• 한국전산구조공학회논문집
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• 제19권4호
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• pp.407-418
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• 2006

본 논문에서는 일차전단변형이론(FSDT)을 이용한 복합재료 적층평판의 고정밀 해석기법을 소개한다. 전단수정계수가 자동적으로 포함되도록 횡방향 전단 변형에너지를 혼합변분이론(mixed variational theorem)을 이용하여 개선하였다. 혼합변분이론에서는 변분을 횡방향 응력들에 대해서만 취하였다. 가정된 횡방향 전단응력은 효율적인 고차이론(Cho and Parmerter, 1993)으로부터 구하였다 횡방향 수직응력은 3차 다항식으로 가정하였고, 무전단 응력조건과 평판의 윗면과 아랫면에서의 응력을 만족하는 조건을 부과함으로써 얻었다. 한편, 변위들에 대해서는 일차전단변형이론의 변위장을 사용하였다. 이렇게 해서 얻어진 변형 에너지를 본 논문에서는 EFSDTM3D이라고 명명 하였다. 본 논문에서 개발된 EFSDTM3D는 변위와 응력의 계산에서 고전적인 FSDT와 같은 정도의 계산 효율을 가지면서, 동시에 변위와 응력의 두께방향의 정확도를 면내 방향 응력들에 대한 최소오차자승법에 기초하여 응력 회복 과정을 적용함으로써 개선하였다. 계산된 결과는 고전적인 FSDT, 3차원 탄성해, 그리고 참고문헌 중에서 이용 가능한 결과들과 비교하여 검증하였다.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.621-639
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• 2011

The purpose of this paper is to introduce a general iterative process by viscosity approximation method with parallel method to ap-proximate a common element of the set of solutions of a mixed equilibrium problem and of the set of common fixed points of a finite family of $k_i$-strict pseudo-contractions in a Hilbert space. We obtain a strong convergence theorem of the proposed iterative method for a finite family of $k_i$-strict pseudo-contractions to the unique solution of variational inequality which is the optimality condition for a minimization problem under some mild conditions imposed on parameters. The results obtained in this paper improve and extend the corresponding results announced by Liu (2009), Plubtieng-Panpaeng (2007), Takahashi-Takahashi (2007), Peng et al. (2009) and some well-known results in the literature.

• Steel and Composite Structures
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• 제22권1호
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• pp.161-182
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• 2016

A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) analysis of functionally graded material (FGM) axisymmetric circular plates with simply-supported and clamped edges. The strong formulation of this 3D elasticity axisymmetric problem is derived on the basis of the Reissner mixed variational theorem (RMVT), which consists of the Euler-Lagrange equations of this problem and its associated boundary conditions. The primary field variables are naturally independent of the circumferential coordinate, then interpolated in the radial coordinate using the early proposed DRK interpolation functions, and finally the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The state space DRK solutions can then be obtained by means of the transfer matrix method. The accuracy and convergence of this method are examined by comparing their solutions with the accurate ones available in the literature.

• 대한수학회보
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• 제53권5호
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• pp.1585-1596
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• 2016

In this paper we investigate the existence of nontrivial solutions for the following fractional boundary value problem (FBVP) $$\{_tD_T^{\alpha}(_0D_t^{\alpha}u(t))={\nabla}W(t,u(t)),\;t{\in}[0,T],\\u(0)=u(T)=0,$$ where ${\alpha}{\in}(1/2,1)$, $u{\in}{\mathbb{R}}^n$, $W{\in}C^1([0,T]{\times}{\mathbb{R}}^n,{\mathbb{R}})$ and ${\nabla}W(t,u)$ is the gradient of W(t, u) at u. The novelty of this paper is that, when the nonlinearity W(t, u) involves a combination of superquadratic and subquadratic terms, under some suitable assumptions we show that (FBVP) possesses at least two nontrivial solutions. Recent results in the literature are generalized and significantly improved.

• Smart Structures and Systems
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• 제16권5호
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• pp.781-806
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• 2015

A unified formulation of finite layer methods (FLMs), based on the Reissner mixed variational theorem (RMVT), is developed for the three-dimensional (3D) coupled electro-elastic analysis of simply-supported, functionally graded piezoelectric material (FGPM) plates with open- and closed-circuit surface conditions and under electro-mechanical loads. In this formulation, the material properties of the plate are assumed to obey an exponent-law varying exponentially through the thickness coordinate, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement components. The relevant orders used for expanding these variables in the thickness coordinate can be freely chosen as the linear, quadratic and cubic orders. Four different mechanical/electrical loading conditions applied on the top and bottom surfaces of the plate are considered, and the corresponding coupled electro-elastic analysis of the loaded FGPM plates is undertaken. The accuracy and convergence rate of the RMVT-based FLMs are assessed by comparing their solutions with the exact 3D piezoelectricity ones available in the literature.