• Title/Summary/Keyword: Nonlinear Stiffness

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A Damage Model for Predicting the Nonlinear Behavior of Rock (암석의 비선형 거동해석을 위한 손상모델 개발)

  • 장수호;이정인;이연규
    • Journal of the Korean Geotechnical Society
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    • v.18 no.5
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    • pp.83-97
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    • 2002
  • An experimental model which considers post-peak behaviors and pre-peak damage characteristics representing changes of elastic moduli in each damage level was developed. From experiments, some damage thresholds of rocks were determined, and regression analyses were carried out in order to represent changes of elastic moduli in each damage level as functions of confining pressure. In addition, it was intended to simulate post-peak behaviors with Hoek-Brown constants, $m_r\;and\;s_r$ for post-failure. The developed experimental model was implemented into $FLAC^{2D}$ by a FISH function. From results of parametric studies on Hoek-Brown constants for post-peak, it was revealed that uniaxial compressive strength more highly depends upon $s_r$, although it depends on both $m_r\;and\;s_r$. It was also shown that the post-peak slopes of stress-stain curves depend mainly on $m_r$. When the optimum models obtained from parametric studies were applied to numerical analysis, they predicted maximum strengths obtained from experiments and well simulated stiffness changes due to damage levels.

Numerical study on buckling of steel web plates with openings

  • Serror, Mohammed H.;Hamed, Ahmed N.;Mourad, Sherif A.
    • Steel and Composite Structures
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    • v.22 no.6
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    • pp.1417-1443
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    • 2016
  • Cellular and castellated steel beams are used to obtain higher stiffness and bending capacity using the same weight of steel. In addition, the beam openings may be used as a pass for different mechanical fixtures such as ducts and pipes. The aim of this study is to investigate the effect of different parameters on both elastic and inelastic critical buckling stresses of steel web plates with openings. These parameters are plate aspect ratio; opening shape (circular or rectangular); end distance to the first opening; opening spacing; opening size; plate slenderness ratio; steel grade; and initial web imperfection. The web/flange interaction has been simplified by web edge restraints representing simply supported boundary conditions. A numerical parametric study has been performed through linear and nonlinear finite element (FE) models, where the FE results have been verified against both experimental and numerical results in the literature. The web plates are subject to in-plane linearly varying compression with different loading patterns, ranging from uniform compression to pure bending. A buckling stress modification factor (${\beta}$-factor) has been introduced as a ratio of buckling stress of web plate with openings to buckling stress of the corresponding solid web plate. The variation of ${\beta}$-factor against the aforementioned parameters has been reported. Furthermore, the critical plate slenderness ratio separating elastic buckling and yielding has been identified and discussed for two steel grades of DIN-17100, namely: ST-37/2 and ST-52/3. The FE results revealed that the minimum ${\beta}$-factor is 0.9 for web plates under uniform compression and 0.7 for those under both compression and tension.

Nonlocal elasticity approach for free longitudinal vibration of circular truncated nanocones and method of determining the range of nonlocal small scale

  • Li, C.;Sui, S.H.;Chen, L.;Yao, L.Q.
    • Smart Structures and Systems
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    • v.21 no.3
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    • pp.279-286
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    • 2018
  • The free longitudinal vibration of a circular truncated nanocone is investigated based on the nonlocal elasticity theory. Exact analytical formulations for tapered nanostructures are derived and the nonlinear differential governing equation of motion is developed. The nonlocal small scale effect unavailable in classical continuum theory is addressed to reveal the long-range interaction of atoms implicated in nonlocal constitutive relation. Unlike most previous studies applying the truncation method to the infinite higher-order differential equation, this paper aims to consider all higher-order terms to show the overall nonlocality. The explicit solution of nonlocal stress for longitudinal deformation is determined and it is an infinite series incorporating the classical stress derived in classical mechanics of materials and the infinite higher-order derivative of longitudinal displacement. Subsequently, the first three modes natural frequencies are calculated numerically and the significant effects of nonlocal small scale and vertex angle on natural frequencies are examined. The coupling phenomenon of natural frequency is observed and it is induced by the combined effects of nonlocal small scale and vertex angle. The critical value of nonlocal small scale is defined, and after that a new proposal for determining the range of nonlocal small scale is put forward since the principle of choosing the nonlocal small scale is still unclear at present. Additionally, two different types of nonlocal effects, namely the nonlocal stiffness weakening and strengthening, reversed phenomena existing in nanostructures are observed and verified. Hence the opposite nonlocal effects are resolved again clearly. The nano-engineers dealing with a circular truncated nanocone-based sensors and oscillators may benefit from the present work.

Seismic Performance and Flexural Over-strength of Circular RC Column (원형 RC 기둥의 내진성능과 휨 초과강도)

  • Ko, Seong-Hyun
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.17 no.5
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    • pp.49-58
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    • 2013
  • Eight small scale circular reinforced concrete columns were tested under cyclic lateral load with constant axial load. Test specimens were designed with 4.5 aspect ratio. The selected test variables are longitudinal steel ratio, transverse steel ratio, yielding strength of longitudinal steel and axial load ratio. The test results of columns with different longitudinal steel ratio, transverse steel ratio and axial load ratio showed different seismic performance such as equivalent damping ratio, residual displacement and effective stiffness. It was found that the column with low strength of longitudinal steel showed significantly reduced seismic performance, especially for equivalent damping ratio and residual displacement. The regulation of flexural over-strength is adopted by Korea Bridge Design Specifications (Limited state design, 2012). The test results are compared with nominal strength, result of nonlinear moment-curvature analysis and the design specifications such as AASHTO LRFD and Korea Bridge Design Specifications (Limited state design).

Application of Hybrid Seismic Isolation System to Realize High Seismic Performance for Low-rise Lightweight Buildings (저층 경량건물의 고성능 내진을 위한 복합면진시스템의 적용)

  • Chun, Young-Soo
    • Land and Housing Review
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    • v.4 no.2
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    • pp.185-192
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    • 2013
  • This study presents application effects of hybrid seismic isolation system to realize high seismic performance for low-rise lightweight buildings through a non-linear analysis and onsite experiments. The complex seismic isolation system applied in this study is a method of mixing sliding bearing and laminated rubber bearing in order to overcome limitation of laminated rubber bearing in increasing natural period of the whole seismic isolation system. As a result of the non-linear analysis, seismic isolation buildings designed with complex seismic isolation system are safe because its maximum response displacement is within allowable design displacement even for a strong earthquake which rarely occurs and its maximum response shear is less than design seismic force. As a result of the onsite experiment, the rigidity of seismic isolation stories corresponds to approximately 95.8% of the design equivalent stiffness value. This indicates that actual properties of the whole seismic isolation system correspond to design values.

Development of Airframe Structure for Disaster and Public Safety Multicopter UAV (재난치안용 멀티콥터 무인기 기체구조 개발)

  • Shin, Jeong Woo;Lee, Seunggyu;Noh, Jeong Ho
    • Journal of Aerospace System Engineering
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    • v.14 no.3
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    • pp.69-77
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    • 2020
  • Airframe structure development of the 35 kg class 'Disaster and Public Safety Multicopter' UAV is described in this paper. To reduce the airframe weight, T-700 grade CFRP composite material was used, and the fuselage was designed with the semi-monocoque structure and plate installed with the control and communication devices designed in a sandwich structure. The specimen tests for the laminated plate and pipe were conducted to verify the strength and stiffness of the designed parts. The stacking sequence of composite materials was determined by the static strength and vibration analysis, and landing gear strut was designed by the nonlinear analysis with decent speed and ground clearance requirements. The static strength test was performed to evaluate the structural integrity and to verify the landing gear behavior.

Stochastic vibration suppression analysis of an optimal bounded controlled sandwich beam with MR visco-elastomer core

  • Ying, Z.G.;Ni, Y.Q.;Duan, Y.F.
    • Smart Structures and Systems
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    • v.19 no.1
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    • pp.21-31
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    • 2017
  • To control the stochastic vibration of a vibration-sensitive instrument supported on a beam, the beam is designed as a sandwich structure with magneto-rheological visco-elastomer (MRVE) core. The MRVE has dynamic properties such as stiffness and damping adjustable by applied magnetic fields. To achieve better vibration control effectiveness, the optimal bounded parametric control for the MRVE sandwich beam with supported mass under stochastic and deterministic support motion excitations is proposed, and the stochastic and shock vibration suppression capability of the optimally controlled beam with multi-mode coupling is studied. The dynamic behavior of MRVE core is described by the visco-elastic Kelvin-Voigt model with a controllable parameter dependent on applied magnetic fields, and the parameter is considered as an active bounded control. The partial differential equations for horizontal and vertical coupling motions of the sandwich beam are obtained and converted into the multi-mode coupling vibration equations with the bounded nonlinear parametric control according to the Galerkin method. The vibration equations and corresponding performance index construct the optimal bounded parametric control problem. Then the dynamical programming equation for the control problem is derived based on the dynamical programming principle. The optimal bounded parametric control law is obtained by solving the programming equation with the bounded control constraint. The controlled vibration responses of the MRVE sandwich beam under stochastic and shock excitations are obtained by substituting the optimal bounded control into the vibration equations and solving them. The further remarkable vibration suppression capability of the optimal bounded control compared with the passive control and the influence of the control parameters on the stochastic vibration suppression effectiveness are illustrated with numerical results. The proposed optimal bounded parametric control strategy is applicable to smart visco-elastic composite structures under deterministic and stochastic excitations for improving vibration control effectiveness.

Experimental and numerical investigation of reinforced concrete beams containing vertical openings

  • Parol, Jafarali;Ben-Nakhi, Ammar;Al-Sanad, Shaikha;Al-Qazweeni, Jamal;Al-Duaij, Hamad J.;Kamal, Hasan
    • Structural Engineering and Mechanics
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    • v.72 no.3
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    • pp.383-393
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    • 2019
  • Horizontal openings in reinforced concrete (RC) beams are quite often used to accommodate service pipelines. Several research papers are available in the literature describing their effect. RC beams with vertical openings are commonly used to accommodate service lines in residential buildings in Kuwait. However, there are lack of design guidelines and best practices reported in the literature for RC beams with vertical openings, whereas the detailed guidelines are available for beams with horizontal openings. In the present paper, laboratory experiments are conducted on nine RC beams with and without vertical openings. Parametric study has been carried out using nonlinear finite element analysis (FEA) with changes in the diameter of the opening, various positions of the opening along the length and width of the beam, edge distance, etc. 50 finite element simulations were conducted. The FEA results are verified using the results from the laboratory experiments. The study showed that the load carrying capacity of the beam is reduced by 20% for the RC beam with vertical openings placed near the center of the beam compared to a solid beam without an opening. Significant reduction in load carrying capacity is observed for beams with an opening near the support (${\approx}15%$). The overall stiffness of the beam, crack pattern and failure modes were not affected due to the presence of the vertical opening. Furthermore, an artificial neural network (ANN) analysis is carried out using the FEA generated data. The results and observations from the ANN and FEA are in good agreement with experimental results.

Cyclic testing of scaled three-story special concentrically braced frame with strongback column

  • Chen, Chui-Hsin;Tsai, Yi-Rung;Tang, Yao
    • Earthquakes and Structures
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    • v.17 no.2
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    • pp.163-173
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    • 2019
  • For Special Concentrically Braced Frame (SCBF), it is common that the damage concentrates at a certain story instead of spreading over all stories. Once the damage occurs, the soft-story mechanism is likely to take place and possibly to result in the failure of the whole system with more damage accumulation. In this study, we use a strongback column which is an additional structural component extending along the height of the building, to redistribute the excessive deformation of SCBF and activate more structural members to dissipate energy and thus avoid damage concentration and improve the seismic performance of SCBF. We tested one-third-scaled, three-story, double-story X SCBF specimens with static cyclic loading procedure. Three specimens, namely S73, S42 and S0, which represent different combinations of stiffness and strength factors ${\alpha}$ and ${\beta}$ for the strongback columns, were designed based on results of numerical simulations. Specimens S73 and S42 were the specimens with the strongback columns, and S0 is the specimen without the strongback column. Test results show that the deformation distribution of Specimen S73 is more uniform and more brace members in three stories perform nonlinearly. Comparing Drift Concentration Factor (DCF), we can observe 29% and 11% improvement in Specimen S73 and S42, respectively. This improvement increases the nonlinear demand of the third-story braces and reduces that of the first-story braces where the demand used to be excessive, and, therefore, postpones the rupture of the first-story braces and enhances the ductility and energy dissipation capacity of the whole SCBF system.

Numerical finite element study of a new perforated steel plate shear wall under cyclic loading

  • Farrokhi, Ali-Akbar;Rahimi, Sepideh;Beygi, Morteza Hosseinali;Hoseinzadeh, Mohamad
    • Earthquakes and Structures
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    • v.22 no.6
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    • pp.539-548
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    • 2022
  • Steel plate shear walls (SPSWs) are one of the most important and widely used lateral load-bearing systems. The reason for this is easier execution than reinforced concrete (RC) shear walls, faster construction time, and lower final weight of the structure. However, the main drawback of SPSWs is premature buckling in low drift ratios, which affects the energy absorption capacity and global performance of the system. To address this problem, two groups of SPSWs under cyclic loading were investigated using the finite element method (FEM). In the first group, several series of circular rings have been used and in the second group, a new type of SPSW with concentric circular rings (CCRs) has been introduced. Numerous parameters include in yield stress of steel plate wall materials, steel panel thickness, and ring width were considered in nonlinear static analysis. At first, a three-dimensional (3D) numerical model was validated using three sets of laboratory SPSWs and the difference in results between numerical models and experimental specimens was less than 5% in all cases. The results of numerical models revealed that the full SPSW undergoes shear buckling at a drift ratio of 0.2% and its hysteresis behavior has a pinching in the middle part of load-drift ratio curve. Whereas, in the two categories of proposed SPSWs, the hysteresis behavior is complete and stable, and in most cases no capacity degradation of up to 6% drift ratio has been observed. Also, in most numerical models, the tangential stiffness remains almost constant in each cycle. Finally, for the innovative SPSW, a relationship was suggested to determine the shear capacity of the proposed steel wall relative to the wall slenderness coefficient.