• Interaction and multiscale mechanics
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• 제7권1호
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• pp.525-542
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• 2014

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2005년도 학술발표회(1)
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• pp.285-286
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• 2005

• Earthquakes and Structures
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• 제24권3호
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• pp.217-235
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• 2023

Orthogonal pairs of rollers on concave beds (OPRCB) are a low-cost, low-tech rolling-based isolating system, whose high efficiency has been shown in a previous study. However, seismic performance of OPRCB isolators has only been studied in the two-dimensional (2D) state so far. This is while their performance in the three-dimensional (3D) state differs from that of the 2D state, mainly since the vertical accelerations due to rollers' motion in their beds, simultaneously in two orthogonal horizontal directions, are added up and resulting in bigger vertical inertia forces and higher rolling resistance. In this study, first, Lagrange equations were used to derive the governing equations of motion of the OPRCB-isolated buildings in 3D. Then, some regular shear-type OPRCB-isolated buildings were considered subjected to three-component excitations of far- and near-source earthquakes, and their responses were compared to those of their fixed-base counterparts. Finally, the effects of more realistic modeling and analysis were examined by comparing the responses of isolated buildings in 2D and 3D states. Response histories were obtained by the fourth-order Runge-Kutta-Nystrom method, considering the geometrical nonlinearity of isolators. Results reveal that utilizing the OPRCB isolators effectively reduces the acceleration response, however, depending on the system specifications and earthquake characteristics, the maximum responses of isolated buildings in the 3D state can be up to 40% higher than those in the 2D state.

• 소음진동
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• 제6권5호
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• pp.567-574
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• 1996

This paper concerns an articulated space robot with flexible links. The equations of its motion are derived by means of the Lagrangian mechanics. Assuming that magnitude of elastic motions are relatively small, the perturbation approach is taken to separate the original equations of motion into linear and nonlinear equations. Th effect the desired payload motion, open loop control inputs are first determined based on the nonlinear equations. One the other hand, in order to reduce the positional errors during the maneuver, vibration suppression is actively done with a feedforward control for disturbance cancellation to some extent. Additionally, for performance robustness against residual disturbance, an LQ control modified to have a prescribed degree of stability is applied based on the linear equations. Measurement equations are formulated to be used for the maximum likelihood estimator to reconstruct states from the original robot equations of motion. Finally, numerical simulations show effectiveness of the proposed control design scheme.

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.697-726
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• 1999

In this paper we develop a now procedure to control stepsize for linear multistep methods applied to semi-explicit index 1 differential-algebraic equations. in contrast to the standard approach the error control mechanism presented here is based on monitoring and contolling both the local and global errors of multistep formulas. As a result such methods with the local-global stepsize control solve differential-algebraic equation with any prescribed accuracy (up to round-off errors). For implicit multistep methods we give the minimum number of both full and modified Newton iterations allowing the iterative approxima-tions to be correctly used in the procedure of the local-global stepsize control. We also discuss validity of simple iterations for high accuracy solving differential-algebraic equations. Numerical tests support the the-oretical results of the paper.

• 대한수학회지
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• 제37권4호
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• pp.625-643
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• 2000

In this paper we formulate an optimal control problem governed by time-delay Volterra integral equations; the problem includes control constraints as well as terminal equality and inequality constraints on the terminal state variables. First, using a special type of state and control variations, we represent a relatively simple and self-contained method for deriving new necessary conditions in the form of Pontryagin minimum principle. We show that these results immediately yield classical Pontryagin necessary conditions for control processes governed by ordinary differential equations (with or without delay). Next, imposing suitable convexity conditions on the functions involved, we derive Mangasarian-type and Arrow-type sufficient optimality conditions.

• 전기의세계
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• 제29권3호
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• pp.193-200
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• 1980

A new algorithm for power system stability calculations is developed which considers the nonlinear state equations of 8 state variables for each generator dynamics, expollential load models in respect to bus voltages for nonlinear loads, network equations expressed in terms of bus-injected current sources, various kinds of generator and transmission line outages, abrupt changes in loads, and operations of various kinds of portective relaying systems such as distance relaying, reclosing load shedding by under-frequency relays. In the algorithm are included efficient and reliable schemes for solving network equations by means of the Newton-Raphson iterative method and the Optimally-Ordered Triangular Factorization Technique, and simple procedures for determining fault-point negative and zero sequence impedances for unbalanced line faults. An application of the Optimally-Ordered Triangular Factorization Techniques results in remarkable savings in computing time and memory requirements.

• 대한기계학회논문집A
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• 제24권5호
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• pp.1075-1083
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• 2000

The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method. The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method.

• 전기학회논문지
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• 제56권6호
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• pp.1000-1006
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• 2007

This paper presents a methodology to calculate an optimal solution of equilibrium to differential algebraic equations for power systems. It employs a nonlinear interior point method to solve the optimization formulation which includes dynamic equations representing the two-axis synchronous generator model with AVR and speed governing controls, algebraic equations, and steady-state nonlinear loads. This paper also adopts two algorithms for the improvement of solution convergence. In power system analysis and control, equilibrium optimization (EOPT) is applicable for diverse purposes that need the consideration of dynamic model characteristics at a steady-state condition.

• Wind and Structures
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• 제13권2호
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• pp.109-125
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• 2010

This work presents some analytical and numerical results of a dynamic analysis of the dimensionless 2-D sheet flight equations. Two empirical models for aerodynamic forces and moments are used and compared. Results show that the initial condition of rest is always unstable, and for long times three distinct flight regimes are possible, depending on the initial angle of attack, the Tachikawa number, Ta (in fact, the parameter chosen was its inverse, ${\Omega}$), and a mass ratio ${\Phi}$. The final orbits in the velocity space and their maximum kinetic energy are compared with a theoretical asymptotic state of the motion equations, and some design considerations are proposed.