• Title/Summary/Keyword: Newmark-$\beta$ method

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Transient Analysis of High-rise Wall-Frame Structures with Outriggers under Seismic Load (초고층 전단벽-골조 아웃리거 구조시스템의 지진하중에 대한 시간이력해석)

  • Kim, Jin Man;Choe, Eun Hui;Park, Dae Gyu;Lee, Jae Hong
    • Journal of Korean Society of Steel Construction
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    • v.20 no.2
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    • pp.303-312
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    • 2008
  • In this paper, the seismic behavior of shear wal-frame systems is analyzed. The governing equations of the wall-frame systems with outrigger truss are formulated through the continuum approach and the whole structure is idealized as a shear-flexural cantileverwith rotational spring. The effect of shear deformation and flexural deformation of the wall-frame and outrigger trusses are considered and incorporated in the formulation of the wall-frame structures with and without outriggers are compared by using finite element analysis incorporated with the Newmark-${\beta}$ method. Numerical results are obtained and compared with the finite element package MIDAS. The proposed method is found to be simple and efficient, and provides reason ably accurate results in the early design stage of tall building structures.

A Study on a Nonlinear Cable Finite Element (非線形 케이블 有限要素에 관한 硏究)

  • 장승필;박정일
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.1 no.1
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    • pp.93-101
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    • 1989
  • A geometrically nonlinear cable finite element is presented to use in the static or dynamic modeling of offshore and onshore structures such as guyed tower, tension leg platform or mooring buoy, submarine cable, cable-stayed bridge, suspension bridge, cable roof and so on. The cable finite element is derived directly from the compatibility equations and flexibility matrix of elastic catenary cable theory for the arbitary plane loading and geome try. A general and virsatile computer program has been developed to perform the analyses of cable member itself or cable guyed or suspened structures, in which Newmark-$\beta$ method is used to obtain a time domain solution and Newton-Raphson iteration method is used to solve the nonlinear system of compatibility equations of cable and algebraic static or dynamic equations at each time step. The results from the static and dynamic analysis of a cable member by the computer program are summarized and presented.

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An algorithm for quantifying dynamic buckling and post-buckling behavior of delaminated FRP plates with a rectangular hole stiffened by smart (SMA) stitches

  • Soltanieh, Ghazaleh;Yam, Michael C.H.
    • Smart Structures and Systems
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    • v.28 no.6
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    • pp.745-760
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    • 2021
  • Dynamic buckling of structure is one of the failure modes that needs to be considered since it may result in catastrophic failure of the structure in a short period of time. For a thin fiber-reinforced polymer (FRP) plate under compression, buckling is an inherent hazard which will be intensified by the existence of defects like holes, cracks, and delamination. On the other hand, the growth of the delamination is another prime concern for thin FRP plates. In the current paper, reinforcing the plates against buckling is realized by using SMA wires in the form of stitches. A numerical framework is proposed to simulate the dynamic instability emphasizing the effect of the SMA stitches in suppressing delamination growth. The suggested algorithm is more accurate than the other methods when considering the transformation point of the SMA wires and the modeling of the cohesive zone using simple and yet reliable technique. The computational design of the method by producing the line by line orders leads to a simple algorithm for simulating the super-elastic behavior. The Lagoudas constitutive model of the SMA material is implemented in the form of user material subroutines (VUMAT). The normal bilinear spring model is used to reproduce the cohesive zone behavior. The nonlinear finite element formulation is programmed into FORTRAN using the Newmark-beta numerical time-integration approach. The obtained results are compared with the results obtained by the finite element method using ABAQUS/Explicit solver. The obtained results by the proposed algorithm and those by ABAQUS are in good agreement.

Tethers tension force effect in the response of a squared tension leg platform subjected to ocean waves

  • El-gamal, Amr R.;Essa, Ashraf;Ismail, Ayman
    • Ocean Systems Engineering
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    • v.4 no.4
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    • pp.327-342
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    • 2014
  • The tension leg platform (TLP) is one of the compliant structures which are generally used for deep water oil exploration. With respect to the horizontal degrees of freedom, it behaves like a floating structure moored by vertical tethers which are pretension due to the excess buoyancy of the platform, whereas with respect to the vertical degrees of freedom, it is stiff and resembles a fixed structure and is not allowed to float freely. In the current study, a numerical study for square TLP using modified Morison equation was carried out in the time domain with water particle kinematics using Airy's linear wave theory to investigate the effect of changing the tether tension force on the stiffness matrix of TLP's, the dynamic behavior of TLP's; and on the fatigue stresses in the cables. The effect was investigated for different parameters of the hydrodynamic forces such as wave periods, and wave heights. The numerical study takes into consideration the effect of coupling between various degrees of freedom. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables. Nonlinear equation was solved using Newmark's beta integration method. Only uni-directional waves in the surge direction was considered in the analysis. It was found that for short wave periods (i.e., 10 sec.), the surge response consisted of small amplitude oscillations about a displaced position that is significantly dependent on tether tension force, wave height; whereas for longer wave periods, the surge response showed high amplitude oscillations that is significantly dependent on wave height, and that special attention should be given to tethers fatigue because of their high tensile static and dynamic stress.

Study on Steering Ratio of Four-Row Rigid Tracked Vehicle on Extremely Cohesive Soft Soil Using Numerical Simulation (수치해석을 이용한 연약지반 4열 강체 무한궤도 차량의 최적 선회비 연구)

  • Kim, Hyung-Woo;Lee, Chang-Ho;Hong, Sup;Choi, Jong-Su;Yeu, Tae-Kyeong;Min, Cheon-Hong
    • Journal of Ocean Engineering and Technology
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    • v.27 no.6
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    • pp.81-89
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    • 2013
  • This paper considers the steering characteristics of a four-row tracked vehicle crawling on extremely cohesive soft soil, where each side is composed of two parallel tracks. The four-row tracked vehicle (FRTV) is assumed to be a rigid body with 6-DOF. A dynamic analysis program for the tracked vehicle is developed using the Newmark-${\beta}$ method based on an incremental-iterative scheme. A terra-mechanics model of an extremely cohesive soft soil is implemented in the form of the relationships of the normal pressure to the sinkage, the shear resistance to the shear displacement, and the dynamic sinkage to the shear displacement. In order to investigate the steering characteristics of the four-row tracked vehicle, a series of dynamic simulations is conducted with respect to the distance between the left and right tracks (pitch), steering ratios, driving velocity, reference track velocity, lengths of the tracks, and properties of the cohesive soft soil. Through these numerical simulations, the possibility of using a kinematic steering ratio is explored.

Preliminary Study on the Development of a Performance Based Design Platform of Vertical Breakwater against Seismic Activity - Centering on the Weakened Shear Modulus of Soil as Shear Waves Go On (직립식 방파제 성능기반 내진 설계 Platform 개발을 위한 기초연구 - 전단파 횟수 누적에 따른 지반 강도 감소를 중심으로)

  • Choi, Jin Gyu;Cho, Yong Jun
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.30 no.6
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    • pp.306-318
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    • 2018
  • In order to evaluate the seismic capacity of massive vertical type breakwaters which have intensively been deployed along the coast of South Korea over the last two decades, we carry out the preliminary numerical simulation against the PoHang, GyeongJu, Hachinohe 1, Hachinohe 2, Ofunato, and artificial seismic waves based on the measured time series of ground acceleration. Numerical result shows that significant sliding can be resulted in once non-negligible portion of seismic energy is shifted toward the longer period during its propagation process toward the ground surface in a form of shear wave. It is well known that during these propagation process, shear waves due to the seismic activity would be amplified, and non-negligible portion of seismic energy be shifted toward the longer period. Among these, the shift of seismic energy toward the longer period is induced by the viscosity and internal friction intrinsic in the soil. On the other hand, the amplification of shear waves can be attributed to the fact that the shear modulus is getting smaller toward the ground surface following the descending effective stress toward the ground surface. And the weakened intensity of soil as the number of attacking shear waves are accumulated can also contribute these phenomenon (Das, 1993). In this rationale, we constitute the numerical model using the model by Hardin and Drnevich (1972) for the weakened shear modulus as shear waves go on, and shear wave equation, in the numerical integration of which $Newmark-{\beta}$ method and Modified Newton-Raphson method are evoked to take nonlinear stress-strain relationship into account. It is shown that the numerical model proposed in this study could duplicate the well known features of seismic shear waves such as that a great deal of probability mass is shifted toward the larger amplitude and longer period when shear waves propagate toward the ground surface.

A Study on Dynamic Behaviour of Cable-Stayed Bridge by Vehicle Load (차량하중에 의한 사장교의 동적거동에 관한 연구)

  • Park, Cheun Hyek;Han, Jai Ik
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.14 no.6
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    • pp.1299-1308
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    • 1994
  • This paper is considered on the dynamic behavior and the dynamic impact coefficient on the cable-stayed bridge under the vehicle load. The method of static analysis, that is, the transfer matrix method is used to get influence values about displacements, section forces of girder and cable forces. Gotten influence values were used as basic data to analyse dynamic behavior. This paper used the transfer matrix method because it is relatively simpler than the finite element method, and calculating speed of computer is very fast and the precision of computation is high. In the process of dynamic analysis, the uncoupled equation of motion is derived from simultaneous equation of the motion of cable-stayed bridge and vehicle travelling by using mode shape, which was borne from system of undamped free vibration. The solution of the uncoupled equation of motion, that is, time history of response of deflections, velocity and acceleration on reference coordinate system, is found by Newmark-${\beta}$ method, a kind of direct integral method. After the time history of dynamic response was gotten, and it was transfered to the time history of dynamic response of cable-stayed bridge by linear transformation of coordinates. As a result of this numerical analysis, effect of dynamic behavior for cable-stayed bridge under the vehicle load has varied depending on parameter of design, that is, the ratio of span, the ratio of main span length, tower height, the flexural rigidity of longitudinal girder, the flexural rigidity of tower, and the cable stiffness, investigated. Very good agreements with the existing solution in the literature are shown for the uncracked plate as well as the cracked plate.

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Seismic Performance Evaluation of a Cone-type Friction Pendulum Bearing System (원추형 마찰진자베어링의 내진성능평가)

  • Jeon, Bub-Gyu;Chang, Sung-Jin;Park, Kyung-Rock;Kim, Nam-Sik;Jung, Duk-Young
    • Journal of the Earthquake Engineering Society of Korea
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    • v.15 no.2
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    • pp.23-33
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    • 2011
  • In this study, a CFPBS (Cone-type Friction Pendulum Bearing System) was developed which controls the acceleration delivered to the structure to prevent damage and degradation of the critical communication equipment in case of an earthquake. The isolation performance of the CFPBS was evaluated by numerical analysis. The CFPBS was manufactured in the shape of a cone differenced from the existing FPS (Friction Pendulum System), and a pattern was engraved on the friction surface. The natural frequencies of the CFPBS were evaluated from a free-vibration test with the seismic isolator system consisting of four CFPBSs. In order to verify its earthquake-resistant performance, a numerical analysis program was created from the equation of the CFPBS induced from the equations of motion. A simplified theoretical equation of the CFPBS was proposed to manufacture the equipment which could demonstrate the necessary performance. Artificial seismic waves satisfying the maximum earthquake scale of the Korean Building Code-Structural (KBC-2005) were created and verified to review the earthquake-resistant performance of the CFPBS by numerical analysis. The superstructural mass of the CFPBS and skew angle of the friction surface were considered for numerical analysis with El Centro NS (1940), Kobe NS (1995) and artificial seismic waves. The CFPBS isolation performance evaluation was based on the results of numerical analysis and the executed comparative analysis between the results from numerical analysis and the simplified theoretical equation under the same conditions.