• 대한기계학회논문집
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• 제7권1호
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• pp.52-63
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• 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.

• 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.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
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• pp.11-18
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• 2001

In this paper, a new algorithm of coupling Element-Free Galerkin Method(EFGM) and Boundary Element Method(BEM) using the variational formulation is presented. A global variational coupling formulation of EFGM-BEM is achieved by combining the variational form on each subregion. In the formulation, Lagrange multiplier method is introduced to satisfy the compatibility conditions between EFGM subregion and BEM subregion. Some numerical examples are studied to verify accuracy and efficiency of the proposed method, in which numerical performance of the method is compared with that of conventional method such as EFGM-BEM direct coupling method, EFGM and BEM. The proposed method incorporating the merits of EFGM and BEM is expected to be applied to special engineering problems such as the crack propogation problems in very large domain, and underground structures with joints.

• Interaction and multiscale mechanics
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• 제1권3호
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• pp.329-337
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• 2008

This paper presents the derivation of the generalized governing equations in theory of elasticity, their weak forms and the some applications in the numerical analysis of structural mechanics. Unlike the differential equations in classical elasticity theory, the generalized equations of the equilibrium and compatibility equations presented here take the form of integral equations, and the generalized equilibrium equations contain the classical differential equations and the boundary conditions in a single equation. By using appropriate test functions, the weak forms of these generalized governing equations can be established. It can be shown that various variational principles in structural analysis are merely the special cases of these weak forms of generalized governing equations in elasticity. The present weak forms of elasticity equations extend greatly the choices of the trial functions for approximate solutions in the numerical analysis of various engineering problems. Therefore, the weak forms of generalized governing equations in elasticity provide a powerful modeling tool in the computational structural mechanics.

• 대한수학회지
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• 제53권1호
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• pp.161-185
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• 2016

We consider a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and an electrically conductive obstacle, the so-called foundation. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with Signorini's conditions and a version of Coulomb's law of dry friction in which the adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation for the model, in the form of a system for the displacements, the electric potential and the adhesion. Under a smallness assumption which involves only the electrical data of the problem, we prove the existence of a unique weak solution of the model. The proof is based on arguments of time-dependent quasi-variational inequalities, differential equations and Banach's fixed point theorem.

• 전산구조공학
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• 제7권4호
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• pp.85-101
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• 1994

적층판의 동적거동에 대한 유한요소해석모델개발을 목적으로 전단변형을 적합하게 고려한 적층판이론에 대한 변분원리를 유도하였다. 유도방법은 Sandhu 등에 의해 개발된 다변수 경계치문제의 변분원리이론을 따랐으며, 지배방정식의 미분연산자 매트릭스를 self-adjoint로 만들기 위하여 convolution을 이중선형사상으로 사용하였다. 유도된 적층판의 범함수에는 경계조건, 초기조건뿐만 아니라 유한요소해석모델에서 생길 수 있는 요소간 불연속조건도 포함시킬 수 있다. 상태변수의 적합함수공간을 확장하거나 특정조건을 적용하므로서 다양한 형태의 범함수를 유도할 수 있으며, 이를 통해 다양한 유한요소해석모델의 개발이 가능함을 논하였다.

• 한국한의학연구원논문집
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• 제2권1호
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• pp.337-380
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• 1996

'Nei Jing(內徑)' first defined the interrelationship of the true and tile false between evil factor affecting health(雅氣) and vital essence energy(精氣). According to 「'Nei Jing(內徑)', the above interrelationship is explained as 'If state of evil domination is considered as sthenia-syndrome(雅氣盛則實), if the consumption of healthy energy Is considered as asenia-syndrome(精氣尊則虛): 'Nei Jing(內徑)', proposed major features of the medicall treatment by 'regluate the vatal energy of asthenia and sthenia, treat the sthenia-syndrome by purgation, and treat the asenia-syndrome by therapy of invigoration(調其氣之虛實, 實則瀉之, 虛則補之): The above interrelationship was interpreted as 'treat the asthenia-syndrome of child organ by invigorating the mother organ(虛者補其母)'in the 69th of 'The Classic on Difficulty',(難經 六十九難). Go-Mu(高武) of Myung-dynasty describe therapy for invigoration and purgation of itself-meridian(自經 補瀉法), which locating acupuncture points according to the Therorr of Five Element in the five shu points of itself-meridian(自經 五유穴), based on the generation in the ${\ulcorner}$A Synthetical Book of Acupuncture and Moxibustion(針灸聚英)${\lrcorner}$, Sae-hyun Jang(張世賢) further extended location acupuncture points of the five shu points to the other-meridian in the ${\ulcorner}$Gyeo Jung Do Ju Nan Gyung(校正圖註難經)${\lrcorner}$ Sa-Ahm's 5 Element Acupuncture Method(舍嚴五行鍼法) was originated in 1644, the middle of the Yi-dynasty. It linked the reinforcing and reducing in acupuncture therapy which incorporated tlle asthenia-syndrome and sthenia-syndrome of the hollow organs, based on principle of the Yin Yang 5 Element Theory(陰陽五行學說), not only to the generation in the 5 element(相生關係) but also to the restriction in the 5 element(相剋關係). Furthermore it was devised for the medical treatment by comning therapy for invigoration and purgation of itself-meridian(自經 補瀉法) with that of the other-meridian. Even though many original forms(正形) of the therapy for invigoration and purgation of the Yin Yang 5 Element Theory comply with the principle of the generation and the restriction based on the principle of the Yin Yang 5 Element Theory are abailable, variational forms(變形) are also recognized by examining the nature of the Sa-Ahm's 5 Element Acupuncture Method(舍嚴五行鍼法), For this reason, it is very difficult to understand the Sa-Ahm's 5 Element Acupuncture Method(舍嚴五行鍼法) thoroughly. therefore, those variational forms are obstacles for the beginners to study the Sa-Ahm's 5 Element Acupuncture Method. In order to understand the principle of the practical clinical application of the Sa-Ahm's 5 Element Acupuncture Method, this study investigated which principle was based on the variations of the locating acupuncture points' method for the acupuncture prescription.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.113-128
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• 2014

Consider a class of p(x)-Kirchhoff type equations of the form $$\left\{-M\left({\int}_{\Omega}\;\frac{1}{p(x)}{\mid}{\nabla}u{\mid}^{p(x)}\;dx\right)\;div\;({\mid}{\nabla}u{\mid}^{p(x)-2}{\nabla}u)={\lambda}V(x){\mid}u{\mid}^{q(x)-2}u\;in\;{\Omega},\\u=0\;on\;{\partial}{\Omega},$$ where p(x), $q(x){\in}C({\bar{\Omega}})$ with 1 < $p^-\;:=inf_{\Omega}\;p(x){\leq}p^+\;:=sup_{\Omega}p(x)$ < N, $M:{\mathbb{R}}^+{\rightarrow}{\mathbb{R}}^+$ is a continuous function that may be degenerate at zero, ${\lambda}$ is a positive parameter. Using variational method, we obtain some existence and multiplicity results for such problem in two cases when the weight function V (x) may change sign or not.

• 수산해양기술연구
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• 제32권4호
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• pp.432-446
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• 1996

A stochastic Hamilton variational principle(SHVP) is formulated for dynamic problems of linear continuum. The SHVP allows incorporation of probabilistic distributions into the finite element analysis. The formulation is simplified by transformation of correlated random variables to a set of uncorrelated random variables through a standard eigenproblem. A procedure based on the Fourier analysis and synthesis is presented for eliminating secularities from the perturbation approach. In addition to, a method to analyse stochastic design sensitivity for structural dynamics is present. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element codes. An alternative form of the constraint functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The algorithms developed can readily be adapted to existing deterministic finite element codes. The numerical results for stochastic analysis by proceeding approach of cantilever, 2D-frame and 3D-frame illustrates in this paper.

• 대한수학회보
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• 제50권5호
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• pp.1693-1710
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• 2013

In this paper, we consider the biharmonic elliptic systems of the form $$\{{\Delta}^2u=F_u(u,v)+{\lambda}{\mid}u{\mid}^{q-2}u,\;x{\in}{\Omega},\\{\Delta}^2v=F_v(u,v)+{\delta}{\mid}v{\mid}^{q-2}v,\;x{\in}{\Omega},\\u=\frac{{\partial}u}{{\partial}n}=0,\; v=\frac{{\partial}v}{{\partial}n}=0,\;x{\in}{\partial}{\Omega},$$, where ${\Omega}{\subset}\mathbb{R}^N$ is a bounded domain with smooth boundary ${\partial}{\Omega}$, ${\Delta}^2$ is the biharmonic operator, $N{\geq}5$, $2{\leq}q$ < $2^*$, $2^*=\frac{2N}{N-4}$ denotes the critical Sobolev exponent, $F{\in}C^1(\mathbb{R}^2,\mathbb{R}^+)$ is homogeneous function of degree $2^*$. By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on ${\lambda}$ and ${\delta}$.