole space $$\{-(a+b{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}\;{\mid}{\nabla}u{\mid}^2dx){\Delta}u=u^5+{\lambda}k(x)g(u),\;x{\in}{\mathbb{R}}^3,\\u{\in}{\mathcal{D}}^{1,2}({\mathbb{R}}^3),$$ where λ > 0 is a real number and k, g satisfy some conditions. We mainly investigate the existence of ground state solution via variational method and concentration-compactness principle.