• Structural Engineering and Mechanics
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• v.88 no.5
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• pp.405-417
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• 2023

This paper reveals theoretical research to the nonlinear dynamic response and initial geometric imperfections sensitivity of the spinning graphene platelets reinforced metal foams (GPLRMF) cylindrical shell under different boundary conditions in thermal environment. For the theoretical research, with the framework of von-Karman geometric nonlinearity, the GPLRMF cylindrical shell model which involves Coriolis acceleration and centrifugal acceleration caused by spinning motion is assumed to undergo large deformations. The coupled governing equations of motion are deduced using Euler-Lagrange principle and then solved by a combination of Galerkin's technique and modified Lindstedt Poincare (MLP) model. Furthermore, the impacts of a set of parameters including spinning velocity, initial geometric imperfections, temperature variation, weight fraction of GPLs, GPLs distribution pattern, porosity distribution pattern, porosity coefficient and external excitation amplitude on the nonlinear harmonic resonances of the spinning GPLRMF cylindrical shells are presented.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.1A
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• pp.1-13
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• 2010

This paper presents an investigation on the geometric nonlinear behavior of cable-stayed bridges using geometric nonlinear finite element analysis method. The girder and mast in cable-stayed bridges show the combined axial load and bending moment interaction due to horizontal and vertical forces of inclined cable. So these members are considered as beam-column member. In this study, the nonlinear finite element analysis method is used to resolve the geometric nonlinear behavior of cable-stayed bridges in consideration of beam-column effect, large displacement effect (known as P-${\delta}$ effect) and cable sag effect. To analyze a cable-stayed bridge model, nonlinear 6-degree of freedom frame element and nonlinear 3-degree of freedom equivalent truss element is used. To resolve the geometric nonlinear behavior for various live load cases, the initial shape analysis is performed for considering dead load before live load analysis. Then the geometric nonlinear analysis for each live load case is performed. The deformed shapes of each model, load-displacement curves of each point and load-tensile force curves for each cable are presented for quantitative study of geometric nonlinear behavior of cable-stayed bridges.

• Advances in materials Research
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• v.8 no.3
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• pp.219-235
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• 2019

This research is devoted to analyzing mechanical-thermal post-buckling behavior of a micro-size beam reinforced with graphene platelets (GPLs) based on geometric imperfection effects. Graphene platelets have three types of dispersion within the structure including uniform-type, linear-type and nonlinear-type. The micro-size beam is considered to be perfect (ideal) or imperfect. Buckling mode shape of the micro-size beam has been assumed as geometric imperfection. Modified couple stress theory has been used for describing scale-dependent character of the beam having micro dimension. Via an analytical procedure, post-buckling path of the micro-size beam has been derived. It will be demonstrated that nonlinear buckling characteristics of the micro-size beam are dependent on geometric imperfection amplitude, thermal loading, graphene distribution and couple stress effects.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.43-49
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• 1995

Sasol Advanced Synthol Reactor was divided into two chambers by grid plate perforated with diffuser holes. The reactor has high stress level beacuse of membrane stress due to internal pressure, thermal stress due to temperature difference and local stress due to structural discontinuity at the juncture of grid plate and shell. Moreover, geometric nonlinear behaviors may appear in the grid plate because of pressure difference between two chambers. In order to survey the stress level and geometric nonlinear behaviors around grid plate, heat transfer analysis, linear static analysis and geometric nonlinear analysis were performed using NISA II developed by EMRC. This paper demonstrates the result of accessment for linear static and geometric nonlinear analysis under various load combinations.

• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.381-396
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• 2008

The aerostatic instability of cable-supported bridges is studied, with emphasis placed on modeling of the geometric nonlinear effects of various components of cable-supported bridges. Two-node catenary cable elements, which are more rational than truss elements, are adopted for simulating cables with large or small sags. Aerostatic loads are expressed in terms of the mean drag, lift and pitching moment coefficients. The geometric nonlinear analysis is performed with the dead loads and wind loads applied in two stages. The critical wind velocity for aerostatic instability is obtained as the condition when the pitching angle of the bridge deck becomes unbounded. Unlike those existing in the literature, each intermediate step of the incremental-iterative procedure is clearly given and interpreted. As such, the solutions obtained for the bridges are believed to be more rational than existing ones. Comparisons and discussions are given for the examples studied.

• Steel and Composite Structures
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• v.50 no.2
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• pp.149-158
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• 2024

Considering that different boundary conditions can have an important impact on structural vibration characteristics. In this paper, the nonlinear forced vibration behavior of functionally graded material (FGM) doubly curved shells with initial geometric imperfections under different boundary conditions is studied. Considering initial geometric imperfections and von Karman geometric nonlinearity, the nonlinear governing equations of FGM doubly curved shells are derived using Reissner's first order shear deformation (FOSD) theory. Three different boundary conditions of four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS) were studied, and a system of nonlinear ordinary differential equations was obtained with the help of Galerkin principle. The nonlinear forced vibration response of the FGM doubly curved shell is obtained by using the modified Lindstedt Poincare (MLP) method. The accuracy of this method was verified by comparing it with published literature. Finally, the effects of curvature ratio, power law index, void coefficient, prestress, and initial geometric imperfections on the resonance of FGM doubly curved shells under different boundary conditions are fully discussed. The relevant research results can provide certain guidance for the design and application of doubly curved shell.

• Steel and Composite Structures
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• v.47 no.6
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• pp.795-811
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• 2023

When studying the resonance problem of nanoplates, the existing papers do not consider the influences of geometric nonlinearity and initial geometric imperfection, so this paper is to fill this gap. In this paper, based on the nonlocal strain gradient theory (NSGT), the nonlinear resonances of functionally graded (FG) nanoplates with initial geometric imperfection under different boundary conditions are established. In order to consider the small size effect of plates, nonlocal parameters and strain gradient parameters are introduced to expand the assumptions of the first-order shear deformation theory. Subsequently, the equations of motion are derived using the Euler-Lagrange principle and solved with the help of perturbation method. In addition, the effects of initial geometrical imperfection, functionally graded index, strain gradient parameter, nonlocal parameter and porosity on the nonlinear forced vibration behavior of nanoplates under different boundary conditions are discussed.

• Journal of Korean Society of Steel Construction
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• v.23 no.1
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• pp.13-27
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• 2011

This paper presents an investigation of the structural stability of cable-stayed bridges, using geometric nonlinear finite-element analysis and considering various geometric nonlinearities, such as the sag effect of the cables, the beam-column effect of the girder and mast, and the large displacement effect. In this analytic research, a nonlinear frame element and a nonlinear equivalent truss element were used to model the girder, mast, and cable member. The live-load cases that were considered in this research were assumed based on the traffic loads. To perform reasonable analytic research, initial shape analyses in the dead-load case were performed before live-load analysis. In this study, the geometric nonlinear responses of the cable-stayed bridges with different cable arrangement types were compared. After that, parametric studies on the characteristics of the structural stability in critical live-load cases were performed considering various geometric parameters, such as the cable arrangement type, the stiffness ratios of the girder and mast, the area of the cables, and the number of cables. Through this parametric study, the effect of geometric shapes on the structural stability of cable-stayed bridges was investigated.

• Geomechanics and Engineering
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• v.31 no.3
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• pp.329-337
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• 2022

In this paper, the thermal post-buckling characteristics of functionally graded (FG) pipes with initial geometric imperfection are studied. Considering the influence of initial geometric defects, temperature and geometric nonlinearity, Euler-Lagrange principle is used to derive the nonlinear governing equations of the FG pipes. Considering three different boundary conditions, the two-step perturbation method is used to solve the nonlinear governing equations, and the expressions of thermal post-buckling responses are also obtained. Finally, the correctness of this paper is verified by numerical analyses, and the effects of initial geometric defects, functional graded index, elastic foundation, porosity, thickness of pipe and boundary conditions on thermal post-buckling response are analyzed. It is found that, bifurcation buckling exists for the pipes without initial geometric imperfection. In contrast, there is no bifurcation buckling phenomenon for the pipes with initial geometric imperfection. Meanwhile, the elastic stiffness can significantly improve thermal post-buckling load and thermal post-buckling strength. The larger the porosity, the greater the thermal buckling load and the thermal buckling strength.

• Steel and Composite Structures
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• v.46 no.1
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• pp.93-105
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• 2023

This paper examines a high-speed railway CRTS-II ballastless track-bridge system. Using the stationary potential energy theory, the mapping analytical solution between the bridge deformation and the rail vertical geometric irregularity was derived. A theoretical model (TM) considering the nonlinear stiffness of interlayer components was also proposed. By comparing with finite element model results and the measured field data, the accuracy of the TM was verified. Based on the TM, the effect of bridge deformation amplitude, girder end cantilever length, and interlayer nonlinear stiffness (fastener, cement asphalt mortar layer (CA mortar layer), extruded sheet, etc.) on the rail vertical geometric irregularity were analyzed. Results show that the rail vertical deformation extremum increases with increasing bridge deformation amplitude. The girder end cantilever length has a certain influence on the rail vertical geometric irregularity. The fastener and CA mortar layer have basically the same influence on the rail deformation amplitude. The extruded sheet and shear groove influence the rail geometric irregularity significantly, and the influence is basically the same. The influence of the shear rebar and lateral block on the rail vertical geometric irregularity could be negligible.