• Nuclear Engineering and Technology
• /
• 제28권3호
• /
• pp.311-319
• /
• 1996

We reconstruct the assembly pinwise flux using several types of boundary conditions and confirm that the reconstructed fluxes are the same with the reference flux if the boundary condition is exact. We test EPRI-9R benchmark problem with four boundary conditions, such as Dirichlet boundary condition, Neumann boundary condition, homogeneous mixed boundary condition (albedo type), and inhomogeneous mixed boundary condition. We also test reconstruction of the pinwise flux from nodal values, specifically from the AFEN [1, 2] results. From the nodal flux distribution we obtain surface flux and surface current distributions, which can be used to construct various types of boundary conditions. The result show that the Neumann boundary condition cannot be used for iterative schemes because of its ill-conditioning problem and that the other three boundary conditions give similar accuracy. The Dirichlet boundary condition requires the shortest computing time. The inhomogeneous mixed boundary condition requires only slightly longer computing time than the Dirichlet boundary condition, so that it could also be an alternative. In contrast to the fixed-source type problem resulting from the Dirichlet, Neumann, inhomogeneous mixed boundary conditions, the homogeneous mixed boundary condition constitutes an eigenvalue problem and requires longest computing time among the three (Dirichlet, inhomogeneous mixed, homogeneous mixed) boundary condition problems.

• Steel and Composite Structures
• /
• 제28권6호
• /
• pp.655-670
• /
• 2018

A coupled method, that combines the Ritz method and the finite element (FE) method, is proposed to solve the vibration problem of rectangular thin and thick plates with general boundary conditions. The eigenvalue partial differential equation(s) of the plate is (are) first reduced to a set of eigenvalue ordinary differential equations by the application of the Ritz method. The resulting eigenvalue differential equations are then reduced to an eigenvalue algebraic equation system using the finite element method. The natural boundary conditions of the plate problem including the free edge and free corner boundary conditions are also implemented in a simple and accurate manner. Various boundary conditions including simply supported, clamped and free boundary conditions are considered. Comparisons with existing numerical and analytical solutions show that the proposed mixed method can produce highly accurate results for the problems considered using a small number of Ritz terms and finite elements. The proposed mixed Ritz-FE formulation is also compared with the mixed FE-Ritz formulation which has been recently proposed by the present author and his co-author. It is found that the proposed mixed Ritz-FE formulation is more efficient than the mixed FE-Ritz formulation for free vibration analysis of rectangular plates with Levy-type boundary conditions.

• Journal of applied mathematics & informatics
• /
• 제28권1_2호
• /
• pp.109-130
• /
• 2010

In this paper, a numerical method for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with the mixed type boundary conditions is presented. Parameter-uniform error bounds for the numerical solution and also to numerical derivative are established. Numerical results are provided to illustrate the theoretical results.

• Steel and Composite Structures
• /
• 제52권5호
• /
• pp.595-608
• /
• 2024

This study presents a static analysis of thin shallow cylindrical and spherical panels, as well as plates (which are a special case of shells), under Levy-type mixed boundary conditions and various loading conditions. The study utilizes the boundary discontinuous double Fourier series method, where displacements are expressed as trigonometric functions, to analyze the system of partial differential equations. The panels are subjected to a simply supported type 3 (SS3) boundary condition on two opposite edges, while the remaining two edges are subjected to clamped type 3 (C3) boundary conditions. The study presents comprehensive tabular and graphical results that demonstrate the effects of curvature on the deflections and moments of thin shallow shells made from symmetric and antisymmetric cross-ply laminated composites, as well as isotropic steel materials. The proposed model is validated through comparison with existing literature, and the convergence characteristics are demonstrated. The changing trends of displacements and moments are explained in detail by investigating the effect of various parameters, such as stacking lamination, material types, curvature, and loading conditions.

• Nonlinear Functional Analysis and Applications
• /
• 제26권3호
• /
• pp.531-551
• /
• 2021

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing p(x)-Laplacian. More precisely, we consider the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.

• Steel and Composite Structures
• /
• 제20권5호
• /
• pp.1043-1066
• /
• 2016

A new analytical solution based on a third order shear deformation theory for the problem of static analysis of cross-ply doubly-curved shells is presented. The boundary-discontinuous generalized double Fourier series method is used to solve highly coupled linear partial differential equations with the mixed type simply supported boundary conditions prescribed on the edges. The complementary boundary constraints are introduced through boundary discontinuities generated by the selected boundary conditions for the derivation of the complementary solution. The numerical accuracy of the solution is compared by studying the comparisons of deflections, stresses and moments of symmetric and anti-symmetric laminated shells with finite element results using commercially available software under uniformly distributed load. Results are in good agreement with finite element counterparts. Additional results of the symmetric and anti-symmetric laminated and sandwich shells under single point load at the center and pressure load, are presented to provide data for the unsolved boundary conditions, benchmark comparisons and verifications.

• Journal of applied mathematics & informatics
• /
• 제26권5_6호
• /
• pp.819-837
• /
• 2008

A mixed type dual to the control problem in order to unify Wolfe and Mond-Weir type dual control problem is presented in various duality results are validated and the generalized invexity assumptions. It is pointed out that our results can be extended to the control problems with free boundary conditions. The duality results for nonlinear programming problems already existing in the literature are deduced as special cases of our results.

• Journal of Mechanical Science and Technology
• /
• 제15권6호
• /
• pp.685-692
• /
• 2001

This paper reports on the mixed lubrication characteristics between the cam and the tappet contact surface of direct acting type valve train systems. First, the dynamic characteristics are solved by using the lumped mass method to determine the load conditions at the contact point. Then, the minimum oil film thickness is calculated with consideration of elastohydrodynamic line contact theory and the friction force is obtained by using the mixed lubrication model which separates the hydrodynamic and the boundary friction. Finally, the average surface temperatures are calculated by using the flash temperature theory. The results show that, there are some peaks in the friction force due to the asperity contact friction, and flash temperature at the position of minimum oil film thickness. It is thought that there is a relationship between the surface temperature and cam surface wear, and therefore, the analysis on the worn cam profile has been performed.

• 대한기계학회논문집
• /
• 제8권3호
• /
• pp.232-240
• /
• 1984

본 논문에서는 Stern이 제시한 경로적분식을 기본방정식으로 하여 예리한 임 의 노치내각을 가진(크랙의 경우 0˚), 즉 r$^{.lambda.}$ 형태의 특이점을 포함한 모우드-I 및 II 응력확대계수를 위한 특성해 및 보조해를 규정하고 선택모형문제로 예리한 노치 내각을 달리한 대칭 하중의 인장문제와 끝단 전단력하중하의 일단 고정보의 비대칭문 제의 응력확대계수를 기존의 재래식 유한요소법과 결합하여 계산하였다. 또한 각각 의 경우 적분경로 및 요소분할을 달리하여 수치해의 안정성 및 경로 독립성을 검토하 였다.

• 유체기계공업학회:학술대회논문집
• /
• 유체기계공업학회 1999년도 유체기계 연구개발 발표회 논문집
• /
• pp.245-251
• /
• 1999

The structural analysis of a reactor coolant pump(RCP) of a nuclear power plant is very important for the safety assessment of the plant. Accurate boundary conditions for the heat transfer coefficient are required for reliable thermal stress analysis of the pump casing, especially in transient operations of the pump since the coolant properties are largely dependent on operational conditions. In the present study, a 3D mixed flow type coolant pump was modeled from the RCP drawings and analyzed in the steady state and number of transient flow conditions by using a commercial code STAR-CD. From the result of the computation, it is seem that the average heat transfer coefficients for the cases considered are found to be the suggested values of the manufacturer, Westinghouse Energy System. The unevenness in local heat transfer coefficients, however, is found to be considerable so that the use of average heat transfer coefficients in all boundaries might not give reliable thermal stresses.