• Computers and Concrete
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• v.16 no.3
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• pp.429-448
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• 2015

The dams are huge structures storing a large amount of water and failures of them cause especially irreparable loss of lives during the earthquakes. They are named as a group of structures subjected to fluid-structure interaction. So, the response of the fluid and its hydrodynamic pressures on the dam should be reflected more accurately in the structural analyses to determine the real behavior as soon as possible. Different mathematical and analytical modelling approaches can be used to calculate the water hydrodynamic pressure effect on the dam body. In this paper, it is aimed to determine the dynamic response of concrete gravity dams using different water modelling approaches such as Westergaard, Lagrange and Euler. For this purpose, Sariyar concrete gravity dam located on the Sakarya River, which is 120km to the northeast of Ankara, is selected as a case study. Firstly, the main principals and basic formulation of all approaches are given. After, the finite element models of the dam are constituted considering dam-reservoir-foundation interaction using ANSYS software. To determine the structural response of the dam, the linear transient analyses are performed using 1992 Erzincan earthquake ground motion record. In the analyses, element matrices are computed using the Gauss numerical integration technique. The Newmark method is used in the solution of the equation of motions. Rayleigh damping is considered. At the end of the analyses, dynamic characteristics, maximum displacements, maximum-minimum principal stresses and maximum-minimum principal strains are attained and compared with each other for Westergaard, Lagrange and Euler approaches.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.319-333
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• 2013

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces: $${\sum_{1{\leq}i_<j{\leq}n}}\;f(\frac{r_ix_i+r_jx_j}{k})=\frac{n-1}{k}{\sum_{i=1}^n}r_if(x_i)$$.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.81-93
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• 2013

We consider a distributed optimal flux control problem: finding the potential of which gradient approximates the target vector field under an elliptic constraint. Introducing the Lagrange multiplier and a change of variables the Euler-Lagrange equation turns into a coupled equation of an elliptic equation and a reaction diffusion equation. The change of variables reduces iteration steps dramatically when the Gauss-Seidel iteration is considered as a solution method. For the elliptic equation solver we consider the Cell Boundary Element (CBE) method, which is the finite element type flux preserving methods.

• Journal of Ocean Engineering and Technology
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• v.10 no.3
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• pp.96-104
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• 1996

Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.52-57
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• 1987

In this paper, it is dealt with the dynamic motion equations for a robot arm. Four kinds of the dynamic equations which are the Lagrange-Euler equations, the Recursive L-E equations, the Newton-Euler equations and the improved N-E equation are derived on robot PUMA 600. Finally the algorithms on these equations are programmed using PASCAL. and are compared with each other. As the results, it is found that the improved N-E equations has the most fastest execution time among the equations and can be used in real time processing.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.321-321
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• 2000

This paper presents a sliding mode controller based on variable structure for the tip position control of a single-link flexible manipulator. Dynamic equations of a single-link flexible manipulator are derived from the Euler-Lagrange equation using a Lagrangian assumed modes method based on Bernoulli-Euler Beam theory. Simulation results are presented to show the validity of the system modeling, controller design.

• Journal of the Korean Vacuum Society
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• v.12 no.S1
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• pp.33-35
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• 2003

The electrooptic properties of the reflected light in a reflective mode, $45^{\circ}C$twisted nematic liquid crystal (TNLC) cell were investigated in the voltage regions near and away from the Freedericksz transition threshold. The measured reflectivity away from the threshold voltage ($V_th$) could not be described by the model which assurnes a constant tilt angle as well as a linearized distribution of twist angle across the cell, although the data are well fitted near $V_th$. We found that in the voltage region away from $V_th$, the model considering the distributions of the tilt angle and the twist angle should be applied for the calculation of the reflectivity. The director-axis distributions were obtained from the numerical integration of the Euler-Lagrange equation.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.369-380
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• 2019

Inspired by the problem of finding hyperelastic curves in a Riemannian manifold, we present a study on the variational problem of a hyperelastic curve in Lie group. In a Riemannian manifold, we reorganize the characterization of the hyperelastic curve with appropriate constraints. By using this equilibrium equation, we derive an Euler-Lagrange equation for the hyperelastic energy functional defined in a Lie group G equipped with bi-invariant Riemannian metric. Then, we give a solution of this equation for a null hyperelastic Lie quadratic when Lie group G is SO(3).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.315-321
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• 2009

In this paper, a level set based energy functional is proposed, the minimization of which results in simultaneous reference background image modeling and foreground segmentation. Due to the mutual constraint of the two processes, a good estimate of the background can be obtained with a small number of frames, and due to the use of the level set, an Euler-Lagrange equation that directly solves the problem can be derived.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.10
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• pp.2457-2466
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• 1993

A simple method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. Although the method is based upon the mode synthesis formulation procedure, the equations of the combined whole structure are not constructed compared with the conventional methods. Lagrange multi-pliers are used to enforce the conditions of geometric compatibility between the substructure interfaces and they are treated as external forces on each substructure itself. Substructure eigenvalue problem is defined with the substructure interface free of fixed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurated and efficient in calculating transient responses compared with the direct numerical integration method.