• Title/Summary/Keyword: compatibility equations

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An Iterative Method to Determine Deformed Shape of Cable (케이블 처짐 형상 결정을 위한 반복 계산법의 개발)

  • 정진환;조현영;박용명;계만수
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.15 no.4
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    • pp.715-725
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    • 2002
  • In this study, a method to determine the deformed shape of planar cable under vertical loads was presented. To obtain the deformed shape of cable by general cable theorem, a sag at arbitrary point is usually given. However, in general cases without a given sag, the proposed method determines the deformed shape of cable based on the equations of cable theorem and geometric compatibility by iterative way. The method was also extended to slove extensible cable. It was acknowledged from numerical analysis and model tests in laboratory that the proposed method is valid lot analysis of extensible cable as well as unextensible cable.

Strong formulation finite element method for arbitrarily shaped laminated plates - Part I. Theoretical analysis

  • Fantuzzi, Nicholas;Tornabene, Francesco
    • Advances in aircraft and spacecraft science
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    • v.1 no.2
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    • pp.125-143
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    • 2014
  • This paper provides a new technique for solving the static analysis of arbitrarily shaped composite plates by using Strong Formulation Finite Element Method (SFEM). Several papers in literature by the authors have presented the proposed technique as an extension of the classic Generalized Differential Quadrature (GDQ) procedure. The present methodology joins the high accuracy of the strong formulation with the versatility of the well-known Finite Element Method (FEM). The continuity conditions among the elements is carried out by the compatibility or continuity conditions. The mapping technique is used to transform both the governing differential equations and the compatibility conditions between two adjacent sub-domains into the regular master element in the computational space. The numerical implementation of the global algebraic system obtained by the technique at issue is easy and straightforward. The main novelty of this paper is the application of the stress and strain recovery once the displacement parameters are evaluated. Computer investigations concerning a large number of composite plates have been carried out. SFEM results are compared with those presented in literature and a perfect agreement is observed.

Monte Carlo analysis of earthquake resistant R-C 3D shear wall-frame structures

  • Taskin, Beyza;Hasgur, Zeki
    • Structural Engineering and Mechanics
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    • v.22 no.3
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    • pp.371-399
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    • 2006
  • The theoretical background and capabilities of the developed program, SAR-CWF, for stochastic analysis of 3D reinforced-concrete shear wall-frame structures subject to seismic excitations is presented. Incremental stiffness and strength properties of system members are modeled by extended Roufaiel-Meyer hysteretic relation for bending while shear deformations for walls by Origin-Oriented hysteretic model. For the critical height of shear-walls, division to sub-elements is performed. Different yield capacities with respect to positive and negative bending, finite extensions of plastic hinges and P-${\delta}$ effects are considered while strength deterioration is controlled by accumulated hysteretic energy. Simulated strong motions are obtained from a Gaussian white-noise filtered through Kanai-Tajimi filter. Dynamic equations of motion for the system are formed according to constitutive and compatibility relations and then inserted into equivalent It$\hat{o}$-Stratonovich stochastic differential equations. A system reduction scheme based on the series expansion of eigen-modes of the undamaged structure is implemented. Time histories of seismic response statistics are obtained by utilizing the computer programs developed for different types of structures.

The Compatibility of MSDS through the Investigation of the Combustible Properties for MEK (MEK의 연소특성 고찰을 통한 MSDS의 적정성)

  • Ha, Dong-Myeong
    • Journal of the Korean Society of Safety
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    • v.23 no.3
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    • pp.36-41
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    • 2008
  • For the safety design and operation of many chemical process, it is necessary to know certain explosion limit, flash point and autoignition temperature(AIT) of handling substances. Also it is necessary to know explosion limit at high temperature and pressure. For the safe handling of MEK(methyl ethyl ketone), explosion limit at $25^{\circ}C$ and the temperature dependence of the explosion limits were investigated. And flash point and AIT for MEK were experimented. By using the literatures data, the lower and upper explosion limits of MEK recommended 1.8 vol% and 11.0 vol%, respectively. In this study, measured the lower and upper flash points of MEK were $-5^{\circ}C$ and $22^{\circ}C$, respectively. This study measured relationship between the AITs and the ignition delay times by using ASTM E659-78 apparatus for MEK, and the experimental AIT of MEK was $507^{\circ}C$. The new equations for predicting the temperature dependence of the explosion limits of MEK is proposed. The values calculated by the proposed equations were a good agreement with the literature data.

Verification of Proposed Design Equation for Stress Evaluation of Unbonded Tendons (비부착 긴장재의 응력을 평가하기 위해 제안된 설계식의 타당성검증)

  • Lim, Jae-Hyung;Moon, Jeong-Ho;Lee, Li-Hyung
    • Magazine of the Korea Concrete Institute
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    • v.11 no.2
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    • pp.127-137
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    • 1999
  • In the previous study in relation to the current study, a test program for the verification of the proposed design equation was carried with fourteen prestressed concrete beams with unbonded tendons. Experimental results were compared with the computed results by the proposed design equations. The previous design equations are ACI code, AASHTO LRFD code, the analysis equation with the strain compatibility, Harajli/Kanj' design equation, Chakrabarti' design equation. As a result of comparative studies, it turned out that the proposed design equation could predict the ultimate tendon stress with comparatively high accuracy.

Stress Analysis of the Hard Disk with Overcoating Layer under the Contact with Head (헤드와의 접촉에 의한 오버코팅층을 포함한 하드 디스크의 응력 해석)

  • Lee, Gang-Yong;Yang, Ji-Hyeok
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.4 s.175
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    • pp.946-954
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    • 2000
  • The purposes of the paper are to calculate stresses and strains of the disk with overcoating layer rotating quickly under normal loading and shear loading by contacting with head and to present material properties preventing the delamination between the disk and overcoating layer. The hard disk is modeled as two-layered disk composed with overcoating layer and the rest layers and the loading onto the disk is assumed axisymmetric. Solutions to equilibrium equations and compatibility equations are derived with the form of polynimial and Bessel function and coefficients satisfying boundary conditions are obtained differently for the case of body force, normal force and shear force. The risk of delamination are investigated for us to calculate the differences of strains at the interface between the disk and overcoating layer and the material properties preventing delamination are presented by calculating the differences of strains according to Young's modulus and density of disk.

Bridge-vehicle coupled vibration response and static test data based damage identification of highway bridges

  • Zhu, Jinsong;Yi, Qiang
    • Structural Engineering and Mechanics
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    • v.46 no.1
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    • pp.75-90
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    • 2013
  • In order to identify damage of highway bridges rapidly, a method for damage identification using dynamic response of bridge induced by moving vehicle and static test data is proposed. To locate damage of the structure, displacement energy damage index defined from the energy of the displacement response time history is adopted as the indicator. The displacement response time histories of bridge structure are obtained from simulation of vehicle-bridge coupled vibration analysis. The vehicle model is considered as a four-degree-of-freedom system, and the vibration equations of the vehicle model are deduced based on the D'Alembert principle. Finite element method is used to discretize bridge and finite element model is set up. According to the condition of displacement and force compatibility between vehicle and bridge, the vibration equations of the vehicle and bridge models are coupled. A Newmark-${\beta}$ algorithm based professional procedure VBAP is developed in MATLAB, and used to analyze the vehicle-bridge system coupled vibration. After damage is located by employing the displacement energy damage index, the damage extent is estimated through the least-square-method based model updating using static test data. At last, taking one simply supported bridge as an illustrative example, some damage scenarios are identified using the proposed damage identification methodology. The results indicate that the proposed method is efficient for damage localization and damage extent estimation.

An accurate substructural synthesis approach to random responses

  • Ying, Z.G.;Zhu, W.Q.;Ye, S.Q.;Ni, Y.Q.
    • Structural Engineering and Mechanics
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    • v.39 no.1
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    • pp.47-75
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    • 2011
  • An accurate substructural synthesis method including random responses synthesis, frequency-response functions synthesis and mid-order modes synthesis is developed based on rigorous substructure description, dynamic condensation and coupling. An entire structure can firstly be divided into several substructures according to different functions, geometric and dynamic characteristics. Substructural displacements are expressed exactly by retained mid-order fixed-interfacial normal modes and residual constraint modes. Substructural interfacial degree-of-freedoms are eliminated by interfacial displacements compatibility and forces equilibrium between adjacent substructures. Then substructural mode vibration equations are coupled to form an exact-condensed synthesized structure equation, from which structural mid-order modes are calculated accurately. Furthermore, substructural frequency-response function equations are coupled to yield an exact-condensed synthesized structure vibration equation in frequency domain, from which the generalized structural frequency-response functions are obtained. Substructural frequency-response functions are calculated separately by using the generalized frequency-response functions, which can be assembled into an entire-structural frequency-response function matrix. Substructural power spectral density functions are expressed by the exact-synthesized substructural frequency-response functions, and substructural random responses such as correlation functions and mean-square responses can be calculated separately. The accuracy and capacity of the proposed substructure synthesis method is verified by numerical examples.

Finite Element Modal Analysis of a Spinning Flexible Disk-Spindle System Considering the Flexiblity of Supporting Structures and an Actuator in a HDD (지지구조와 액츄에이터의 유연성을 고려한 HDD 유연 회전 디스크-스핀들 시스템의 유한 요소 고유 진동 해석)

  • Seo, Chan-Hee;Lee, Chang-Suk;Jang, Gun-Hee;Lee, Ho-Sung
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.11a
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    • pp.330-336
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    • 2005
  • This paper presents a method to analyze the vibration of a flexible spinning disk-spindle system with FDBs, flexible base structure and an actuator in a HDD by using the FEM. Finite element equations of each component of a HDD spindle system from the spinning flexible disk to the flexible base plate are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by using the restarted Arnoldi iteration method. The validity of the proposed method is verified by comparing the simulated natural frequencies, mode shapes with the experimental results.

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Attenuation of quasi-Lamb waves in a hydroelastic system "elastic plate+compressible viscous fluid+rigid wall"

  • Akbarov, Surkay D.;Negin, Mesut
    • Structural Engineering and Mechanics
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    • v.81 no.4
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    • pp.443-459
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    • 2022
  • The paper studies the dispersion and attenuation of propagating waves in the "plate+compressible viscous fluid layer" system in the case where the fluid layer flow is restricted with a rigid wall, and in the case where the fluid layer has a free face. The motion of the plate is described by the exact equations of elastodynamics and the flow of the fluid by the linearized Navier-Stokes equations for compressible barotropic Newtonian viscous fluids. Analytical expressions are obtained for the amplitudes of the sought values, and the dispersion equation is derived using the corresponding boundary and compatibility conditions. To find the complex roots of the dispersion equation, an algorithm based on equating the modulus of the dispersion determinant to zero is developed. Numerical results on the dispersion and attenuation curves for various pairs of plate and fluid materials under different fluid layer face conditions are presented and discussed. Corresponding conclusions on the influence of the problem parameters on the dispersion and attenuation curves are made and, in particular, it is established that the change of the free face boundary condition with the impermeability condition can influence the dispersion and attenuation curves not only in the quantitative, but also in the qualitative sense.