• Title/Summary/Keyword: Stiffness matrix

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Investigation of Tensile Behaviors in Open Hole and Bolt Joint Configurations of Carbon Fiber/Epoxy Composites

  • Dong-Wook Hwang;Sanjay Kumar;Dong-Hun Ha;Su-Min Jo;Yun-Hae Kim
    • Composites Research
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    • v.36 no.4
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    • pp.259-263
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    • 2023
  • This study investigated the open hole tensile (OHT) properties of carbon fiber/epoxy composites and compared them to bolt joint tensile (BJT) properties. The net nominal modulus and strength (1376 MPa) were found to be higher than the gross nominal strength (1041 MPa), likely due to increasing hole size. The OHT and BJT specimens exhibited similar stiffness, as expected without bolt rotation causing secondary bending. OHT specimens experienced a sharp drop in stress indicating unstable crack propagation, delamination, and catastrophic failure. BJT specimens failed through shear out on the bolt side and bearing failure on the nut side, involving fiber kinking, matrix splitting, and delamination, resulting in lower strength compared to OHT specimens. The strength retention of carbon fiber/epoxy composites with open holes was 66%. Delamination initiation at the hole's edge caused a reduction in the stress concentration factor. Filling the hole with a bolt suppressed this relieving mechanism, leading to lower strength in BJT specimens compared to OHT specimens. Bolt joint efficiency was calculated as 15%. The reduction in strength in bolted joints was attributed to fiber-matrix splitting and delamination, aligning with Hart Smith's bolted joint efficiency diagram. These findings contribute to materials selection and structural reliability estimation for carbon fiber/epoxy composites. They highlight the behavior of open hole and bolt joint configurations under tensile loading, providing valuable insights for engineering applications.

Free vibration analysis of a laminated trapezoidal plate with GrF-PMC core and wavy CNT-reinforced face sheets

  • Yingqun Zhang;Qian Zhao;Qi Han;N. Bohlooli
    • Steel and Composite Structures
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    • v.48 no.3
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    • pp.275-291
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    • 2023
  • This paper has focused on presenting vibration analysis of trapezoidal sandwich plates with 3D-graphene foam reinforced polymer matrix composites (GrF-PMC) core and FG wavy CNT-reinforced face sheets. The porous graphene foam possessing 3D scaffold structures has been introduced into polymers for enhancing the overall stiffness of the composite structure. Also, 3D graphene foams can distribute uniformly or non-uniformly in the plate thickness direction. The effective Young's modulus, mass density and Poisson's ratio are predicted by the rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. The First-order shear deformation theory of plate is utilized to establish governing partial differential equations and boundary conditions for trapezoidal plate. The governing equations together with related boundary conditions are discretized using a mapping-generalized differential quadrature (GDQ) method in spatial domain. Then natural frequencies of the trapezoidal sandwich plates are obtained using GDQ method. Validity of the current study is evaluated by comparing its numerical results with those available in the literature. It is explicated that 3D-GrF skeleton type and weight fraction, carbon nanotubes (CNTs) waviness and CNT aspect ratio can significantly affect the vibrational behavior of the sandwich structure. The plate's normalized natural frequency decreased and the straight carbon nanotube (w=0) reached the highest frequency by increasing the values of the waviness index (w).

Structural system identification by measurement error-minimization observability method using multiple static loading cases

  • Lei, Jun;Lozano-Galant, Jose Antonio;Xu, Dong;Zhang, Feng-Liang;Turmo, Jose
    • Smart Structures and Systems
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    • v.30 no.4
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    • pp.339-351
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    • 2022
  • Evaluating the current condition of existing structures is of primary importance for economic and safety reasons. This can be addressed by Structural System Identification (SSI). A reliable static SSI depends on well-designed sensor configuration and loading cases, as well as efficient parameter estimation algorithms. Static SSI by the Measurement Error-Minimizing Observability Method (MEMOM) is a model-based deterministic static SSI method that could estimate structural parameters from static responses. In the current state of the art, this method is only applicable when structures are subjected to one loading case. This might lead to lack of information in some local regions of the structure (such as the null curvatures zones). To address this issue, the SSI by MEMOM using multiple loading cases is proposed in this work. Observability equations obtained from different loading cases are concatenated simultaneously and an optimization procedure is introduced to obtain the estimations by minimizing the discrepancy between the predicted response and the measured one. In addition, a Genetic-Algorithm (GA)-based Optimal Sensor Placement (OSP) method is proposed to tackle the OSP problem under multiple static loading cases for the very first time. In this approach, the Fisher Information Matrix (FIM)'s determinant is used as the metric of the goodness of sensor configurations. The numerical examples of a 3-span continuous bridge and a 13-story frame, are analyzed to validate the applicability of the extended SSI by MEMOM and the GA-based OSP method.

Level Set Based Topological Shape Optimization of Hyper-elastic Nonlinear Structures using Topological Derivatives (위상 민감도를 이용한 초탄성 비선형 구조의 레벨셋 기반 위상 및 형상 최적설계)

  • Kim, Min-Geun;Ha, Seung-Hyun;Cho, Seonho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.25 no.6
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    • pp.559-567
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    • 2012
  • A level set based topological shape optimization method for nonlinear structure considering hyper-elastic problems is developed. To relieve significant convergence difficulty in topology optimization of nonlinear structure due to inaccurate tangent stiffness which comes from material penalization of whole domain, explicit boundary for exact tangent stiffness is used by taking advantage of level set function for arbitrary boundary shape. For given arbitrary boundary which is represented by level set function, a Delaunay triangulation scheme is used for current structure discretization instead of using implicit fixed grid. The required velocity field in the actual domain to update the level set equation is determined from the descent direction of Lagrangian derived from optimality conditions. The velocity field outside the actual domain is determined through a velocity extension scheme based on the method suggested by Adalsteinsson and Sethian(1999). The topological derivatives are incorporated into the level set based framework to enable to create holes whenever and wherever necessary during the optimization.

Prediction of the Natural Frequency of Pile Foundation System in Sand during Earthquake (사질토 지반에 놓인 지진하중을 받는 말뚝 기초 시스템의 고유 진동수 예측)

  • Yang, Eui-Kyu;Kwon, Sun-Yong;Choi, Jung-In;Kim, Myoung-Mo
    • Journal of the Korean Geotechnical Society
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    • v.26 no.1
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    • pp.45-54
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    • 2010
  • It is important to calculate the natural frequency of a piled structure in the design stage in order to prevent resonance-induced damage to the pile foundation and analyze the dynamic behavior of the piled structure during an earthquake. In this paper, a simple but relatively accurate method employing a mass-spring model is presented for the evaluation of the natural frequency of a pile-soil system. Greatly influencing the calculation of the natural frequency of a piled structure, the spring stiffness between a pile and soil was evaluated by using the coefficient of subgrade reaction, the p-y curve, and the subsoil elastic modulus. The resulting natural frequencies were compared with those of 1-g shaking table tests. The comparison showed that the natural frequency of the pile-soil system could be most accurately calculated by constructing a stiffness matrix with the spring stiffness of the Reese (1974) method, which utilizes the coefficient of the subgrade reaction modulus, and Yang's (2009) dynamic p-y backbone curve method. The calculated natural frequencies were within 5% error compared with those of the shaking table tests for the pile system in dry dense sand deposits and 5% to 40% error for the pile system in saturated sand deposits depending on the occurrence of excess pore water pressure in the soil.

Fiber Finite Element Mixed Method for Nonlinear Analysis of Steel-Concrete Composite Structures (강-콘크리트 합성구조물의 비선형해석을 위한 화이버 유한요소 혼합법)

  • Park, Jung-Woong;Kim, Seung-Eock
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.28 no.6A
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    • pp.789-798
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    • 2008
  • The stiffness method provides a framework to calculate the structural deformations directly from solving the equilibrium state. However, to use the displacement shape functions leads to approximate estimation of stiffness matrix and resisting forces, and accordingly results in a low accuracy. The conventional flexibility method uses the relation between sectional forces and nodal forces in which the equilibrium is always satisfied over all sections along the element. However, the determination of the element resisting forces is not so straightforward. In this study, a new fiber finite element mixed method has been developed for nonlinear anaysis of steel-concrete composite structures in the context of a standard finite element analysis program. The proposed method applies the Newton method based on the load control and uses the incremental secant stiffness method which is computationally efficient and stable. Also, the method is employed to analyze the steel-concrete composite structures, and the analysis results are compared with those obtained by ABAQUS. The comparison shows that the proposed method consistently well predicts the nonlinear behavior of the composite structures, and gives good efficiency.

Real-Time Haptic Rendering for Tele-operation with Varying Communication Time Delay (가변적인 통신지연시간을 갖는 원격 작업 환경을 위한 실시간 햅틱 렌더링)

  • Lee, K.;Chung, S.Y.
    • Journal of Power System Engineering
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    • v.13 no.2
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    • pp.71-82
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    • 2009
  • This paper presents a real-time haptic rendering method for a realistic force feedback in a remote environment with varying communication time-delay. The remote environment is assumed as a virtual environment based on a computer graphics, for example, on-line shopping mall, internet game and cyber-education. The properties of a virtual object such as stiffness and viscosity are assumed to be unknown because they are changed according to the contact position and/or a penetrated depth into the object. The DARMAX model based output estimator is proposed to trace the correct impedance of the virtual object in real-time. The output estimator is developed on the input-output relationship. It can trace the varying impedance in real-time by virtue of P-matrix resetting algorithm. And the estimator can trace the correct impedance by using a white noise that prevents the biased input-output information. Realistic output forces are generated in real-time, by using the inputs and the estimated impedance, even though the communication time delay and the impedance of the virtual object are unknown and changed. The generated forces trace the analytical forces computed from the virtual model of the remote environment. Performance is demonstrated by experiments with a 1-dof haptic device and a spring-damper-based virtual model.

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Mechanical and Thermal Behavior of Polyamide-6/Clay Nanocomposite Using Continuum-based Micromechanical Modeling

  • Weon, Jong-Il
    • Macromolecular Research
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    • v.17 no.10
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    • pp.797-806
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    • 2009
  • The mechanical and thermal behaviors of polyamide-6/clay nanocomposites were studied using the continuum-based, micromechanical models such as Mori-Tanaka, Halpin-Tsai and shear lag. Mechanic-based model prediction provides a better understanding regarding the dependence of the nanocomposites' reinforcement efficiency on conventional filler structural parameters such as filler aspect ratio ($\alpha$), filler orientation (S), filler weight fraction (${\Psi}_f$), and filler/matrix stiffness ratio ($E_f/E_m$). For an intercalated and exfoliated nanocomposite, an effective, filler-based, micromechanical model that includes effective filler structural parameters, the number of platelets per stack (n) and the silicate inter-layer spacing ($d_{001}$), is proposed to describe the mesoscopic intercalated filler and the nanoscopic exfoliated filler. The proposed model nicely captures the experimental modulus behaviors for both intercalated and exfoliated nanocomposites. In addition, the model prediction of the heat distortion temperature is examined for nanocomposites with different filler aspect ratio. The predicted heat distortion temperature appears to be reasonable compared to the heat distortion temperature obtained by experimental tests. Based on both the experimental results and model prediction, the reinforcement efficiency and heat resistance of the polyamide-6/clay nanocomposites definitely depend on both conventional (${\alpha},\;S,\;{\Psi}_f,\;E_f/E_m$) and effective (n, $d_{001}$) filler structural parameters.

Shaft resistance of bored cast-in-place concrete piles in oil sand - Case study

  • Barr, L.;Wong, R.C.K.
    • Geomechanics and Engineering
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    • v.5 no.2
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    • pp.119-142
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    • 2013
  • Pile load tests using Osterberg cells (O-cell) were conducted on cast-in-place concrete piles founded in oil sand fill and in situ oil sand at an industrial plant site in Fort McMurray, Alberta, Canada. Interpreted pile test results show that very high pile shaft resistance (with the Bjerrum-Burland or Beta coefficient of 2.5-4.5) against oil sand could be mobilized at small relative displacements of 2-3% of shaft diameter. Finite element simulations based on linear elastic and elasto-plastic models for oil sand materials were used to analyze the pile load test measurements. Two constitutive models yield comparable top-down load versus pile head displacement curves, but very different behaviour in mobilization of pile shaft and end bearing resistances. The elasto-plastic model produces more consistent matching in both pile shaft and end bearing resistances whereas the linear elastic under- and over-predicts the shaft and end bearing resistances, respectively. The mobilization of high shaft resistance in oil sand under pile load is attributed to the very dense and interlocked structure of oil sand which results in high matrix stiffness, high friction angle, and high shear dilation.

A new 3D interface element for three dimensional finite element analysis of FRP strengthened RC beams

  • Kohnehpooshi, O.;Noorzaei, J.;Jaafar, M.S.;Saifulnaz, M.R.R.
    • Interaction and multiscale mechanics
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    • v.4 no.4
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    • pp.257-271
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    • 2011
  • The analysis of interfacial stresses in structural component has been the subject of several investigations but it still requires more effort and studies. In this study a general three-dimensional interface element has been formulated for stress and displacement analyses in the interfacial area between two adjacent plate bending element and brick element. Interface element has 16 nodes with 5 degrees of freedom (DOF) in each node adjacent to plate bending element and 3 DOF in each node adjacent to brick element. The interface element has ability to transfer three translations from each side of interface element and two rotations in the side adjacent to the plate element. Stiffness matrix of this element was formulated and implemented in three-dimensional finite element code. Application of this element to the reinforced concrete (RC) beam strengthened with fiber reinforced polymer (FRP) including variation of deflection, slip between plate and concrete, normal and shear stresses distributions in FRP plates have been verified using experimental and numerical work of strengthened RC beams carried out by some researchers. The results show that this interface element is effective and can be used for structural component with these types of interface elements.