• Korean Journal of Mathematics
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• v.14 no.1
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• pp.113-123
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• 2006

The arches may buckle in a symmetrical snap-through mode or in an asymmetry bifurcation mode if the load reaches a certain value. Each bifurcation curve develops as pressure increases. The governing equation is derived according to the bending theory. The balance of forces provides a nonlinear equilibrium equation. Bifurcation theory near trivial solution of the equation is developed, and the buckling pressures are investigated for various spring constants and opening angles.

• Journal of Mechanical Science and Technology
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• v.16 no.10
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• pp.1239-1245
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• 2002

A formulation which seeks steady-state equilibrium positions of constrained multibody systems driven by constant generalized speeds is presented in this paper. Since the relative coordinates are employed, constraint equations at cut joints are incorporated into the formulation. To obtain the steady-state equilibrium position of a multibody system, nonlinear equations are derived and solved iteratively. The nonlinear equations consist of the force equilibrium equations and the kinematic constraint equations. To verify the effectiveness of the proposed formulation, two numerical examples are solved and the results are compared with those of a commercial program.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.879-889
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• 2011

In this paper, we investigate the local asymptotic stability, the invariant intervals, the global attractivity of the equilibrium points, and the asymptotic behavior of the solutions of the difference equation $x_{n+1}=\frac{a+bx_nx_{n-k}}{A+Bx_n+Cx_{n-k}}$, n = 0, 1,${\ldots}$, where the parameters a, b, A, B, C and the initial conditions $x_{-k}$, ${\ldots}$, $x_{-1}$, $x_0$ are positive real numbers.

• Structural Engineering and Mechanics
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• v.41 no.3
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• pp.339-348
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• 2012

The slope stability analysis is usually done using the methods of calculation to rupture. The problem lies in determining the critical failure surface and the corresponding factor of safety (FOS). To evaluate the slope stability by a method of limit equilibrium, there are linear and nonlinear methods. The linear methods are direct methods of calculation of FOS but nonlinear methods require an iterative process. The nonlinear simplified Bishop method's is popular because it can quickly calculate FOS for different slopes. This paper concerns the use of inverse analysis by genetic algorithm (GA) to find out the factor of safety for the slopes using the Bishop simplified method. The analysis is formulated to solve the nonlinear equilibrium equation and find the critical failure surface and the corresponding safety factor. The results obtained by this approach compared with those available in literature illustrate the effectiveness of this inverse method.

• Steel and Composite Structures
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• v.27 no.1
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• pp.13-25
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• 2018

The main objective of this study is to develop a dual approach for geometrically nonlinear finite element analysis of plane truss structures. The geometric nonlinearity is considered using the Total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to displacement-type constraints. The proposed method can fully trace the whole equilibrium path of geometrically nonlinear plane truss structures not only before the limit point but also after it. No stiffness matrix is used in the main approach and the solution is acquired only based on the direct classical stress-strain formulations. As a result, produced errors caused by linearization and approximation of the main equilibrium equation will be eliminated. The suggested algorithm can predict both pre- and post-buckling behavior of the steel plane truss structures as well as any arbitrary point of equilibrium path. In addition, an equilibrium path with multiple limit points and snap-back phenomenon can be followed in this approach. To demonstrate the accuracy, efficiency and robustness of the proposed procedure, numerical results of the suggested approach are compared with theoretical solution, modified arc-length method, and those of reported in the literature.

• 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 the Korean Institute of Intelligent Systems
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• v.11 no.8
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• pp.720-725
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• 2001

Derivation of TSK fuzzy model from nonlinear differential equation is fundamental issue in the field of theoretical fuzzy control. The method which does not yield affine local differential equations at off-equilibrium points is proposed in this paper. A prototype TSK fuzzy model which has triangular membership functions for linguistic terms of the antecedent part is derived systematically. And then GA is used to modify the membership functions optimally. Simulation results show the validity of the proposed method.

• Journal of Korean Association for Spatial Structures
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• v.2 no.1 s.3
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• pp.75-84
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• 2002

In this study, the 'force density method' for shape finding of cable net structures is presented. This concept is based on the force-length ratios or force densities which are defined for each branch of the net structures. This method renders a simple linear 'analytical form finding' possible. If the free choice of the force densities is restricted by further condition, the linear method is extended to a nonlinear one. The nonlinear one can be applied to the detailed computation of networks. In this paper, the general inverse matrix is introduced to solve the nonlinear equilibrium equation including Jacobian matrix which is rectangular matrix. Several examples for linear and nonlinear analysis applied additional constraints are presented. It is shown that the force density method is suitable for form finding of cable net and the general inverse matrix can be applied to solve the nonlinear equation without Lagrangian factors.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.983-986
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• 2005

Free vibration characteristics of a curved pipe conveying fluid is studied when the pipe is clamped at both ends. Using the perturbation method, the non-linear governing equations divided into two parts; the steady state non-linear equilibrium equations and the linearized equations of motion in the neighborhood of the equilibrium position. The natural frequencies are computed from the linearized equations of motion. In this study, the equilibrium positions are determined by two types of equations, i.e., (1) the non-linear equations, and (2) the equations obtained by neglecting the non-linear terms. The natural frequencies obtained from the non-linear equilibrium equations are compared to those obtained from the linearized equilibrium equations. From the results, as the fluid velocity increases, the equilibrium position should be determined from the nonlinear equations for the vibration analysis of the curved pipe conveying fluid.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.3
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• pp.407-415
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• 1999

There are two kinds of instability phenomena for shell-type structures which are snap-through and bifurcation buckling. These are very sensitive according to the shape characteristics including rise-span ratio and especially shape initial imperfection. In this study, the equilibrium path of shallow sinusoidal arches supported by hinges at both ends is investigated to grasp the instability behavior of shell-type structures with initial imperfection. The Galerkin method is used to get the nonlinear discretized equation of governing differential equation considering geometric nonlinearity of arches and the perturbation method is also used to transform the nonlinear equation to incremental form.