• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.459-475
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• 2005

This paper deals with a novel application of the Generalized Differential Quadrature (G.D.Q.) method to the linear elastic static analysis of isotropic rotational shells. The governing equations of equilibrium, in terms of stress resultants and couples, are those from Reissner-Mindlin shear deformation shell theory. These equations, written in terms of internal-resultants circular harmonic amplitudes, are first put into generalized displacements form, by use of the strain-displacements relationships and the constitutive equations. The resulting systems are solved by means of the G.D.Q. technique with favourable precision, leading to accurate stress patterns.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.4.2-4
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• 2003

In this paper, we describe how to approximate the solutions of partial differential equations by bicubic spline functions whose interpolation errors at non-grid points are smaller in general than those by linear interpolations of the original solution at grid points. We show that the bicubic spline function can be represented exactly or approximately by a fuzzy system, and that the resulting fuzzy rule table shows the contours of the solution function. Thus, the fuzzy rule table is identified as a digital image and the contours in the rule table provide approximate contours of the solution of partial differential equations. Several illustrative examples are included.

• Structural Engineering and Mechanics
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• v.26 no.5
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• pp.545-556
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• 2007

In this paper, a hybrid boundary element technique is implemented to analyze nonlinear transient pile soil interaction in Gibson type nonhomeogenous soil. Inelastic modeling of soil media is presented by introducing a rational approximation to the continuum with nonlinear interface springs along the piles. Modified $\ddot{O}$zdemir's nonlinear model is implemented and systems of equations are coupled at interfaces for piles and pile groups. Linear beam column finite elements are used to model the piles and the resulting governing equations are solved using an implicit integration scheme. By enforcing displacement equilibrium conditions at each time step, a system of equations is generated which yields the solution. A numerical example is performed to investigate the effects of nonlinearity on the pile soil interaction.

• Proceedings of the KSR Conference
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• 2004.06a
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• pp.1327-1331
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• 2004

In this paper constant power models for electric trains have been used to analyze the steady states of the AT feeding systems. There are some previous studies utilizing constant impedance models or constant current models. These mentioned models are easy to use, but even so they don't yield exact results because of the innate restraints of the models since linear models cannot represent the characteristic of constant power in inverter-driven trains. It is reasonable that the train be considered as a constant load model when it drives or as a constant source model when it applies regenerative brake. Nonlinear equations which reflect constant power model for train have been developed by considering mutual impedances between wires and AT's turn-ratio of 1:1, then these equations have been solved by N-R iterative method. The proposed method doesn't need any specific assumptions through either the process of developing equations or the process of acquiring solutions, so it can be said to be stricter than other conventional methods.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.73-82
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• 2019

In this work, we give necessary and sufficient conditions under which every solution of a class of first-order neutral differential equations of the form $$(x(t)+p(t)x({\tau}(t)))^{\prime}+q(t)Hx({\sigma}(t)))=0$$ either oscillates or converges to zero as $t{\rightarrow}{\infty}$ for various ranges of the neutral coefficient p. Our main tools are the Knaster-Tarski fixed point theorem and the Banach's contraction mapping principle.

• Coupled systems mechanics
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• v.3 no.1
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• pp.73-88
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• 2014

The paper deals with a model founded on the physical processes in concrete subject to high temperatures. The model is developed in the framework of continuum damage mechanics and the theory of porous media and is demonstrated on selected structures. The model comprises balance equations for heat transfer, mass transfer of water and vapour, for linear momentum and for reaction. The balance equations are completed by constitutive equations considering the special behaviour of concrete at high temperatures. Furthermore, the limitation and decline of admissible stresses is achieved by using a composed, temperature depending crack surface with a formulation for the damage evolution. Finally, the complete coupled model is applied to several structures and to different concrete in order to determine their influence on the high-temperature-behaviour.

• Fibers and Polymers
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• v.7 no.4
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• pp.424-431
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• 2006

Roll drafting, a mechanical operation attenuating fiber bundles to an appropriate thickness, is an important operation unit for manufacturing staple yams. It influences not only the linear density regularity of the slivers or staple yams that are produced, but also the quality of the textile product and the efficiency of the thereafter processes. In this research, the dynamic states of the fiber bundle in the roll drafting zone were analyzed by simulation, based on the mathematical model that describes the dynamic behavior of the flowing bundle. The state variables are the linear density and velocity of the fiber bundles and we simulated the dynamics states of the bundle flow, e.g., the profiles of the linear density and velocity in the draft zone for various values of the model parameters and boundary conditions, including the initial conditions to obtain their influence on the dynamic state. Results showed that the mean velocity profile of the fiber bundle was strongly influenced by draft ratio and process speed, while the input sliver linear density has hardly affected the process dynamics. Velocity variance of individual fibers that could be supposed to be a disturbing factor in drafting was also influenced by the process speed. But the major disturbance occurred due to the velocity slope discontinuity at the front roll, which was strongly influenced by the process speed. Thickness of input sliver didn't play any important role in the process dynamics.

• Coupled systems mechanics
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• v.8 no.2
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• pp.147-168
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• 2019

This work aims to simulate three-dimensional heavy oil flow in a reservoir with heater-wells. Mass, momentum and energy balances, as well as correlations for rock and fluid properties, are used to obtain non-linear partial differential equations for the fluid pressure and temperature, and for the rock temperature. Heat transfer is simulated using a two-equation model that is more appropriate when fluid and rock have very different thermal properties, and we also perform comparisons between one- and two-equation models. The governing equations are discretized using the Finite Volume Method. For the numerical solution, we apply a linearization and an operator splitting. As a consequence, three algebraic subsystems of linearized equations are solved using the Conjugate Gradient Method. The results obtained show the suitability of the numerical method and the technical feasibility of heating the reservoir with static equipment.

• Journal of Theoretical and Applied Mechanics
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• v.3 no.1
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• pp.66-80
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• 2002

The bilinear formulation proposed earlier by Peters and Izadpanah to develop finite elements in time to solve undamped linear systems, Is extended (and found to be readily amenable) to develop time finite elements to obtain transient responses of both linear and nonlinear, and damped and undamped systems. The formulation Is used in the h-, p- and hp-versions. The resulting linear and nonlinear algebraic equations are differentiated to obtain the first- and second-order sensitivities of the transient response with respect to various system parameters. The present developments were tested on a series of linear and nonlinear examples and were found to yield, when compared with results obtained using other methods, excellent results for both the transient response and Its sensitivity to system parameters. Mostly. the results were obtained using the Legendre polynomials as basis functions, though. in some cases other orthogonal polynomials namely. the Hermite. the Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of the time finite element method, and the one often overlooked in its past applications, is the ease In which the sensitivity of the transient response with respect to various system parameters can be obtained. The results of sensitivity analysis can be used for approximate schemes for efficient solution of design optimization problems. Also. the results can be applied to gradient-based parameter identification schemes.

• Transactions of the Korean Society of Automotive Engineers
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• v.15 no.2
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• pp.165-174
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• 2007

Variable displacement type piston pump uses various controllers for controlling more than one state quantity like pressure, flow, power, and so on. These controllers need the mathematical model closely expressing dynamic behavior of pump for analyzing the stability of control systems which usually use various kinds of state variables. This paper derives the nonlinear mathematical model for variable displacement type piston pump. This model consists of two 1st oder differential equations by the continuity equations and one 2nd oder differential equation by the motion equation. To simplify the model we obtain the linear state variable model by differentiating the three nonlinear equations. And we verify this linearized model by comparison of simulation with experimentation and analyze the stability for the flow/pressure control. Finally this paper suggests the design compensation to ensure the stability of the systems.