• Title/Summary/Keyword: Stiffness matrix

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Spectral Element Formulation for Analysis of Lamb Wave Propagation on a Plate Induced by Surface Bonded PZT Transducers (표면 부착형 PZT소자에 의해 유발된 판 구조물의 램파 전달 해석을 위한 스펙트럼 요소 정식화)

  • Lim, Ki-Lyong;Kim, Eun-Jin;Kang, Joo-Sung;Park, Hyun-Woo
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.18 no.11
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    • pp.1157-1169
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    • 2008
  • This paper presents spectral element formulation which approximates Lamb wave propagation by PZT transducers bonded on a thin plate. A two layer beam model under 2-D plane strain condition is introduced to simulate high-frequency dynamic responses induced by a piezoelectric (PZT) layer rigidly bonded on a base plate. Mindlin-Herrmann and Timoshenko beam theories are employed to represent the first symmetric and anti-symmetric Lamb wave modes on a base plate, respectively. The Euler-Bernoulli beam theory and 1-D linear piezoelectricity are used to model the electro-mechanical behavior of a PZT layer. The equations of motions of a two layer beam model are derived through Hamilton's principle. The necessary boundary conditions associated with the electro-mechanical properties of a PZT layer are formulated in the context of dual functions of a PZT layer as an actuator and a sensor. General spectral shape functions of response field and the associated boundary conditions are obtained through equations of motions converted into frequency domain. Detailed spectrum element formulation for composing the dynamic stiffness matrix of a two layer beam model is presented as well. The validity of the proposed spectral element is demonstrated through numerical examples.

An Analysis of the Springing Phenomenon of a Ship Advancing in Waves (파랑 중에 전진하는 선박에 대한 스프링잉 현상 해석)

  • H.Y. Lee;H. Shin;H.S. Park;J.H. Park
    • Journal of the Society of Naval Architects of Korea
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    • v.38 no.3
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    • pp.41-46
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    • 2001
  • The very large vessels like VLCC and container ship have been built recently and those vessels have smaller structural strength in comparison with the other convectional skips. As a result the fatigue destruction of upper deck occurs a frequently due to the springing phenomenon at the encountering frequencies. In this study, the hydrodynamic loads are calculated by three-dimensional source distribution method with the translating and pulsating Green function. A ship is longitudinally divided into 23 sections and the added mass, damping and hydrodynamic force of each section is calculated. focusing only on the vertical motion. Stiffness matrix is calculated by the Euler beam theory. The calculation is carried out for Esso Osaka.

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Transverse cracking based numerical analysis and its effects on cross-ply laminates strength under thermo-mechanical degradation

  • Abdelatif, Berriah;Abdelkader, Megueni;Abdelkader, Lousdad
    • Structural Engineering and Mechanics
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    • v.60 no.6
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    • pp.1063-1077
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    • 2016
  • Components manufactured from composite materials are frequently subjected to superimposed mechanical and thermal loadings during their operating service. Both types of loadings may cause fracture and failure of composite structures. When composite cross-ply laminates of type [$0_m/90_n]_s$ are subjected to uni-axial tensile loading, different types of damage are set-up and developed such as matrix cracking: transverse and longitudinal cracks, delamination between disoriented layers and broken fibers. The development of these modes of damage can be detrimental for the stiffness of the laminates. From the experimental point of view, transverse cracking is known as the first mode of damage. In this regard, the objective of the present paper is to investigate the effect of transverse cracking in cross-ply laminate under thermo-mechanical degradation. A Finite Element (FE) simulation of damage evolution in composite crossply laminates of type [$0_m/90_n]_s$ subjected to uni-axial tensile loading is carried out. The effect of transverse cracking on the cross-ply laminate strength under thermo-mechanical degradation is investigated numerically. The results obtained by prediction of the numerical model developed in this investigation demonstrate the influence of the transverse cracking on the bearing capacity and resistance to damage as well as its effects on the variation of the mechanical properties such as Young's modulus, Poisson's ratio and coefficient of thermal expansion. The results obtained are in good agreement with those predicted by the Shear-lag analytical model as well as with the obtained experimental results available in the literature.

Sparassis crispa (Wulf.) Extract Inhibits IL-1β Stimulated Inflammatory Mediators Production on SW1353 Human Chondrocytes (인간 유래 연골세포에서 꽃송이버섯 추출물의 염증성 매개인자 억제 효과)

  • Kim, Eun-Nam;Jeong, Gil-Saeng
    • Korean Journal of Pharmacognosy
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    • v.49 no.4
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    • pp.305-311
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    • 2018
  • Osteoarthritis (OA) is the most common form of joint disease, characterized by articular cartilage, osteonecrosis, and osteochondral bone erosion. It is an early, progressive disease that combines joint stiffness and joint pain and reduces cartilage function and condition. Interleukin-1 beta ($IL-1{\beta}$) is thought to be important to the pathogenesis of OA and significantly increases the expression of matrix metalloproteinases (MMPs), which play an important role in cartilage degradation in OA. Sparassis crispa (Wulf.) is an edible / medicinal mushroom that has been reported to variety of biological activities. In this study, investigated the Anti-inflammatory effect of Sparassis crispa (Wulf.) ethanol extract (SCE) on $IL-1{\beta}$ stimulated SW1353 chondrocytes. SCE decreased the expression and activity of MMPs by $IL-1{\beta}$ and decreased the levels of cyclooxygenase-2 (COX-2) and inducible nitric oxide synthase (iNOS) associated with the inhibition of prostaglandin E2($PGE_2$) in $IL-1{\beta}$ stimulated SW-1353 chondrocytes. In addition, SCE inhibits the expression of MAPK (mitogen-activated protein kinase) and $NF-{\kappa}B$ (nuclear factor-kappa B) signaling in $IL-1{\beta}$ stimulated SW-1353 cells, and SCE inhibits the production of reactive oxygen species (ROS) through heme oxygenase-1 (HO-1) expression. Thus, it is suggested that SCE has a potential as an anti-inflammatory agent in osteoarthritis treatments.

Effects of NaCl Concentration and Solution Temperature on the Galvanic Corrosion Between CFRP and A516Gr.55 Carbon Steel

  • Hur, Seung Young;Kim, Ki Tae;Kim, Young Sik
    • Corrosion Science and Technology
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    • v.18 no.4
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    • pp.129-137
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    • 2019
  • CFRP (Carbon Fiber Reinforced Plastics) is composed of carbon fiber and plastic resin, and is approximately 20 - 50% lighter than metallic materials. CFRP has a low density, higher specific stiffness, specific strength, and high corrosion resistance. Because of these excellent properties, which meet various regulation conditions needed in the industrial fields, CFRP has been widely used in many industries including aviation and ship building. However, CFRP reveals water absorption in water immersion or high humidity environments, and water absorption occurs in an epoxy not carbon fiber, and can be facilitated by higher temperature. Since these properties can induce volume expansion inside CFRP and change the internal stress state and degrade the chemical bond between the fiber and the matrix, the mechanical properties including bond strength may be lowered. This study focused on the effects of NaCl concentration (0.01 - 1% NaCl) and solution temperature ($30-75^{\circ}C$) on the galvanic corrosion between CFRP and A516Gr.55 carbon steel. When NaCl concentration increases 10 times, corrosion rate of a specimen was not affected, but that of galvanic coupled carbon steel increased by 46.9% average. However, when solution temperature increases $10^{\circ}C$, average corrosion rate increased approximately 22%, regardless of single or galvanic coupled specimen.

Continuous force excited bridge dynamic test and structural flexibility identification theory

  • Zhou, Liming;Zhang, Jian
    • Structural Engineering and Mechanics
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    • v.71 no.4
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    • pp.391-405
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    • 2019
  • Compared to the ambient vibration test mainly identifying the structural modal parameters, such as frequency, damping and mode shapes, the impact testing, which benefits from measuring both impacting forces and structural responses, has the merit to identify not only the structural modal parameters but also more detailed structural parameters, in particular flexibility. However, in traditional impact tests, an impacting hammer or artificial excitation device is employed, which restricts the efficiency of tests on various bridge structures. To resolve this problem, we propose a new method whereby a moving vehicle is taken as a continuous exciter and develop a corresponding flexibility identification theory, in which the continuous wheel forces induced by the moving vehicle is considered as structural input and the acceleration response of the bridge as the output, thus a structural flexibility matrix can be identified and then structural deflections of the bridge under arbitrary static loads can be predicted. The proposed method is more convenient, time-saving and cost-effective compared with traditional impact tests. However, because the proposed test produces a spatially continuous force while classical impact forces are spatially discrete, a new flexibility identification theory is required, and a novel structural identification method involving with equivalent load distribution, the enhanced Frequency Response Function (eFRFs) construction and modal scaling factor identification is proposed to make use of the continuous excitation force to identify the basic modal parameters as well as the structural flexibility. Laboratory and numerical examples are given, which validate the effectiveness of the proposed method. Furthermore, parametric analysis including road roughness, vehicle speed, vehicle weight, vehicle's stiffness and damping are conducted and the results obtained demonstrate that the developed method has strong robustness except that the relative error increases with the increase of measurement noise.

Vector form intrinsic finite-element analysis of static and dynamic behavior of deep-sea flexible pipe

  • Wu, Han;Zeng, Xiaohui;Xiao, Jianyu;Yu, Yang;Dai, Xin;Yu, Jianxing
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.12 no.1
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    • pp.376-386
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    • 2020
  • The aim of this study was to develop a new efficient strategy that uses the Vector form Intrinsic Finite-element (VFIFE) method to conduct the static and dynamic analyses of marine pipes. Nonlinear problems, such as large displacement, small strain, and contact and collision, can be analyzed using a unified calculation process in the VFIFE method according to the fundamental theories of point value description, path element, and reverse motion. This method enables analysis without the need to integrate the stiffness matrix of the structure, because only motion equations of particles established according to Newton's second law are required. These characteristics of the VFIFE facilitate the modeling and computation efficiencies in analyzing the nonlinear dynamic problem of flexible pipe with large deflections. In this study, a three-dimensional (3-D) dynamical model based on 3-D beam element was established according to the VFIFE method. The deep-sea flexible pipe was described by a set of spatial mass particles linked by 3-D beam element. The motion and configuration of the pipe are determined by these spatial particles. Based on this model, a simulation procedure to predict the 3-D dynamical behavior of flexible pipe was developed and verified. It was found that the spatial configuration and static internal force of the mining pipe can be obtained by calculating the stationary state of pipe motion. Using this simulation procedure, an analysis was conducted on the static and dynamic behaviors of the flexible mining pipe based on a 1000-m sea trial system. The results of the analysis proved that the VFIFE method can be efficiently applied to the static and dynamic analyses of marine pipes.

Characteristics of Static Buckling Load of the Hexagonal Spatial Truss Models using Timber (목재를 이용한 육각형 공간 트러스 모델의 정적좌굴하중 특성)

  • Ha, Hyeonju;Shon, Sudeok;Lee, Seungjae
    • Journal of Korean Association for Spatial Structures
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    • v.22 no.3
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    • pp.25-32
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    • 2022
  • In this paper, the instability of the domed spatial truss structure using wood and the characteristics of the buckling critical load were studied. Hexagonal space truss was adopted as the model to be analyzed, and two boundary conditions were considered. In the first case, the deformation of the inclined member is only considered, and in the second case, the deformation of the horizontal member is also considered. The materials of the model adopted in this paper are steel and timbers, and the considered timbers are spruce, pine, and larch. Here, the inelastic properties of the material are not considered. The instability of the target structure was observed through non-linear incremental analysis, and the buckling critical load was calculated through the singularities and eigenvalues of the tangential stiffness matrix at each incremental step. From the analysis results, in the example of the boundary condition considering only the inclined member, the critical buckling load was lower when using timber than when using steel, and the critical buckling load was determined according to the modulus of elasticity of timber. In the case of boundary conditions considering the effect of the horizontal member, using a mixture of steel and timber case had a lower buckling critical load than the steel case. But, the result showed that it was more effective in structural stability than only timber was used.

Model order reduction for Campbell diagram analysis of shaft-disc-blade system in 3D finite elements

  • Phuor, Ty;Yoon, GilHo
    • Structural Engineering and Mechanics
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    • v.81 no.4
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    • pp.411-428
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    • 2022
  • This paper presents the Campbell diagram analysis of the rotordynamic system using the full order model (FOM) and the reduced order model (ROM) techniques to determine the critical speeds, identify the stability and reduce the computational time. Due to the spin-speed-dependent matrices (e.g., centrifugal stiffening matrix), several model order reduction (MOR) techniques may be considered, such as the modal superposition (MS) method and the Krylov subspace-based MOR techniques (e.g., Ritz vector (RV), quasi-static Ritz vector (QSRV), multifrequency quasi-static Ritz vector (MQSRV), multifrequency/ multi-spin-speed quasi-static Ritz vector (MMQSRV) and the combined Ritz vector & modal superposition (RV+MS) methods). The proposed MMQSRV method in this study is extended from the MQSRV method by incorporating the rotational-speed-dependent stiffness matrices into the Krylov subspace during the MOR process. Thus, the objective of this note is to respond to the question of whether to use the MS method or the Krylov subspace-based MOR technique in establishing the Campbell diagram of the shaft-disc-blade assembly systems in three-dimensional (3D) finite element analysis (FEA). The Campbell diagrams produced by the FOM and various MOR methods are presented and discussed thoroughly by computing the norm of relative errors (ER). It is found that the RV and the MS methods are dominant at low and high rotating speeds, respectively. More precisely, as the spinning velocity becomes large, the calculated ER produced by the RV method is significantly increased; in contrast, the ER produced by the MS method is smaller and more consistent. From a computational point of view, the MORs have substantially reduced the time computing considerably compared to the FOM. Additionally, the verification of the 3D FE rotordynamic model is also provided and found to be in close agreement with the existing solutions.

Numerical Formulation of Thermo-Hydro-Mechanical Interface Element (열-수리-역학 거동 해석을 위한 경계면 요소의 수식화)

  • Shin, Hosung;Yoon, Seok
    • Journal of the Korean Geotechnical Society
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    • v.38 no.9
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    • pp.45-52
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    • 2022
  • Because discontinuity in the rock mass and contact of soil-structure interaction exhibits coupled thermal-hydromechanical (THM) behavior, it is necessary to develop an interface element based on the full governing equations. In this study, we derive force equilibrium, fluid continuity, and energy equilibrium equations for the interface element. Additionally, we present a stiffness matrix of the elastoplastic mechanical model for the interface element. The developed interface element uses six nodes for displacement and four nodes for water pressure and temperature in a two-dimensional analysis. The fully coupled THM analysis for fluid injection into a fault can model the complicated evolution of injection pressure due to decreasing effective stress in the fault and thermal contraction of the surrounding rock mass. However, the result of hydromechanical analysis ignoring thermal phenomena overestimates hydromechanical variables.