• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.189-201
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• 2022

The aim of the current work is to investigate the numerical study of a nonlinear Volterra-Fredholm integro-differential equation with initial conditions. Our approximation techniques modified adomian decomposition method (MADM) and variational iteration method (VIM) are based on the product integration methods in conjunction with iterative schemes. The convergence of the proposed methods have been proved. We conclude the paper with numerical examples to illustrate the effectiveness of our methods.

• Journal of Korean Society of Steel Construction
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• v.14 no.6
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• pp.729-734
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• 2002

The effect of several simplified methods of seismic analysis is estimated. The pounding/contacting of superstructures were considered in the multispan simply supported bridge and the multispan continuous bridge. Although nonlinear time history analysis is generally used for seismic analysis of bridges, many codes including AASHTO propose several simplified analysis methods. AASHTO, however, does not mention pounding. Therefore, the simplified methods may produce results that are different from those of nonlinear time history analysis. This study developed nonlinear analytical models of the two types of bridges mentioned. The models were then modified to the simplified linear models for simplified analysis. The results of the simplified methods were compared with those of nonlinear time history analysis. It was found that including of the pounding/contacting element in the simplified methods generated responses similar to those of the nonlinear time history analysis.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.7 no.4
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• pp.13-20
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• 1987

Methods of nonlinear structural design sensitivity analysis are developed in parallel with the nonlinear finite element structural analysis methods and numerically evaluated. Direct decomposition and iterative solution methods for the secant stiffness approach and direct use of tangent stiffness in the design sensitivity analysis phase are derived and presented as the methods of nonlinear structural analysis and design sensitivity analysis are closely related. From the considerations of theoretical and numerical behavior, the tangent stiffness approach is shown to be efficient as the intermediate results of structural analysis can be effectively used in the design sensitivity analysis stage.

• Steel and Composite Structures
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• v.18 no.5
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• pp.1197-1214
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• 2015

There is a great difference in mechanical behavior between design model one-time loading and step-by-step construction process. This paper presents practical computational methods for simulating the structural behavior of long-span rigid steel structures during construction processes. It introduces the positioning principle of node rectification for installation which is especially suitable for rigid long-span steel structures. Novel improved nonlinear analytical methods, known as element birth and death of node rectification, are introduced based on several calculating methods, as well as a forward iteration of node rectification method. These methods proposed in this paper can solve the problem of element's 'floating' and can be easily incorporated in commercial finite element software. These proposed methods were eventually implemented in the computer simulation and analysis of the main stadium for the Universiade Sports Center during the construction process. The optimum construction scheme of the structure is determined by the improved algorithm and the computational results matched well with the measured values in the project, thus indicating that the novel nonlinear time-varying analysis approach is effective construction simulation of complex rigid long-span steel structures and provides useful reference for future design and construction.

• Advances in Computational Design
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• v.2 no.1
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• pp.71-87
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• 2017

This study focuses on the efficiency and applicability of dynamic relaxation methods in form-finding of membrane structures. Membrane structures have large deformations that require complex nonlinear analysis. The first step of analysis of these structures is the form-finding process including a geometrically nonlinear analysis. Several numerical methods for form-finding have been introduced such as the dynamic relaxation, force density method, particle spring systems and the updated reference strategy. In the present study, dynamic relaxation method (DRM) is investigated. The dynamic relaxation method is an iterative process that is used for the static equilibrium analysis of geometrically nonlinear problems. Five different examples are used in this paper. To achieve the grading of the different dynamic relaxation methods in form-finding of membrane structures, a performance index is introduced. The results indicate that viscous damping methods show better performance than kinetic damping in finding the shapes of membrane structures.

• Structural Engineering and Mechanics
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• v.46 no.1
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• pp.137-151
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• 2013

In this paper, two new methods called Improved Amplitude-Frequency Formulation (IAFF) and Energy Balance Method (EBM) are applied to solve high nonlinear oscillators. Two cases are given to illustrate the effectiveness and the convenience of these methods. The results of Improved Amplitude-Frequency Formulation are compared with those of EBM. The comparison of the results obtained using these methods reveal that IAFF and EBM are very accurate and can therefore be found widely applicable in engineering and other science. Finally, to demonstrate the validity of the proposed methods, the response of the oscillators, which were obtained from analytical solutions, have been shown graphically and compared with each other.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10b
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• pp.740-745
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• 1988

New design methods for constructing nonlinear adaptive control system are considered. The proposed adaptive controllers are applicable to the case where the degree of the controlled process is unknown. It is shown that the degree of the controller is determined independently of the degree of the process. Several types of nonlinear functions are introduced to deal with uncertainties of the degree of the process. Finally, some simulation results show the effectiveness and simplicity of the proposed methods.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.953-966
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• 2010

In this paper, we develop discontinuous Galerkin methods with penalty terms, namaly symmetric interior penalty Galerkin methods to solve nonlinear parabolic equations. By introducing an appropriate projection of u onto finite element spaces, we prove the optimal convergence of the fully discrete discontinuous Galerkin approximations in ${\ell}^2(L^2)$ normed space.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.85-97
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• 2002

In this paper, finite volume element methods for nonlinear parabolic problems are proposed and analyzed. Optimal order error estimates in $W^{1,p}$ and $L_p$ are derived for $2{\leq}p{\leq}{\infty}$. In addition, superconvergence for the error between the approximation solution and the generalized elliptic projection of the exact solution (or and the finite element solution) is also obtained.

• East Asian mathematical journal
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• v.26 no.5
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• pp.615-626
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• 2010

In this paper, we analyze discontinuous Galerkin methods with penalty terms, namly symmetric interior penalty Galerkin methods, to solve nonlinear parabolic equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ${\ell}^{\infty}$ ($L^2$) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.