• Steel and Composite Structures
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• 제24권1호
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• pp.53-63
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• 2017

The paper presents the simplified matrix stiffness method for analysis of composite and prestressed beams. The method is based on the previously developed "exact" analysis method that uses the mathematical theory of linear integral operators to derive all relations without any mathematical simplifications besides inevitable idealizations related to the material rheological properties. However, the method is limited since the closed-form solution can be found only for specific forms of the concrete creep function. In this paper, the authors proposed the simplified analysis method by introducing the assumption that the unknown deformations change linearly with the concrete creep function. Adopting this assumption, the nonhomogeneous integral system of equations of the "exact" method simplifies to the system of algebraic equations that can be easily solved. Therefore, the proposed method is more suitable for practical applications. Its high level of accuracy in comparison to the "exact" method is preserved, which is illustrated on the numerical example. Also, it is more accurate than the well-known EM method.

• Kyungpook Mathematical Journal
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• 제45권1호
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• pp.105-114
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• 2005

In this paper we investigate the growth of finite order solutions of the differential equation $f^{(k)}\;+\;A_{k-1}(Z)f^{(k-l)}\;+\;{\cdots}\;+\;A_1(z)f^{\prime}\;+\;A_0(z)f\;=\;F(z)$, where $A_0(z),\;{\cdots}\;,\;A_{k-1}(Z)\;and\;F(z)\;{\neq}\;0$ are entire functions. We find conditions on the coefficients which will guarantees the existence of an asymptotic value for a transcendental entire solution of finite order and its derivatives. We also estimate the lower bounds of order of solutions if one of the coefficient is dominant in the sense that has larger order than any other coefficients.

• 대한인간공학회지
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• 제24권4호
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• pp.7-13
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• 2005

We developed an accurate and reliable photogrammetric method available instead of the direct measurement method and the three-dimensional scanning method. Our research was restricted to a head on the body. Approaching three-dimensionally, we calibrated a distorted image of a photograph and got linear equations of camera beams. Then we assigned z values of landmarks in the head and obtained three-dimensional coordinates for each landmark putting those z values in linear equations of camera beams and finally could calculate measurement results from those three-dimensional coordinates. When we compared results obtained by a program, 'Venus Face Measurement(VFM)' that we had developed applying our method with results obtained by the direct measurement method, VFM showed very accurate and reliable results. In conclusion the photogrammetric method developed in this study was testified to an outstanding measurement method as a substitute for the direct measurement method and the three-dimensional scanning method.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.81-84
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• 1996

We propose the robust nonlinear controller design methodology, the $H_{\infty}$ constrained quasi - linear quadratic Gaussian control (QLQG/ $H_{\infty}$), for the statistically-linearized multivariable system with hard nonlinearties such as Coulomb friction, deadzone, etc. The $H_{\infty}$ performance constraint is involved in the optimization process by replacing the covariance Lyapunov equation with the Riccati equation whose solution leads to an upper bound of the QLQG performance. Because of the system's nonlinearity, however, one equation among three Riccati equations contain the nonlinear correction terms that are very difficult to solve numerically. To treat this problem, we use simple algebraic techniques. With some analytic transformation for Riccati equations, the nonlinear correction terms can be so eliminated that the set of a linear controller to the different operating points are designed. Synthesizing these via inverse random input describing function (IRIDF) technique, the final nonlinear controller can be designed.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
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• pp.786-789
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• 1989

A nonlinear self-tuning regulator for a neutralization process of a weak acid and strong base system is proposed. Rearranging the state equation of the process model, we first obtain equations which are linear for a manipulated variable or unknown parameters. Then to these equations we apply the standard procedure used in designing linear self-tuning regulators. Simulation results show that the regulator provides very good performances for various realistic situations and traces variations of the unknown parameters. Since computations are simple and additional measurements except the effluent pH value are only flow rates of influent streams, it can be easily applied to real processes such as a waste water treatment process.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 봄 학술발표회 논문집
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• pp.53-60
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• 2003

This paper explores the governing differential equations for the non-linear behavior of shear deformable simple beam with a concentrated load. In order to apply the Bernoulli-Euler beam theory to simple beam, the bending moment equation on any point of the elastica is obtained by concentrated load. The Runge-Kutta and Regula-Felsi methods, respectively, are used to integrate the governing differential equations and to compute the beam's rotation at the left end of the beams. The characteristic values of deflection curves for various load parameters are calculated and discussed

• 한국철도학회:학술대회논문집
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• 한국철도학회 2005년도 춘계학술대회 논문집
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• pp.536-543
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• 2005

Derivation procedures of exact dynamic stiffness matrices of thin-walled curved beams subjected to axial forces are rigorously presented for the spatial free vibration analysis. An exact dynamic stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. Firstly this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using element force-displacement relationships. The natural frequencies of the nonsymmetric thin-walled curved beam are evaluated and compared with analytical solutions or results by ABAQUS's shell elements in order to demonstrate the validity of this study.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2000년도 추계학술대회 논문집
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• pp.358-365
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• 2000

For the general case of loading conditions and boundary conditions, it is very difficult to obtain closed form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. In consequence, most of previous finite element formulations are introduce approximate displacement fields to use shape functions as Hermitian polynomials, and so on. The Purpose of this study is to presents a consistent derivation of exact dynamic stiffness matrices of thin-walled straight beams, to be used ill tile free vibration analysis, in which almost types of boundary conditions are exist An exact dynamic element stiffness matrix is established from governing equations for a uniform beam element of nonsymmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequency is evaluated for the thin-walled straight beam structure, and the results are compared with analytic solutions in order to verify the accuracy of this study.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권2호
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• pp.101-113
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• 2018

The dual singular function method(DSFM) is a numerical algorithm to get optimal solution including corner singularities for Poisson and Helmholtz equations. In this paper, we apply DSFM to solve heat equation which is a time dependent problem. Since the DSFM for heat equation is based on DSFM for Helmholtz equation, it also need to use Sherman-Morrison formula. This formula requires linear solver n + 1 times for elliptic problems on a domain including n reentrant corners. However, the DSFM for heat equation needs to pay only linear solver once per each time iteration to standard numerical method and perform optimal numerical accuracy for corner singularity problems. Because the Sherman-Morrison formula is rather complicated to apply computation, we introduce a simplified formula by reanalyzing the Sherman-Morrison method.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.731-736
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• 2000

The vibration of an axially moving string is studied when the string has geometric non-linearity and translating acceleration. Based upon the von karman strain theory, The equation for the longitudinal vibration is linear and uncoupled, while the equation for the transverse vibration is non-linear and coupled between the longitudinal and transverse deflections. The governing equations are discretized by using the Galerkin approximation. With the discretized nonlinear equations, the time responses are investigated by using the generalized-${\alpha}$ method.