• Smart Structures and Systems
• /
• 제13권1호
• /
• pp.111-135
• /
• 2014

Based on the Reissner mixed variational theorem (RMVT), finite rectangular layer methods (FRLMs) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, fiber-reinforced composite material (FRCM) and functionally graded material (FGM) sandwich plates subjected to bi-axial compressive loads. In this work, the material properties of the FGM layers are assumed to obey the power-law distributions of the volume fractions of the constituents through the thickness, 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 field variables of each individual layer, respectively, and an h-refinement process is adopted to yield the convergent solutions. The accuracy and convergence of the RMVT-based FRLMs with various orders used for expansions of each field variables through the thickness are assessed by comparing their solutions with the exact 3D and accurate two-dimensional ones available in the literature.

• Korean Journal of Mathematics
• /
• 제19권4호
• /
• pp.423-436
• /
• 2011

We obtain a theorem that shows the existence of multiple solutions for the mixed type nonlinear elliptic equation with Dirichlet boundary condition. Here the nonlinear part contain the jumping nonlinearity and the subcritical growth nonlinearity. We first show the existence of a positive solution and next find the second nontrivial solution by applying the variational method and the mountain pass method in the critical point theory. By investigating that the functional I satisfies the mountain pass geometry we show the existence of at least two nontrivial solutions for the equation.

• Steel and Composite Structures
• /
• 제27권6호
• /
• pp.789-801
• /
• 2018

A weak-form formulation of finite annular prism methods (FAPM) based on Reissner's mixed variational theorem (RMVT), is developed for the quasi three-dimensional (3D) static analysis of two-directional functionally graded (FG) circular plates with various boundary conditions and under mechanical loads. The material properties of the circular plate are assumed to obey either a two-directional power-law distribution of the volume fractions of the constituents through the radial-thickness surface or an exponential function distribution varying doubly exponentially through it. These FAPM solutions of the loaded FG circular plates with both simply-supported and clamped edges are in excellent agreement with the solutions obtained using the 3D analytical approach and two-dimensional advanced plate theories available in the literature.

• Steel and Composite Structures
• /
• 제39권3호
• /
• pp.291-306
• /
• 2021

Based on Reissner's mixed variational theorem (RMVT), the authors develop a semi-analytical finite element (FE) method for a three-dimensional (3D) bending analysis of nonhomogeneous orthotropic, complete and incomplete toroidal shells subjected to uniformly-distributed loads. In this formulation, the toroidal shell is divided into several finite annular prisms (FAPs) with quadrilateral cross-sections, where trigonometric functions and serendipity polynomials are used to interpolate the circumferential direction and meridian-radial surface variations in the primary field variables of each individual prism, respectively. The material properties of the toroidal shell are considered to be nonhomogeneous orthotropic over the meridianradial surface, such that homogeneous isotropic toroidal shells, laminated cross-ply toroidal shells, and single- and bi-directional functionally graded toroidal shells can be included as special cases in this work. Implementation of the current FAP methods shows that their solutions converge rapidly, and the convergent FAP solutions closely agree with the 3D elasticity solutions available in the literature.

• 한국전산구조공학회논문집
• /
• 제25권6호
• /
• pp.505-512
• /
• 2012

본 논문에서는 일차전단변형 평판 이론(FSDT)의 개선을 통한 복합재료 적층평판의 효율적 열응력 해석 기법을 제안한다. 횡방향 응력 성분에 대해서만 변분을 취하는 혼합변분이론(Mixed variational theorem)을 이용하여 횡방향 변형에너지를 개선하였다. 가정된 횡방향 전단응력 성분들은 효율적 고차이론으로부터 구하였으며, 면내 변위 성분들은 일차적층평판 이론의 변위장을 사용하였다. 또한, 열응력 해석에 있어서 횡방향 수직 변형을 효과적으로 고려하기 위해서 횡방향 수직 변위를 두께방향에 대하여 포물선으로 가정하였다. 이 과정을 통하여 얻어진 전단변형 에너지를 본 논문에서는 횡방향 수직 변형이 고려된 개선된 일차전단변형이론(EFSDTM_TN)이라고 명명하였다. 제안된 EFSDTM_TN은 복합재료 적층평판의 열탄성 거동을 해석함에 있어서 횡방향 수직 변형이 고려된 일차전단변형 평판 이론(FSDT_TN)과 비슷한 수준의 계산만을 필요로 하며, 동시에 후처리 과정을 통하여 열변형 및 열응력의 두께방향 분포를 정확하게 예측할 수 있도록 개선하였다. 계산된 결과는 FSDT_TN, 3차원 탄성해 등의 결과와 비교하여 검증하였다.

• Korean Journal of Mathematics
• /
• 제17권4호
• /
• pp.419-428
• /
• 2009

We show the existence of at least one nontrivial solution of the homogeneous mixed type nonlinear elliptic problem. Here mixed type nonlinearity means that the nonlinear part contain the jumping nonlinearity and the critical growth nonlinearity. We first investigate the sub-level sets of the corresponding functional in the Soboles space and the linking inequalities of the functional on the sub-level sets. We next investigate that the functional I satisfies the mountain pass geometry in the critical point theory. We obtain the result by the mountain pass method, the critical point theory and variational method.

• Nonlinear Functional Analysis and Applications
• /
• 제27권1호
• /
• pp.83-97
• /
• 2022

In this paper, we introduce and study generalized mixed operator quasi-equilibrium problems(GMQOEP) in Hausdorff topological vector spaces and prove the existence results for the solution of (GMQOEP) in compact and noncompact settings by employing 1-person game theorems. Moreover, using coercive condition, hemicontinuity of the functions and KKM theorem, we prove new results on the existence of solution for the particular case of (GMQOEP), that is, generalized mixed operator equilibrium problem (GMOEP).

• Advances in nano research
• /
• 제6권2호
• /
• pp.163-182
• /
• 2018

Based on the Reissner mixed variational theorem (RMVT), the authors present a nonlocal Timoshenko beam theory (TBT) for the nonlinear free vibration analysis of multi-walled carbon nanotubes (MWCNT) embedded in an elastic medium. In this formulation, four different edge conditions of the embedded MWCNT are considered, two different models with regard to the van der Waals interaction between each pair of walls constituting the MWCNT are considered, and the interaction between the MWCNT and its surrounding medium is simulated using the Pasternak-type foundation. The motion equations of an individual wall and the associated boundary conditions are derived using Hamilton's principle, in which the von $K{\acute{a}}rm{\acute{a}}n$ geometrical nonlinearity is considered. Eringen's nonlocal elasticity theory is used to account for the effects of the small length scale. Variations of the lowest frequency parameters with the maximum modal deflection of the embedded MWCNT are obtained using the differential quadrature method in conjunction with a direct iterative approach.

• 한국기계가공학회지
• /
• 제21권4호
• /
• pp.53-59
• /
• 2022

In this study, an enhanced first-order shear deformation theory is proposed to efficiently and accurately predict the thermo-mechanical-viscoelastic coupled behavior of laminated composite structures. To this end, transverse shearstress and displacement fields are independently assumed, and the strain-energy relationship between these fields issystematically established using the mixed variational theorem (MVT). In MVT, the transverse shear stress fields are obtained from the third-order zigzag model, whereas the displacement fields of the conventional first-order model are considered to amplify the benefits of numerical efficiency. Additionally, a transverse displacement field with a smooth parabolic distribution is introduced to accurately predict the thermal behavior of composite structures. Furthermore, the concept of Laplace transformation is newly employed to simplify the viscoelastic problem, similar to the linear-elastic problem. To demonstrate the performance of the proposed theory, the numerical results obtained herein were compared with those available in the literature.

• 한국전산구조공학회논문집
• /
• 제33권5호
• /
• pp.279-286
• /
• 2020

본 연구에서는 점근해석 및 논로컬 이론에서 요구하는 4차 이상의 고차 미분근사를 수행하기 위하여 계방정식에 혼합변분이론을 적용하여 MLS 차분법으로부터 구해지는 고차 미분근사의 정확도를 큰 폭으로 향상시킨다. 또한, MLS 차분법에 존재하는 세 가지 조건변수에 따른 고차미분근사의 정확도를 비교·분석한다. 혼합변분이론의 합응력을 후처리하여 변위의 미분을 근사할 경우 기존의 변위장 기반 계방정식의 차분 결과에 비해 미분 차수가 2차 낮아진다. 해석 범위내 절점 수가 과도하게 많거나 기저 차수가 클 경우 MLS 차분법의 영향영역 내에서 과적합(overfitting)이 발생한다. 또한 영향영역이 최적 범위 이상으로 넓어질 경우 근사의 정확도가 떨어진다. 위 내용을 사인 하중을 받는 단순지지보 수치예제로부터 확인하였다.