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The mixed-mode stress intensity factors of 2-D angled cracks are evaluated by Petrov-Galerkin natural element (PG-NE) method in which Voronoi polygon-based Laplace interpolation functions and CSFE basis functions are used for the trial and test functions respectively. The interaction integral is implemented in a frame of PG-NE method in which the weighting function defined over a crack-tip integral domain is interpolated by Laplace interpolation functions. Two Cartesian coordinate systems are employed and the displacement, strains and stresses which are solved in the grid-oriented coordinate system are transformed to the other coordinate system aligned to the angled crack. The present method is validated through the numerical experiments with the angled edge and center cracks, and the numerical accuracy is examined with respect to the grid density, crack length and angle. Also, the stress intensity factors obtained by the present method are compared with other numerical methods and the exact solution. It is observed from the numerical results that the present method successfully and accurately evaluates the mixed-mode stress intensity factors of 2-D angled cracks for various crack lengths and crack angles.
본 연구는 2.5MW급 풍력발전기용 기어박스의 동특성 분석에 관한 것으로서, 유연핀(flexible pin) 채용에 따른 유성기어축의 미스얼라인먼트(misalignment) 개선여부와 충격하중에 따른 기어박스의 동응답 특성을 유한요소해석을 통해 고찰하였다. 내부의 복잡한 기어시스템의 하중전달을 정확하게 그리고 효과적으로 반영하기 위해 치접촉을 등가 치강성계수를 갖는 스프링요소와 물림률을 이용하여 모델링하였다. 기어의 등가 치강성계수는 기어치에 대한 변형해석을 통해 계산하였으며, 동특성 분석을 위해 기어박스 입력단에 충격 토오크를 부과하였다. 수치실험을 통해 등가 치강성모델의 타당성을 검증하였으며, 양단 그리고 일단 고정축과의 상대 비교를 통해 유연핀 적용에 따른 유성기어축의 미스얼라인먼트 개선여부를 확인할 수 있었다. This study is concerned with the numerical investigation of dynamic characteristics of 2.5MW-class wind turbine gearbox in which the misalignment improvement of plenary gear shafts by the flexible pins and the dynamic impact response are analyzed by the finite element method. The tooth contact between gears is modelled using the line element having the equivalent tooth stiffness and the contact ratio to accurately and effectively reflect the load transmission in the internal complex gear system. The equivalent tooth stiffness is calculated by utilizing the tooth deformation analysis and the impulse torque is applied to the input shaft for the dynamics response characteristic analysis. Through the numerical experiments, the equivalent tooth stiffness model was validated and the misalignment improvement of planetary gear shafts was confirmed from the comparison with the cases of fixed shafts at one and both ends.
The power steering hose in automotive power steering system is composed of a rubber hose and two metal fittings. The rubber hose is reinforced by fabric braided layers, while metal fittings are firmly clamped to both ends of rubber hose by the special swaging job. Since the main function of power steering hose is to circulate internal oil without oil leakage, the swaging process of metal fitting should be elaborately designed based on the profound investigation of process characteristics. However, owing to the complex micro structure of braided layers, the swaging process has been investigated either by time- and cost-consuming experiment or by the simple numerical analysis in which the braided layers are simplified as an isotropic solid. To overcome the demerit of experiment and to improve the accuracy of numerical method, an effective numerical analysis method by considering the anisotropy of braided layer is presented in this paper. The braided layers are modeled as an orthotropic solid and their equivalent material properties are derived by utilizing the homogenization method. Through the numerical experiments, the difference between the simple isotropic model and the current orthotropic one is compared, and the swaging process characteristics are investigated to the helix angle.
This paper is concerned with the numerical calculation of mixed-mode stress intensity factors (SIFs) of 2-D isotropic functionally graded materials (FGMs) by the natural element method (more exactly, Petrov-Galerkin NEM). The spatial variation of elastic modulus in non-homogeneous FGMs is reflected into the modified interaction integral (1,2). The local NEM grid near the crack tip is refined, and the directly approximated strain and stress fields by PG-NEM are enhanced and smoothened by the patch recovery technique. Two numerical examples with the exponentially varying elastic modulus are taken to illustrate the proposed method. The mixed-mode SIFs are parametrically computed with respect to the exponent index in the elastic modulus and external loading and the crack angle and compared with the other reported results. It has been justified from the numerical results that the present method successfully and accurately calculates the mixed-mode stress intensity factors of 2-D non-homogeneous functionally graded materials.
본 논문은 균열선단 그리드 세분화기법을 소개하고 자연요소법을 이용한 균열해석에 이 기법을 적용함으로서 그 유효성을 고찰하였다. 유한요소법에 있어서의 국부적 h-세분화와 같이 높은 응력 특이성을 보이는 균열선단 주위를 따라 자연요소법 그리드를 국부적으로 세분화하였다. 본 논문에서 소개되는 그리드 세분화기법은 2단계로 구성되며, 1단계에서는 그리드 점들이 추가되고 2단계에서는 균열선단 절점을 공유하는 델라우니 삼각형들이 나뉘게 된다. 제안하는 그리드 세분화기법의 타당성과 균열해석에서의 유효성을 입증하기 위해 대칭 엣지 균열을 갖는 평면 변형률 상태의 사각 평판을 해석하였다. 수치해석 결과의 상대비교를 위해 균일한 자연요소 그리드를 이용한 균열해석도 수행하였으며, 균열선단이 세분화된 그리드는 균일한 그리드와는 달리 이론해와 조밀한 그리드와 유사한 균열선단 응력분포를 나타내었다. 또한, 총 그리드 절점수에 대한 해석결과의 전역 상대오차에서도 세분화된 그리드가 균일한 그리드에 비해 높은 수렴율 나타내었다. This paper introduces a near-tip grid refinement and explores its usefulness in the crack analysis by the natural element method(NEM). As a sort of local h-refinement in finite element method(FEM), a NEM grid is locally refined around the crack tip showing high stress singularity. This local grid refinement is completed in two steps in which grid points are added and Delaunay triangles sharing the crack tip node are divided. A plane strain rectangular plate with symmetric edge cracks is simulated to validate the proposed local grid refinement and to examine its usefulness in the crack analysis. The crack analysis is also simulated using a uniform NEM grid for comparison. Unlike the uniform grid, the refined grid provides near-tip stress distributions similar to the analytic solutions and the fine grid. In addition, the refined grid shows higher convergence than the uniform grid, the global relative error to the total number of grid points.
The goal of current study is to numerically investigate the dynamic response characteristics of cylindrical baffled liquid storage tank, which is subjected to a vertical acceleration at boosting, with respect to the number of baffles. Both the storage tank and baffles are modeled as flexible elastic structures, and the suppression of sloshing-induced dynamic responses by baffles are evaluated in terms of the hydrodynamic pressure, the dynamic displacement and stress. Through the numerical experiments, it has been observed that the introduction of baffles to the partially filled liquid tank remarkably decreases the maximum values of displacement and effective stress at both the bottom plate and baffles. And, the variation of displacement and effective stress is stabilized much faster when baffles are installed and the baffle number increases. Thus, it has been verified that the baffled liquid storage tank can be stably and safely applied to the liquid fuel storage tank for various transport vehicles.
A semi-analytical numerical approach for the effective structural dynamic response analysis of spar floating substructure for offshore wind turbine subject to wave-induced excitation is introduced in this paper. The wave-induced rigid body motions at the center of mass are analytically solved using the dynamic equations of rigid ship motion. After that, the flexible structural dynamic responses of spar floating substructure for offshore wind turbine are numerically analyzed by letting the analytically derived rigid body motions be the external dynamic loading. Restricted to one-dimensional sinusoidal wave excitation at sea state 3, pitch and heave motions are considered. Through the numerical experiments, the time responses of heave and pitch motions are solved and the wave-induced dynamic displacement and effective stress of flexible floating substructure are investigated. The hydrodynamic interaction between wave and structure is modeled by means of added mass and wave damping, and its modeling accuracy is verified from the comparison of natural frequencies obtained by experiment with a 1/100 scale model.