• Title/Summary/Keyword: Newton′s equilibrium

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Geometrically non-linear static analysis of a simply supported beam made of hyperelastic material

  • Kocaturk, T.;Akbas, S.D.
    • Structural Engineering and Mechanics
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    • v.35 no.6
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    • pp.677-697
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    • 2010

  • This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

  • https://doi.org/10.12989/sem.2010.35.6.677 인용 KSCI

Large deflection analysis of orthotropic, elliptic membranes

  • Chucheepsakul, Somchai;Kaewunruen, Sakdirat;Suwanarat, Apiwat
    • Structural Engineering and Mechanics
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    • v.31 no.6
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    • pp.625-638
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    • 2009

  • Applications of membrane mechanisms are widely found in nano-devices and nano-sensor technologies nowadays. An alternative approach for large deflection analysis of the orthotropic, elliptic membranes - subject to gravitational, uniform pressures often found in nano-sensors - is described in this paper. The material properties of membranes are assumed to be orthogonally isotropic and linearly elastic, while the principal directions of elasticity are parallel to the coordinate axes. Formulating the potential energy functional of the orthotropic, elliptic membranes involves the strain energy that is attributed to inplane stress resultant and the potential energy due to applied pressures. In the solution method, Rayleigh-Ritz method can be used successfully to minimize the resulting total potential energy generated. The set of equilibrium equations was solved subsequently by Newton-Raphson. The unparalleled model formulation capable of analyzing the large deflections of both circular and elliptic membranes is verified by making numerical comparisons with existing results of circular membranes as well as finite element solutions. The results are found in excellent agreements at all cases. Then, the parametric investigations are given to delineate the impacts of the aspect ratios and orthotropic elasticity on large static tensions and deformations of the orthotropic, elliptic membranes.

  • https://doi.org/10.12989/sem.2009.31.6.625 인용 KSCI

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.

  • https://doi.org/10.12652/Ksce.2008.28.6A.789 인용 PDF

Modeling of Wheeled-Mobile Robots and Path-Tracking using Time-Scaling Method (구륜이동로봇의 모델링과 Time-Scaling 기법을 이용한 경로추적)

  • Kim, Choung-Soo
    • Journal of the Korea Computer Industry Society
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    • v.5 no.9
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    • pp.993-1004
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    • 2004

  • We propose the method for kinematic and dynamic modeling and Path-tracking of four-wheeled mobile robots with 2 d.o.f having the limited drive-torques. Controllability of wheeled-mobile robots is revealed by using the kinematic model. Instantaneously coincident coordinate system, force/torque propagation and Newton's equilibrium law are used to induce the dynamic model. When drive-torques generated by inverse dynamics exceed the limitation, we make wheeled-mobile robots follow the reference path by modifying the planned reference trajectory with time-scaling. The controller is introduced to compensate for error owing to modeling uncertainty and measurement noise. And simulation results prove that the method proposed by this paper is efficient.

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A Study on the Analytical Technique of Stability and Buckling Characteristics of the Single Layer Latticed Domes (단층 래티스돔의 안정해석기법 및 좌굴특성에 관한 연구)

  • Han, Sang-Eul
    • Computational Structural Engineering
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    • v.9 no.3
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    • pp.209-216
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    • 1996

  • The primary objective of this paper is to grasp many characteristics of buckling behavior of latticed spherical domes under various conditions. The Arc-Length Method proposed by E.Riks is used for the computation and evaluation of geometrically nonlinear fundamental equilibrium paths and bifurcation points. And the direction of the path after the bifurcation point is decided by means of Hosono's concept. Three different nonlinear stiffness matrices of the Slope-Deflection Method are derived for the system with rigid nodes and results of the numerical analysis are examined in regard to geometrical parameters such as slenderness ratio, half-open angle, boundary conditions, and various loading types. But in case of analytical model 2 (rigid node), the post-buckling path could not be surveyed because of Newton-Raphson iteration process being diversed on the critical point since many eigenvalues become zero simultaneously.

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Form Finding of a Single-layered Pneumatic Membrane Structures by Using Nonlinear Force Method (비선형 내력법을 이용한 단일 공기막의 형상 탐색)

  • Shon, Sudeok;Ha, Junhong;Lee, Seungjae
    • Journal of Korean Association for Spatial Structures
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    • v.21 no.4
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    • pp.49-56
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    • 2021

  • This study aims to develop a form-finding algorithm for a single-layered pneumatic membrane. The initial shape of this pneumatic membrane, which is an air-supported type pneumatic membrane, is to find a state in which a given initial tension and internal pneumatic pressure are in equilibrium. The algorithm developed to satisfy these conditions is that a nonlinear optimization problem based on the force method considering the deformed shape is formulated, and, it's able to find the shape by iteratively repeating the process of obtaining a solution of the governing equations. An computational technique based on the Gauss-Newton method was used as a method for obtaining solutions of nonlinear equations. In order to verify the validity of the proposed form-finding algorithm, a single-curvature pneumatic membrane example and a double-curvature air pneumatic membrane example were adopted, respectively. In the results of these examples, it was possible to well observe the step-by-step convergence process of the shape of the pneumatic membrane, and it was also possible to confirm the change in shape according to the air pressure. In addition, the calculation results of the shape and internal force after deformation due to initial tension, air pressure, and self-weight were obtained.

  • https://doi.org/10.9712/KASS.2021.21.4.49 인용 PDF KSCI

Performance-based structural fire design of steel frames using conventional computer software

  • Chan, Y.K.;Iu, C.K.;Chan, S.L.;Albermani, F.G.
    • Steel and Composite Structures
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    • v.10 no.3
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    • pp.207-222
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    • 2010

  • Fire incident in buildings is common, so the fire safety design of the framed structure is imperative, especially for the unprotected or partly protected bare steel frames. However, software for structural fire analysis is not widely available. As a result, the performance-based structural fire design is urged on the basis of using user-friendly and conventional nonlinear computer analysis programs so that engineers do not need to acquire new structural analysis software for structural fire analysis and design. The tool is desired to have the capacity of simulating the different fire scenarios and associated detrimental effects efficiently, which includes second-order P-D and P-d effects and material yielding. Also the nonlinear behaviour of large-scale structure becomes complicated when under fire, and thus its simulation relies on an efficient and effective numerical analysis to cope with intricate nonlinear effects due to fire. To this end, the present fire study utilizes a second-order elastic/plastic analysis software NIDA to predict structural behaviour of bare steel framed structures at elevated temperatures. This fire study considers thermal expansion and material degradation due to heating. Degradation of material strength with increasing temperature is included by a set of temperature-stress-strain curves according to BS5950 Part 8 mainly, which implicitly allows for creep deformation. This finite element stiffness formulation of beam-column elements is derived from the fifth-order PEP element which facilitates the computer modeling by one member per element. The Newton-Raphson method is used in the nonlinear solution procedure in order to trace the nonlinear equilibrium path at specified elevated temperatures. Several numerical and experimental verifications of framed structures are presented and compared against solutions in literature. The proposed method permits engineers to adopt the performance-based structural fire analysis and design using typical second-order nonlinear structural analysis software.

  • https://doi.org/10.12989/scs.2010.10.3.207 인용 KSCI

Ultimate strength estimation of composite plates under combined in-plane and lateral pressure loads using two different numerical methods

  • Ghannadpour, S.A.M.;Shakeri, M.;Barvaj, A. Kurkaani
    • Steel and Composite Structures
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    • v.29 no.6
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    • pp.785-802
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    • 2018

  • In this paper, two different computational methods, called Rayleigh-Ritz and collocation are developed to estimate the ultimate strength of composite plates. Progressive damage behavior of moderately thick composite laminated plates is studied under in-plane compressive load and uniform lateral pressure. The formulations of both methods are based on the concept of the principle of minimum potential energy. First order shear deformation theory and the assumption of large deflections are used to develop the equilibrium equations of laminated plates. Therefore, Newton-Raphson technique will be used to solve the obtained system of nonlinear algebraic equations. In Rayleigh-Ritz method, two degradation models called complete and region degradation models are used to estimate the degradation zone around the failure location. In the second method, a new energy based collocation technique is introduced in which the domain of the plate is discretized into the Legendre-Gauss-Lobatto points. In this new method, in addition to the two previous models, the new model named node degradation model will also be used in which the material properties of the area just around the failed node are reduced. To predict the failure location, Hashin failure criteria have been used and the corresponding material properties of the failed zone are reduced instantaneously. Approximation of the displacement fields is performed by suitable harmonic functions in the Rayleigh-Ritz method and by Legendre basis functions (LBFs) in the second method. Finally, the results will be calculated and discussions will be conducted on the methods.

  • https://doi.org/10.12989/scs.2018.29.6.785 인용 KSCI

The Impact of Market Environments on Optimal Channel Strategy Involving an Internet Channel: A Game Theoretic Approach (시장 환경이 인터넷 경로를 포함한 다중 경로 관리에 미치는 영향에 관한 연구: 게임 이론적 접근방법)

  • Yoo, Weon-Sang
    • Journal of Distribution Research
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    • v.16 no.2
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    • pp.119-138
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    • 2011

  • Internet commerce has been growing at a rapid pace for the last decade. Many firms try to reach wider consumer markets by adding the Internet channel to the existing traditional channels. Despite the various benefits of the Internet channel, a significant number of firms failed in managing the new type of channel. Previous studies could not cleary explain these conflicting results associated with the Internet channel. One of the major reasons is most of the previous studies conducted analyses under a specific market condition and claimed that as the impact of Internet channel introduction. Therefore, their results are strongly influenced by the specific market settings. However, firms face various market conditions in the real worlddensity and disutility of using the Internet. The purpose of this study is to investigate the impact of various market environments on a firm's optimal channel strategy by employing a flexible game theory model. We capture various market conditions with consumer density and disutility of using the Internet.

    shows the channel structures analyzed in this study. Before the Internet channel is introduced, a monopoly manufacturer sells its products through an independent physical store. From this structure, the manufacturer could introduce its own Internet channel (MI). The independent physical store could also introduce its own Internet channel and coordinate it with the existing physical store (RI). An independent Internet retailer such as Amazon could enter this market (II). In this case, two types of independent retailers compete with each other. In this model, consumers are uniformly distributed on the two dimensional space. Consumer heterogeneity is captured by a consumer's geographical location (ci) and his disutility of using the Internet channel (${\delta}_{N_i}$).
    shows various market conditions captured by the two consumer heterogeneities.
    (a) illustrates a market with symmetric consumer distributions. The model captures explicitly the asymmetric distributions of consumer disutility in a market as well. In a market like that is represented in
    (c), the average consumer disutility of using an Internet store is relatively smaller than that of using a physical store. For example, this case represents the market in which 1) the product is suitable for Internet transactions (e.g., books) or 2) the level of E-Commerce readiness is high such as in Denmark or Finland. On the other hand, the average consumer disutility when using an Internet store is relatively greater than that of using a physical store in a market like (b). Countries like Ukraine and Bulgaria, or the market for "experience goods" such as shoes, could be examples of this market condition. summarizes the various scenarios of consumer distributions analyzed in this study. The range for disutility of using the Internet (${\delta}_{N_i}$) is held constant, while the range of consumer distribution (${\chi}_i$) varies from -25 to 25, from -50 to 50, from -100 to 100, from -150 to 150, and from -200 to 200.
    summarizes the analysis results. As the average travel cost in a market decreases while the average disutility of Internet use remains the same, average retail price, total quantity sold, physical store profit, monopoly manufacturer profit, and thus, total channel profit increase. On the other hand, the quantity sold through the Internet and the profit of the Internet store decrease with a decreasing average travel cost relative to the average disutility of Internet use. We find that a channel that has an advantage over the other kind of channel serves a larger portion of the market. In a market with a high average travel cost, in which the Internet store has a relative advantage over the physical store, for example, the Internet store becomes a mass-retailer serving a larger portion of the market. This result implies that the Internet becomes a more significant distribution channel in those markets characterized by greater geographical dispersion of buyers, or as consumers become more proficient in Internet usage. The results indicate that the degree of price discrimination also varies depending on the distribution of consumer disutility in a market. The manufacturer in a market in which the average travel cost is higher than the average disutility of using the Internet has a stronger incentive for price discrimination than the manufacturer in a market where the average travel cost is relatively lower. We also find that the manufacturer has a stronger incentive to maintain a high price level when the average travel cost in a market is relatively low. Additionally, the retail competition effect due to Internet channel introduction strengthens as average travel cost in a market decreases. This result indicates that a manufacturer's channel power relative to that of the independent physical retailer becomes stronger with a decreasing average travel cost. This implication is counter-intuitive, because it is widely believed that the negative impact of Internet channel introduction on a competing physical retailer is more significant in a market like Russia, where consumers are more geographically dispersed, than in a market like Hong Kong, that has a condensed geographic distribution of consumers.
    illustrates how this happens. When mangers consider the overall impact of the Internet channel, however, they should consider not only channel power, but also sales volume. When both are considered, the introduction of the Internet channel is revealed as more harmful to a physical retailer in Russia than one in Hong Kong, because the sales volume decrease for a physical store due to Internet channel competition is much greater in Russia than in Hong Kong. The results show that manufacturer is always better off with any type of Internet store introduction. The independent physical store benefits from opening its own Internet store when the average travel cost is higher relative to the disutility of using the Internet. Under an opposite market condition, however, the independent physical retailer could be worse off when it opens its own Internet outlet and coordinates both outlets (RI). This is because the low average travel cost significantly reduces the channel power of the independent physical retailer, further aggravating the already weak channel power caused by myopic inter-channel price coordination. The results implies that channel members and policy makers should explicitly consider the factors determining the relative distributions of both kinds of consumer disutility, when they make a channel decision involving an Internet channel. These factors include the suitability of a product for Internet shopping, the level of E-Commerce readiness of a market, and the degree of geographic dispersion of consumers in a market. Despite the academic contributions and managerial implications, this study is limited in the following ways. First, a series of numerical analyses were conducted to derive equilibrium solutions due to the complex forms of demand functions. In the process, we set up V=100, ${\lambda}$=1, and ${\beta}$=0.01. Future research may change this parameter value set to check the generalizability of this study. Second, the five different scenarios for market conditions were analyzed. Future research could try different sets of parameter ranges. Finally, the model setting allows only one monopoly manufacturer in the market. Accommodating competing multiple manufacturers (brands) would generate more realistic results.

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