• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.457-464
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• 1998

The equilibrium path of shallow sinusoidal arches supported by hinges at both ends is investigated. The displacement increment method is used to get the solution of the nonlinear differential equations for these structures and to plot the equilibrium paths by the results. Using the equilibrium paths, the relations between the position of buckling point and buckling type for the case of sinusoidal distributed loads are inferred. From the result that the buckling type changes according to the normalized rise of arch, it is also shown that the arch rise is the governing factor to stability regions

• Steel and Composite Structures
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• v.28 no.6
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• pp.671-679
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• 2018

The paper is devoted to the stability analysis of a simply supported five layer sandwich beam. The beam consists of five layers: two metal faces, the metal foam core and two binding layers between faces and the core. The main goal is to elaborate a mathematical and numerical model of this beam. The beam is subjected to an axial compression. The nonlinear hypothesis of deformation of the cross section of the beam is formulated. Based on the Hamilton's principle the system of four stability equations is obtained. This system is approximately solved. Applying the Bubnov-Galerkin's method gives an ordinary differential equation of motion. The equation is then numerically processed. The equilibrium paths for a static and dynamic load are derived and the influence of the binding layers is considered. The main goal of the paper is an analytical description including the influence of binding layers on stability, especially on critical load, static and dynamic paths. Analytical solutions, in particular mathematical model are verified numerically and the results are compared with those obtained in experiments.

• Journal of Powder Materials
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• v.6 no.1
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• pp.18-35
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• 1999

Phase equilibria in the system Si3N4-TiC-TiCxN1-x-C-N were determined by thermodynamic calculations (CALPHAD-method). The reaction peaction paths for Si3N4-TiC and SiC-TiC composites in the Ti-Si-C-n system were simulated at I bar N2-pressure and varying terpreatures. At a temperature of 1923 K two tie-triangles (TiC0.34N0.66+SiC+C and TiC0.13N0.87+SiC+Si3N4) and two 2-phase fieds (TiCxN1-x+SiC; 0.13

• Journal of the Korean Regional Science Association
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• v.13 no.2
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• pp.45-54
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• 1997

A regional economy is characterized as a spatial economy. However the literature shows that it has been treated as a point economy since space is little recognized in regional modeling due to mathematical complication. This leads to the fact that regional model does not sufficiently represent regional characteristic. This paper attempts to construct a regional growth model in a partial equilibrium framework specifically taking into consideration land as a primary factor. The model is formulated largely neoclassical. Labor is assumed to move in response to differences in the wage rate, while capital is perfectly mobile across regions. The paper shows that two growth equilibrium points exist, one stable equilibrium point and the other unstable equilibrium point. The unstable growth equilibrium indicates the existence of minimum threshold that a region must overcome the minimum threshold to grow constantly. Consequently, directions of regional growth are characterized by two growth paths depending on the initial condition of a region. That is to say, a region below the minimum threshold is converging toward the lower stable equilibrium point over time. When a regional economy initially lies above the minimum threshold, it will grow forever. A regional economy is not thus necessarily converging a stationary is not thus necessarily converging a stationary equilibrium point through factor movement. Finally, the impacts of the presence of agglomeration economies and diseconomies are analyzed through the phase diagram. The paper also shows that agglomeration economies result in lowering the minimum threshold and in escalating the level of stable equilibrium However, when agglomeration diseconomies prevail, the results are opposite, i.e., rising the minimum threshold of growth and lowering the growth level of stable equilibrium.

• Journal of Korean Society of Transportation
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• v.8 no.1
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• pp.55-71
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• 1990

The behavioral mechanism underlying the traffic assignment model is a choice, or decision-making process of traveling paths between origins and destinations. The deterministic approach to traffic assignment assumes that travelers choose shortest path from their origin-destination pair. Although this assumption seems reasonable, it presumes that all travelers have perfect information regarding travel time, that they make consistently correct decision, and that they all behave in identical fashion. Stochastic user equilibrium assignment relaxes these presumptions by including a random component in traveler's perception of travel time. The objective of this study is to compare "A Model of Deterministic User Equilibrium Assignment" with "Models of Stochastic User Equilibrium Assignment" in the theoretical and practical aspects. Specifically, SUE models are developed to logit and probit based models according to discrete choice functions. The models were applied to sioux Falls net ork consisting of 24 zones, 24 nodes and 76 links. The distribution of perceived travel time was obtained by using the relationship between speed and traffic flow.

• Structural Engineering and Mechanics
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• v.35 no.5
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• pp.555-570
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• 2010

Shallow fixed arches have a nonlinear primary equilibrium path with limit points and an unstable postbuckling equilibrium path, and they may also have bifurcation points at which equilibrium bifurcates from the nonlinear primary path to an unstable secondary equilibrium path. When a shallow fixed arch is subjected to a central step load, the load imparts kinetic energy to the arch and causes the arch to oscillate. When the load is sufficiently large, the oscillation of the arch may reach its unstable equilibrium path and the arch experiences an escaping-motion type of dynamic buckling. Nonlinear dynamic buckling of a two degree-of-freedom arch model is used to establish energy criteria for dynamic buckling of the conservative systems that have unstable primary and/or secondary equilibrium paths and then the energy criteria are applied to the dynamic buckling analysis of shallow fixed arches. The energy approach allows the dynamic buckling load to be determined without needing to solve the equations of motion.

• Steel and Composite Structures
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• v.6 no.5
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• pp.401-415
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• 2006

Based on a non-linear model taking into account flexural-torsional couplings, analytical solutions are derived for lateral buckling of simply supported I beams under some representative load cases. A closed form is established for lateral buckling moments. It accounts for bending distribution, load height application and pre-buckling deflections. Coefficients $C_1$ and $C_2$ affected to these parameters are then derived. Regard to well known linear stability solutions, these coefficients are not constant but depend on another coefficient $k_1$ that represents the pre-buckling deflection effects. In numerical simulations, shell elements are used in mesh process. The buckling loads are achieved from solutions of eigenvalue problem and by bifurcations observed on non linear equilibrium paths. It is proved that both the buckling loads derived from linear stability and eigenvalue problem lead to poor results, especially for I sections with large flanges for which the behaviour is predominated by pre-buckling deflection and the coefficient $k_1$ is large. The proposed solutions are in good agreement with numerical bifurcations observed on non linear equilibrium paths.

• Journal of Mechanical Science and Technology
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• v.19 no.spc1
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• pp.377-387
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• 2005

The equations of motion of two-wheeled vehicles, e.g. bicycles or motorcycles, are developed by using Lagrange's equations for quasi-coordinates. The pure rolling constraints between the ground and the two wheels are considered in the dynamical equations of the system. For each wheel, two nonholonomic and two holonomic constraints are introduced in a set of differential-algebraic equations (DAE). The constraint Jacobian matrix is obtained by collecting all the constraint equations and converting them into the velocity form. Equilibrium, an algorithm for searching for equilibrium points of two-wheeled vehicles and the associated problems are discussed. Formulae for calculating the radii of curvatures of ground-wheel contact paths and the reference point are also given.

• Journal of Korean Society of Transportation
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• v.23 no.4 s.82
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• pp.37-45
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• 2005

This paper presents a relationship between Nash bargaining game and Wardrop user equilibrium, which has been widely used in transportation modeling for route choice problem. Wardrop user equilibrium assumes that drivers in road network have perfect information on the traffic conditions and they choose their optimal paths without cooperation each other. In this regards, if the bargaining game process is introduced in route choice modeling, we may avoid the strong assumptions to some extent. For such purpose, this paper derives a theorem that Nash bargaining solution is equivalent to Wardrop user equilibrium as the barging process continues and prove it with some numerical examples. The model is formulated based on two-person bargaining game. and n-person game is remained for next work.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.11a
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• pp.979-984
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• 2008

This paper discusses how to use basic strut-and-tie models(STM) for practical application. Construction of STM starts with drawing of load paths with equilibrium conditions. Understanding of structural systems including form active systems, vector active systems, and section active systems help us select appropriate systems for possible STM. Simple circular fans can be employed for load paths from concentrated forces to distributed forces. Strength of struts depends on configuration of their nodal zones which meet tension ties and effective compressive strength. The effective compressive strength of struts are assumed to be mainly influenced by transverse strain.