• Journal of the Korean Data and Information Science Society
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• 제20권5호
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• pp.913-917
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• 2009

The measures of leverage in linear regression has been extended to nonlinear regression models. We consider several curvature measures of nonlinearity in an estimation situation. The relationship between measures of leverage and statistical curvature are explored in nonlinear regression models. The circumstances under which the Jacobian leverage reduces to a tangent plane leverage are discussed in connection with the effective residual curvature of the nonlinear model.

• Structural Engineering and Mechanics
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• 제86권6호
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• pp.751-764
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• 2023

In practical engineering such as aerial refueling pipes, the boundary of the fluid-conveying pipe is difficult to be completely immovable. Pipes under movable and immovable boundaries are controlled by different dominant nonlinear factors, where the boundary mobility will affect the nonlinear dynamic characteristics, which should be focused on for adopting different strategies for vibration suppression and control. The nonlinear dynamic instability characteristics of functionally graded fluid-conveying pipes lying on a viscoelastic foundation under movable and immovable boundary conditions are systematically studied for the first time. Nonlinear factors involving nonlinear inertia and nonlinear curvature for pipes with a movable boundary as well as tensile hardening and nonlinear curvature for pipes with an immovable boundary are comprehensively considered during the derivation of the governing equations of the principal parametric resonance. The stability boundary and amplitude-frequency bifurcation diagrams are obtained by employing the two-step perturbation- incremental harmonic balance method (TSP-IHBM). Results show that the movability of the boundary of the pipe has a great influence on the vibration amplitude, bifurcation topology, and the physical meanings of the stability boundary due to different dominant nonlinear factors. This research has guidance significance for nonlinear dynamic design of fluid-conveying pipe with avoiding in the instability regions.

• Wind and Structures
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• 제1권3호
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• pp.255-269
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• 1998

Second-order moments of considerable magnitude arise in tall and slender RC chimneys and towers subject to along-wind loading, on account of eccentricities in the distributed self-weight of the tower in the deflected profile. An accurate solution to this problem of geometric nonlinearity is rendered difficult by the uncertainties in estimating the flexural rigidity of the tower, due to variable cracking of concrete and the 'tension stiffening' effect. This paper presents a rigorous procedure for estimating deflections and second-order moments in wind-loaded RC tubular towers. The procedure is essentially based on a generalised formulation of moment-curvature relationships for RC tubular towers, derived from the experimental and theoretical studies reported by Schlaich et al. 1979 and Menon 1994 respectively. The paper also demonstrates the application of the proposed procedure, and highlights those conditions wherein second-order moments become too significant to be overlooked in design.

• Computers and Concrete
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• 제4권6호
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• pp.457-475
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• 2007

A simple analytical procedure to analyze reinforced concrete (RC) beams with cracked section is proposed on the basis of the simplified moment-curvature relations of RC sections. Unlike previous analytical models which result in overestimation of stiffness and underestimation of structural deformations induced from assuming perfect-bond condition between steel and concrete, the proposed analytical procedure considers fixed-end rotation caused by anchorage. Furthermore, the proposed analytical procedure, compared with previous numerical models, promotes effectiveness of analysis by reflecting several factors which can influence nonlinearity of RC structure into the simplified moment-curvature relation. Finally, correlation studies between analytical and experimental results are conducted to establish the applicability of the proposed analytical procedure to the nonlinear analysis of RC structures.

• Computers and Concrete
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• 제8권4호
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• pp.473-489
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• 2011

In designing a flexural member for structural safety, both the flexural strength and ductility have to be considered. For this purpose, the flexural ductility of reinforced concrete sections has been studied quite extensively. As there have been relatively few studies on the flexural ductility of prestressed concrete sections, it is not well understood how various structural parameters affect the flexural ductility. In the present study, the full-range flexural responses of reinforced and prestressed concrete sections are analyzed taking into account the nonlinearity and stress-path dependence of constitutive materials. From the numerical results, the effects of steel content, yield strength and degree of prestressing on the yield curvature and ultimate curvature are evaluated. It is found that whilst the concept of flexural ductility in terms of the ductility factor works well for reinforced sections, it can be misleading when applied to prestressed concrete sections. For prestressed concrete sections, the concept of flexural deformability in terms of ultimate curvature times overall depth of section may be more appropriate.

• Smart Structures and Systems
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• 제16권5호
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• pp.853-872
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• 2015

Numerical analysis of large amplitude free vibration behaviour of laminated composite spherical shell panel embedded with the piezoelectric layer is presented in this article. For the investigation purpose, a general nonlinear mathematical model has been developed using higher order shear deformation mid-plane kinematics and Green-Lagrange nonlinearity. In addition, all the nonlinear higher order terms are included in the present mathematical model to achieve any general case. The nonlinear governing equation of freely vibrated shell panel is obtained using Hamilton's principle and discretised using isoparametric finite element steps. The desired nonlinear solutions are computed numerically through a direct iterative method. The validity of present nonlinear model has been checked by comparing the responses to those available published literature. In order to examine the efficacy and applicability of the present developed model, few numerical examples are solved for different geometrical parameters (fibre orientation, thickness ratio, aspect ratio, curvature ratio, support conditions and amplitude ratio) with and/or without piezo embedded layers and discussed in details.

• Communications for Statistical Applications and Methods
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• 제7권1호
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• pp.1-12
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• 2000

We explore the structure and usefulness of CERES plot as a basic tool for dealing with curvature as a function of the new predictor in nonlinear regression. If a predictor has a nonlinear effect and there are nonlinear relationships among the predictors the partial residual plot and augmented partial residual plot are not able to display the correct functional form of the predictor. Unlike these plots the CERES plot can show the correct from. In situations where nonlinearity exists in two predictors we extend the idea of CERES plot to three dimensions, This is illustrated by simulated data.

• 한국강구조학회 논문집
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• 제12권4호통권47호
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• pp.375-385
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• 2000

6층 비가새 및 20층 가새 철골구조물에서 기하 비선형, 재료 비선형, 접합부 비선형을 고려할 때 극한 횡하중에 대해 요구되는 접합부 연성도를 파악하였다. 재료 비선형을 고려하기 위하여 단면 모멘트-곡률 관계는 Fiber 모델을 이용하고 부재 강성행렬은 유연도 선형분포 해석모델을 이용하여 유도하였다. 강접합부를 반강접합부로 대체한 6층 구조물의 접합부 연성도는 강접합부인 경우 보다 적었고 20층 구조물에서 요구되는 반강접합부 연성도는 전단접합부의 경우와 거의 같고 강접합부는 전단접합부나 반강접합부에 비하여 큰 연성도가 필요하였다.

• Structural Engineering and Mechanics
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• 제82권4호
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• pp.477-490
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• 2022

This article investigates the nonlinear behavior of two-directional functionally graded materials (TDFGM) doubly curved panels with porosities for the first time. An improved and effectual approach is established based on the improved first-order shear deformation shell theory (IFSDST) and von Karman's type nonlinearity. The IFSDST considers the effects of shear deformation without the need for a shear correction factor. The composition of TDFGM constitutes four different materials, and the modified power-law function is employed to vary the material properties continuously in both thickness and longitudinal directions. A nonlinear finite element method in conjunction with Hamilton's principle is used to obtain the governing equations. Then, the direct iterative method is incorporated to accomplish the numerical results using the frequency-amplitude, nonlinear central deflection relations. Finally, the influence of volume fraction grading indices, porosity distributions, porosity volume, curvature ratio, thickness ratio, and aspect ratio provides a thorough insight into the linear and nonlinear responses of the porous curved panels. Meanwhile, this study emphasizes the influence of the volume fraction gradation profiles in conjunction with the various material and geometrical parameters on the linear frequency, nonlinear frequency, and deflection of the TDFGM porous shells. The numerical analysis reveals that the frequencies and nonlinear deformations can be significantly regulated by changing the volume fraction gradation profiles in a specified direction with an appropriate combination of materials. Hence, TDFGM panels can overcome the drawbacks of the functionally graded materials with a gradation of properties in a single direction.

• 대한수의학회지
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• 제50권1호
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• pp.11-17
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• 2010

Linear and non-linear regressions were used to derive the calibration function for the measurement of roxithromycin plasma concentration. Their results were compared with weighted least squares regression by usual weight factors. In this paper the performance of a non-linear calibration equation with the capacity to account empirically for the curvature, y = ax$^{b}$ + c (b $\neq$ 1) is compared with the commonly used linear equation, y = ax + b, as well as the quadratic equation, y = ax$^{2}$+ bx + c. In the calibration curve (range of 0.01 to 10 ${\mu}g/mL$) of roxithromycin, both heteroscedasticity and nonlinearity were present therefore linear least squares regression methods could result in large errors in the determination of roxithromycin concentration. By the non-linear and weighted least squares regression, the accuracy of the analytical method was improved at the lower end of the calibration curve. This study suggests that the non-linear calibration equation should be considered when a curve is required to be fitted to low dose calibration data which exhibit slight curvature.