• Structural Engineering and Mechanics
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• v.37 no.5
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• pp.475-487
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• 2011

In a flexible multi-body dynamic system the typical topological optimization method for structures cannot be directly applied, as the stiffness varies with position. In this paper, the topological optimization of the flexible multi-body dynamic system is converted into structural optimization using the equivalent static load method. First, the actual boundary conditions of the control system and the approximate stiffness curve of the mechanism are obtained from a flexible multi-body dynamical simulation. Second, the finite element models are built using the absolute nodal coordination for different positions according to the stiffness curve. For efficiency, the static reanalysis method is utilized to solve these finite element equilibrium equations. Specifically, the finite element equilibrium equations of key points in the stiffness curve are fully solved as the initial solution, and the following equilibrium equations are solved using a reanalysis method with an error controlled epsilon algorithm. In order to identify the efficiency of the elements, a non-dimensional measurement is introduced. Finally, an improved evolutional structural optimization (ESO) method is used to solve the optimization problem. The presented method is applied to the optimal design of a die bonder. The numerical results show that the presented method is practical and efficient when optimizing the design of the mechanism.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.59-68
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• 2005

In this study, we establish a theory for dynamic behaviors of an automatic ball balancer, analyze its dynamic characteristics, and provide its design guide line. Equations of motion are derived by using the polar coordinate system instead of the rectangular coordinate system which was previously used in other researches. After non-dimensionalization of the equations, the perturbation method is applied to locate the equilibrium positions and to obtain the linearized equations of motion around the equilibrium positions. The Eigenvalue problem is used to verify the dynamic stability around the equilibrium positions. On the other hand, the time responses are computed from the nonlinear equations of motion by using a time integration method.

• Journal of Mechanical Science and Technology
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• v.17 no.12
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• pp.2034-2041
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• 2003

This study introduced a lattice Boltzmann computational scheme capable of modeling thermo hydrodynamic flows with simpler equilibrium particle distribution function compared with other models. The equilibrium particle distribution function is the local Maxwelian equilibrium function in this model, with all the constants uniquely determined. The characteristics of the proposed model is verified by calculation of the sound speeds, and the shock tube problem. In the lattice Boltzmann method, a thermal fluid or compressible fluid model simulates the reflection of a weak shock wave colliding with a sharp wedge having various angles $\theta$$\sub$w/. Theoretical results using LBM are satisfactory compared with the experimental result or the TVD.

• Journal of Industrial Technology
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• v.15
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• pp.203-208
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• 1995

This paper suggests the three dimensional steady state searching techniques of hard disk/head system, which has some skew angle with flexure. In order to analyze the steady state behaviors of magnetic head slider, the localized Knudsen number and the localized bearing numbers are sued. For finding the steady state of magnetic head slider under the pre-loaded condition, I proposed multi-dimensional Newton-Raphson method which traces the equilibrium position of magnetic head slider, which has 3-degrees of freedom, using Jacobian matrix. The multi-dimensional Newton-Raphson method is very efficient technique for finding the steady state position of magnetic head slider because it approaches to the equilibrium position with changing three parameters simultaneously.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1086-1093
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• 2004

The modal characteristics of constrained multibody systems undergoing constant accelerated motions are investigated in this paper. Relative coordinates are employed to derive the equations of motion, which are generally nonlinear in terms of the coordinates. The dynamic equilibrium position of a constrained multibody system needs to be obtained from the nonlinear equations of motion, which are then linearized at the dynamic equilibrium position. The mass and the stiffness matrices for the modal analysis can be obtained from the linearized equations of motion. To verify the effectiveness and the accuracy of the proposed method, two numerical examples are solved and the results obtained by using the proposed method are compared with those obtained by analytical and other numerical methods. The proposed method is found to be accurate as well as effective in predicting the modal characteristics of constrained multibody systems undergoing constant accelerated motions.

• Journal of KSNVE
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• v.9 no.2
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• pp.363-370
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• 1999

In this study, we establish a theory for dynamic behaviors of an automatic ball balancer, analyze its dynamic characteristics, and provide its design guide line. Equations of motion are derived by using the polar coordinate system instead of the rectangular coordinate system which was previously used in other researches. After nondimensionalization of the equations, the perturbation method is applied to locate the equilibrium positions and to obtain the linearized equations of motion around the equilibrium positions. The Eigenvalue problem is used to verify the dynamic stability around the equilibrium positions. On the other hand, the time responses are computed from the nonlinear equations of motion by using a time integration method.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.69-94
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• 2024

In this paper, we introduce an inertial self-adaptive projection method using Bregman distance techniques for solving pseudomonotone equilibrium problems in reflexive Banach spaces. The algorithm requires only one projection onto the feasible set without any Lipschitz-like condition on the bifunction. Using this method, a strong convergence theorem is proved under some mild conditions. Furthermore, we include numerical experiments to illustrate the behaviour of the new algorithm with respect to the Bregman function and other algorithms in the literature.

• Structural Engineering and Mechanics
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• v.18 no.1
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• pp.59-78
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• 2004

This paper is devoted to illustrate some numerical procedures to solve the boundary equilibrium problems of three-dimensional solids that are subjected to thermal strains. The constitutive equations take into account the bounded tensile strength of the material and they are presented in the framework of non-linear elasticity and small strains. The associated equilibrium problem is solved numerically by means of the finite element method and the numerical techniques, i.e. the Newton-Raphson method and the secant method, are revised in order to assure the solution convergence of the discretized problem. Some numerical examples are illustrated.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1179-1191
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• 2011

In this paper, we introduce a new iterative scheme for finding a common element of the set of fixed points of a finite family of strict pseudocontractions and the solution set of pseudomonotone and Lipschitz-type continuous equilibrium problems. The scheme is based on the idea of extragradient methods and fixed point iteration methods. We show that the iterative sequences generated by this algorithm converge strongly to the common element in a real Hilbert space.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.161-173
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• 2009

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of the variational inequality for an inverse-strongly monotone mapping and the set of solutions of an equilibrium problem in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the three sets. The results of this paper extend and improve the corresponding results announced by many others.