• Steel and Composite Structures
• /
• 제18권1호
• /
• pp.187-212
• /
• 2015

In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates.

• Geomechanics and Engineering
• /
• 제14권6호
• /
• pp.519-532
• /
• 2018

In this work, two dimensional (2D) and quasi three-dimensional (quasi-3D) HSDTs are proposed for bending and free vibration investigation of functionally graded (FG) plates using hyperbolic shape function. Unlike the existing HSDT, the proposed theories have a novel displacement field which include undetermined integral terms and contains fewer unknowns. The material properties of the plate is inhomogeneous and are considered to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The governing equations which consider the effects of both transverse shear and thickness stretching are determined through the Hamilton's principle. The closed form solutions are deduced by employing Navier method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. In-plane stress components have been determined by the constitutive equations of composite plates. The transverse stress components have been determined by integrating the 3D stress equilibrium equations in the thickness direction of the FG plate. The accuracy of the present formulation is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature.

• 자원환경지질
• /
• 제27권3호
• /
• pp.281-287
• /
• 1994

이 논문은 transverse 이방성(異方性) 매질내 Love 채널파동 수치해석에 관한 연구를 요약한 것이다. 먼저, 이를 위하여 상기한 매질내 SH파동방정식으로부터 2차 근사 양(陽)유한차분식을 유도하였다. 이 유한차분식은 매 격자점마다 상이한 물성을 정해줄 수 있기 때문에, 복잡한 모델구조를 추가로, 내부 경계조건 처리를 함이 없이, 매우 효율적으로 해석할 수 있을 것이다. 등방성(等方性) 석탄층에 대한 해석결과, 본 연구에서 작성한 탄성파기록이 기존의 Korn and $St{\ddot{o}}ckl$의 것과 본질적으로 동일함을 확인하였다. 다음, 이방성(異方性) 석탄층에 대한 해석에서는, Love 채널파동의 군(群)속도가 석탄층의 수평방향 속도의 증감에 따라 증감됨을 알 수 있었다. 그러나 현재의 연구단계에선, Love 채널파동을 이용하여 저(低) 속도층의 조성(組成), 층서(層序), 균열등에 관한 정보를 이끌어 낼 수는 없었다. 이러한 정보는 석유탐사 및 개발의 측면에서 중요하기 때문에, 앞으로 이와 관련된 채널파동 연구가 기대된다.

• 한국철도학회:학술대회논문집
• /
• 한국철도학회 2001년도 추계학술대회 논문집
• /
• pp.500-507
• /
• 2001

본 연구에서는 콘크리트도상궤도의 일본식 프리캐스트식 슬래브 궤도와 수정된 단면궤도에 대하여 유한요소 해석을 위한 새로운 강성행렬의 조합을 통하여 각 요소들간의 상호 작용에 대하여 파악하였으며, 상용 프로그램의 이용하여 열차의 횡방향 및 종방향 하중에 대한 정적 해석 및 열차하중을 일련의 주기함수로 가정한 동적 해석을 실시하여, 이미 제안된 바 있는 개선된 단면과 기존의 구조 형식과의 거동의 차이를 파악하였다. 종방향 정적 해석의 결과, 개선된 단면의 응력이 기존의 슬래브궤도의 돌기부에서의 응력 보다 작은 값이 나타났으며, 횡하중에 대한 정ㆍ동적 해석을 수행한 결과 새로운 슬래브 궤도에서 미소하나 변위량의 감소가 발생하였다. 그러나 동적 해석의 결과, 새로운 궤도 시스템이 기존의 일본식 슬래브궤도 시스템에 비하여 가속도 값이 약 30% 이상의 상당한 감소가 있었다.

• Structural Engineering and Mechanics
• /
• 제45권5호
• /
• pp.677-691
• /
• 2013

A semi-analytical finite strip method is developed for analyzing the post-buckling behavior of rectangular composite laminated plates of arbitrary lay-up subjected to progressive end-shortening in their plane and to normal pressure loading. In this method, all the displacements are postulated by the appropriate harmonic shape functions in the longitudinal direction and polynomial interpolation functions in the transverse direction. Thin or thick plates are assumed and correspondingly the Classical Plate Theory (CPT) or Higher Order Plate Theory (HOPT) is applied. The in-plane transverse deflection is allowed at the loaded ends of the plate, whilst the same deflection at the unloaded edges is either allowed to occur or completely restrained. Geometric non-linearity is introduced in the strain-displacement equations in the manner of the von-Karman assumptions. The formulations of the finite strip methods are based on the concept of the principle of the minimum potential energy. The Newton-Raphson method is used to solve the non-linear equilibrium equations. A number of applications involving isotropic plates, symmetric and unsymmetric cross-ply laminates are described to investigate the through-thickness shearing effects as well as the effect of pressure loading, end-shortening and boundary conditions. The study of the results has revealed that the response of the composite laminated plates is particularly influenced by the application of the Higher Order Plate Theory (HOPT) and normal pressure loading. In the relatively thick plates, the HOPT results have more accuracy than CPT.

• The Korean Journal of Pain
• /
• 제8권2호
• /
• pp.350-353
• /
• 1995

The first lesion in neural tissue produced by electrical currents were made in the 19th century by workers using direct current. In 1953, Sweet and Mark clearly demonstrated that DC lesions have unpredictable and ragged borders and may vary in size. They, as well as Hunsperger and Wyss, suggested that the use of high frequency currents might provide improved results and were proved correct. However, $Bovie^{(R)}$ electrosurgical unit may also be used in percutaneous medial branch neurotomy if a lesion made at a point or the dorsal surface of the transverse process just caudal to the most medial end of the superior edge of the transverse process (Bogduk's method). At this point the medial branch lies on the bone and its depth and medial displacement are defined by the bone which precludes the need for lateral radiographs to check placement. A lesion was made at same target point using the $Bovie^{(R)}$ electrosurgical unit in a 41 year male patient who had received a Kaneda operation because of L2 compression fracture. The patient was relieved of pain without any adverse effects.

• 한국전산구조공학회논문집
• /
• 제19권1호
• /
• pp.73-83
• /
• 2006

본 논문에서는 내구성과 수명을 획기적으로 향상시키기 위해 제3세대 건설재료인 섬유강화 플라스틱(FRP) 소재로 제작된 사각형 중공 교량 바닥판의 파괴모드를 실험과 해석을 통해 분석하였다. 재하시험 결과 바닥판의 강축방향의 거동은 파괴 직전까지도 거의 선형탄성적으로 거동한 반면, 약축방향의 거동은 재하초기부터 작은 하중하에서도 큰 비선형성을 보였다. 이 약축방향 비선형성의 원인은 웨브와 플랜지 연결부의 불완전한 일체거동으로 인한 소성거동 때문인 것으로 판단된다. 웨브와 플랜지의 연결부에 소성힌지를 도입한 간단한 구조모델을 이용하여 이를 확인하였다. 접착부의 박리 파괴 가능성도 검토하였으나 이는 대상 중공바닥판의 약축방향 파괴에 직접적으로 관여하는 것은 아닌 것으로 판단된다 약축방향의 구조거동을 개선시키기 위한 방안으로 내부를 폼으로 충전하는 방법을 제시하였으며 그 가능성을 구조해석을 통해 확인하였다.

• Structural Engineering and Mechanics
• /
• 제12권6호
• /
• pp.657-668
• /
• 2001

Fiber reinforced cementitious composites are nowadays widely applied in civil engineering. The postcracking performance of this material depends on the interaction between a steel fiber, which is obliquely across a crack, and its surrounding matrix. While the partly debonded steel fiber is subjected to pulling out from the matrix and simultaneously subjected to transverse force, it may be modelled as a Bernoulli-Euler beam partly supported on an elastic foundation with non-linearly varying modulus. The fiber bridging the crack may be cut into two parts to simplify the problem (Leung and Li 1992). To obtain the transverse displacement at the cut end of the fiber (Fig. 1), it is convenient to directly solve the corresponding differential equation. At the first glance, it is a classical beam on foundation problem. However, the differential equation is not analytically solvable due to the non-linear distribution of the foundation stiffness. Moreover, since the second order deformation effect is included, the boundary conditions become complex and hence conventional numerical tools such as the spline or difference methods may not be sufficient. In this study, moment equilibrium is the basis for formulation of the fundamental differential equation for the beam (Timoshenko 1956). For the cantilever part of the beam, direct integration is performed. For the non-linearly supported part, a transformation is carried out to reduce the higher order differential equation into one order simultaneous equations. The Runge-Kutta technique is employed for the solution within the boundary domain. Finally, multi-dimensional optimization approaches are carefully tested and applied to find the boundary values that are of interest. The numerical solution procedure is demonstrated to be stable and convergent.

• Steel and Composite Structures
• /
• 제18권2호
• /
• pp.443-465
• /
• 2015

In this paper, an efficient and simple trigonometric shear deformation theory is presented for thermal buckling analysis of functionally graded plates. It is assumed that the plate is in contact with elastic foundation during deformation. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the proposed sinusoidal shear deformation theory contains only four unknowns. It is assumed that the mechanical and thermal non-homogeneous properties of functionally graded plate vary smoothly by distribution of power law across the plate thickness. Using the non-linear strain-displacement relations, the equilibrium and stability equations of plates made of functionally graded materials are derived. The boundary conditions for the plate are assumed to be simply supported on all edges. The elastic foundation is modelled by two-parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. The effects of thermal loading types and variations of power of functionally graded material, aspect ratio, and thickness ratio on the critical buckling temperature of functionally graded plates are investigated and discussed.

• Coupled systems mechanics
• /
• 제8권5호
• /
• pp.439-457
• /
• 2019

In this paper, a new application of a four variable refined plate theory to analyze the nonlinear bending of functionally graded plates exposed to thermo-mechanical loadings, is presented. This recent theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces, and similarly, the shear components do not contribute toward bending moments. The derived transverse shear strains has a quadratic variation across the thickness that satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. The solutions are achieved by minimizing the total potential energy. The non-linear strain-displacement relations in the von Karman sense are used to derive the effect of geometric non-linearity. It is concluded that the proposed theory is accurate and simple in solving the nonlinear bending behavior of functionally graded plates.