• Title/Summary/Keyword: Nonlinear Static Equation

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Estimation of 3D active earth pressure under nonlinear strength condition

  • Zhang, D.B.;Jiang, Y.;Yang, X.L.
    • Geomechanics and Engineering
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    • v.17 no.6
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    • pp.515-525
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    • 2019
  • The calculation of active earth pressure behind retaining wall is a typical three-dimensional (3D) problem with spatial effects. With the help of limit analysis, this paper firstly deduces the internal energy dissipation power equations and various external forces power equations of the 3D retaining wall under the nonlinear strength condition, such as to establish the work-energy balance equation. The pseudo-static method is used to consider the effect of earthquake on active earth pressure in horizontal state. The failure mode is a 3D curvilinear cone failure mechanism. For the different width of the retaining wall, the plane strain block is inserted in the symmetric plane. By optimizing all parameters, the maximum value of active earth pressure is calculated. In order to verify the validity of the new expressions obtained by the paper, the solutions are compared with previously published solutions. Agreement shows that the new expressions are effective. The results of different parameters are given in the forms of figures to analysis the influence caused by nonlinear strength parameters.

Rate-sensitive analysis of framed structures Part I: model formulation and verification

  • Izzuddin, B.A.;Fang, Q.
    • Structural Engineering and Mechanics
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    • v.5 no.3
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    • pp.221-237
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    • 1997
  • This paper presents a new uniaxial material model for rate-sensitive analysis addressing both the transient and steady-state responses. The new model adopts visco-plastic theory for the rate-sensitive response, and employs a three-parameter representation of the overstress as a function of the strain-rate. The third parameter is introduced in the new model to control its transient response characteristics, and to provide flexibility in fitting test data on the variation of overstress with strain-rate. Since the governing visco-plastic differential equation cannot be integrated analytically due to its inherent nonlinearity, a new single-step numerical integration procedure is proposed, which leads to high levels of accuracy almost independent of the size of the integration time-step. The new model is implemented within the nonlinear analysis program ADAPTIC, which is used to provide several verification examples and comparison with other experimental and numerical results. The companion paper extends the three-parameter model to trilinear static stress-strain relationships for steel and concrete, and presents application examples of the proposed models.

Spreading Kinetics of Poly(diisobutylene maleic acid) at the Air-water Interface

  • Kim, Nam Jeong
    • Journal of the Korean Applied Science and Technology
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    • v.32 no.4
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    • pp.661-668
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    • 2015
  • The surface rheological properties of polymer monolayer show complicated non-linear viscoelastic flow phenomena when they are subjected to spreading flow. These spreading flow properties are controlled by the characteristics of flow units. The kinetics of the formation of an interfacial film obtained after spreading poly(diisobutylene maleic acid) at air-water interface were studied by measuring of the surface pressure with time. The experimental data were analyzed theoretically according to a nonlinear surface viscoelastic model. The values of dynamic modulus, static modulus, surface viscosities and rheological parameters in various area/ monomer were obtained by appling experimental data to the equation of nonlinear surface viscoelastic model.

Analysis of Flexible Media Behavior by Dynamic Elastica (Dynamic Elastica에 의한 유연매체의 거동해석)

  • Hong, Sung-Kwon;Jee, Jung-Geun;Jang, Yong-Hoon;Park, No-Cheol;Park, Young-Pil
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2004.11a
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    • pp.600-605
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    • 2004
  • In many machines handling lightweight and flexible media such as magnetic tape drives, xerographic copiers and sewing machines, the media must transit an open space. It is important to predict the static and dynamic behavior of the sheets with a high degree of reliability. The nonlinear theory of the dynamic elastica has often been used to a nonlinear dynamic deflection model. In this paper, the governing equation is derived and simulated by the finite differential method. The parametric cubic curve is applied for defining the guide shape. The dynamic contact conditions suggested by Klarbring is used to predict the direction of the flexible media according to the initial velocity and the friction coefficient. The analysis is also compared to the conventional model, showing that after contacting a $45^{\circ}$ wall, the directions of flexible media of two models are different.

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Vector mechanics-based simulation of large deformation behavior in RC shear walls using planar four-node elements

  • Zhang, Hongmei;Shan, Yufei;Duan, Yuanfeng;Yun, Chung Bang;Liu, Song
    • Structural Engineering and Mechanics
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    • v.74 no.1
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    • pp.1-18
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    • 2020
  • For the large deformation of shear walls under vertical and horizontal loads, there are difficulties in obtaining accurate simulation results using the response analysis method, even with fine mesh elements. Furthermore, concrete material nonlinearity, stiffness degradation, concrete cracking and crushing, and steel bar damage may occur during the large deformation of reinforced concrete (RC) shear walls. Matrix operations that are involved in nonlinear analysis using the traditional finite-element method (FEM) may also result in flaws, and may thus lead to serious errors. To solve these problems, a planar four-node element was developed based on vector mechanics. Owing to particle-based formulation along the path element, the method does not require repeated constructions of a global stiffness matrix for the nonlinear behavior of the structure. The nonlinear concrete constitutive model and bilinear steel material model are integrated with the developed element, to ensure that large deformation and damage behavior can be addressed. For verification, simulation analyses were performed to obtain experimental results on an RC shear wall subjected to a monotonically increasing lateral load with a constant vertical load. To appropriately evaluate the parameters, investigations were conducted on the loading speed, meshing dimension, and the damping factor, because vector mechanics is based on the equation of motion. The static problem was then verified to obtain a stable solution by employing a balanced equation of motion. Using the parameters obtained, the simulated pushover response, including the bearing capacity, deformation ability, curvature development, and energy dissipation, were found to be in accordance with the experimental observation. This study demonstrated the potential of the developed planar element for simulating the entire process of large deformation and damage behavior in RC shear walls.

An Analytic Solution of the Shape of a Partially Filled, Submerged Membrane Container (수중 유체저장용 막구조물 형상의 이론적 해석)

  • Choi, Yoon-Rak
    • Journal of Ocean Engineering and Technology
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    • v.22 no.5
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    • pp.39-43
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    • 2008
  • For a partially filled and deeply submersed membrane container, an analytic solution for similarity shape was studied. The static shape of a membrane container can be expressed as a set of nonlinear ordinary differential equations. These equations are combined into an integrable equation. The solution of the equation is derived in terms of elliptic integrals, the arguments of which contain an unknown at the point of inflection. The point of inflection is determined by using the boundary condition at a separating point. Some characteristic values of the similarity shape were evaluated and the shapes are illustrated.

A numerical study on the flow and noise radiation in curved intake (굴곡형 흡입구에서의 유동 및 소음방사 해석)

  • Shim, In-Bo;Lee, Duck-Joo;An, Chang-Su
    • 유체기계공업학회:학술대회논문집
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    • 2001.11a
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    • pp.76-80
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    • 2001
  • Unsteady compressible Euler equation is solved and the high-order, high-resolution numerical solver, physical boundary condition, adaptive nonlinear artificial dissipation model and conformal mapping are applied to computation of steady transonic flow and unsteady acoustics. The acoustic characteristics of axi-symmetric duct and two dimensional straight/S channel are studied and the computation results shows good agreements with linear analysis. In transonic case, local time stepping and canceling-the-residual techniques are used for convergence acceleration. The aspect of flow and acoustics in S-channel and the Pattern of noise radiation is changed by inflow Mach no. and static pressure at fan-face.

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Electromechanical Characteristics of a Squirrel Cage Induction Motor due to Broken Rotor Bars and Rotor Eccentricity (회전자 바 개방과 회전자 편심에 의한 단삼 유도 전동기의 전기 및 기계적 특성 해석)

  • Park, Sang-Jin;Jang, Jeong-Hwan;Jang, Geon-Hui;Lee, Yong-Bok;Kim, Chang-Ho
    • The Transactions of the Korean Institute of Electrical Engineers B
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    • v.51 no.8
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    • pp.425-433
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    • 2002
  • This research investigates the electromechanical characteristics of a sing1e-phase squirrel cage induction motor due to broken rotor bars and rotor eccentricity. Numerical analysis is performed by solving the nonlinear time-stepping finite element equation coupled with the magnetic field equation, circuit equation and mechanical equation of motion. It shows that the asymmetry of magnetic flux due to the broken rotor bars and rotor eccentricity introduce a change in the stator current, torque, speed, magnetic force and vibration of a rotor at the same time. However, even in the existence of rotor eccentricity, 3 broken rotor bar introduces a dominant change in the magnetic force and rotor displacement, i.e., beating phenomenon in time domain and sideband frequencies in frequency spectra, respectively.

An applied model for steel reinforced concrete columns

  • Lu, Xilin;Zhou, Ying
    • Structural Engineering and Mechanics
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    • v.27 no.6
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    • pp.697-711
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    • 2007
  • Though extensive research has been carried out for the ultimate strength of steel reinforced concrete (SRC) members under static and cyclic load, there was only limited information on the applied analysis models. Modeling of the inelastic response of SRC members can be accomplished by using a microcosmic model. However, generally used microcosmic model, which usually contains a group of parameters, is too complicated to apply in the nonlinear structural computation for large whole buildings. The intent of this paper is to develop an effective modeling approach for the reliable prediction of the inelastic response of SRC columns. Firstly, five SRC columns were tested under cyclic static load and constant axial force. Based on the experimental results, normalized trilinear skeleton curves were then put forward. Theoretical equation of normalizing point (ultimate strength point) was built up according to the load-bearing mechanism of RC columns and verified by the 5 specimens in this test and 14 SRC columns from parallel tests. Since no obvious strength deterioration and pinch effect were observed from the load-displacement curve, hysteresis rule considering only stiffness degradation was proposed through regression analysis. Compared with the experimental results, the applied analysis model is so reasonable to capture the overall cyclic response of SRC columns that it can be easily used in both static and dynamic analysis of the whole SRC structural systems.

Static performance analysis of deepwater compliant vertical access risers

  • Lou, Min;Li, Run;Wu, Wugang;Chen, Zhengshou
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.11 no.2
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    • pp.970-979
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    • 2019
  • Compliant Vertical Access Risers (CVARs) are compliant systems that incorporate a differentiated geometric configuration that allows the exploitation of oil and gas in deepwater fields and enables a number of operational advantages in the offshore system. One of the main features of CVAR systems is that they allow direct intervention procedures to be applied to the well bore, enabling workover operations to be performed directly from the production platform. Based on the principles of virtual work and variation, a static geometric nonlinear equation of CVARs is derived and applied in this study. The results of this study show that the two ends of the riser as well as the transition region are subject to high stress, while the positions of the floating platform exert significant effects on the geometry of the riser configuration. Compliance and buoyancy factors should be set moderately to reduce the CVAR stress. In addition, the buoyancy modules should be placed in the lower region, in order to maximize the operation advantages of CVAR.