• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1997년도 추계학술대회논문집
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• pp.28-31
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• 1997

Buckling analysis of thin compressed beam has been carried out. Pre-buckling and post-buckling are simulated by finite element method incorporating with the incremental nonlinear theory and the Newton-Raphson solution technique. In order to find the bifurcation point, the determinent of the stiffness matrix is calculated at every iteration procedure. For post-buckling analysis, a small perturbed initial guess is given along the eigenvector direction at the bifurcation point. Nonlinear elastic buckling and elastic-plastic buckling of cantilever beam are analyzed. The buckling load and buckled shape of the two models are compared.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 봄 학술발표회 논문집
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• pp.211-218
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• 2003

Most structures are expected to deform beyond the limit of linearly elastic behavior when subjected to strong ground motion. Seismic evaluation of structure requires an estimation of the structural performance in terms of displacement demand imposed by earthquakes on the structure. Nonlinear response history analysis(NRHA) is the most rigorous procedure to compute seismic performance among various inelastic analysis methods. But nonlinear analysis procedures necessitate more practical and reliable tools for predicting seismic behavior of structures. This paper presents a nonlinear direct spectrum method(NDSM) to evaluate seismic performance of structures, without iterative computations, given by the structural initial elastic period and yield strength from the pushover analysis, especially for MDF(multi degree of freedom) system. The purpose of this paper is to investigate the accuracy and reliability of this method from a point of view of various earthquakes and structure parameters.

• 한국소음진동공학회논문집
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• 제15권1호
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• pp.46-52
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• 2005

This paper is concerned with the application of perturbation method to the dynamic analysis of free-free beam. In general, the rigid-body motions and elastic vibrations are analyzed separately. However, the rigid-body motions cause vibrations and elastic vibrations also affect rigid-body motions in turn, which indicates that the rigid-body motions and elastic vibrations are coupled in nature. The resulting equations of motion are hybrid and nonlinear. We can discretize the equations of motion by means of admissible functions but still we have to cope with nonlinear equations. In this paper, we propose the use of perturbation method to the coupled equations of motion. The resulting equations consist of zero-order equations of motion which depict the rigid-body motions and first-order equations of motion which depict the perturbed rigid-body motions and elastic vibrations. Numerical results show the efficacy of the proposed method.

• Earthquakes and Structures
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• 제26권4호
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• pp.251-259
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• 2024

In this paper, the thermal post-buckling behavior of graphene platelets reinforced metal foams (GPLRMFs) plate with initial geometric imperfections on nonlinear elastic foundations are studied. First, the governing equation is derived based on the first-order shear deformation theory (FSDT) of plate. To obtain a single equation that only contains deflection, the Galerkin principle is employed to solve the governing equation. Subsequently, a comparative analysis was conducted with existing literature, thereby verifying the correctness and reliability of this paper. Finally, considering three GPLs distribution types (GPL-A, GPL-B, and GPL-C) of plates, the effects of initial geometric imperfections, foam distribution types, foam coefficients, GPLs weight fraction, temperature changes, and elastic foundation stiffness on the thermal post-buckling characteristics of the plates were investigated. The results show that the GPL-A distribution pattern exhibits the best buckling resistance. And with the foam coefficient (GPLs weight fraction, elastic foundation stiffness) increases, the deflection change of the plate under thermal load becomes smaller. On the contrary, when the initial geometric imperfection (temperature change) increases, the thermal buckling deflection increases. According to the current research situation, the results of this article can play an important role in the thermal stability analysis of GPLRMFs plates.

• Geomechanics and Engineering
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• 제1권2호
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• pp.155-168
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• 2009

Breakdown pressures obtained from the classic, linear elastic breakdown model are compared with the corresponding pressures obtained using a nonlinear material model. Compression test results obtained on sandstone and siltstone are used for that purpose together with previously formulated nonlinear model which introduces elasticity functions to address nonlinear stress-strain behaviour of rocks exhibiting stress-dependent mechanical properties. Linear and nonlinear collapse pressures are also compared and it is shown that material nonlinearities have significant effect on both breakdown and collapse pressures and on tangential stresses which control breakdown pressure around a borehole. This means that the estimates of ${\sigma}_H$ made using linear models give stress values which are different than the real values in the earth. Thus the importance of a more accurate analysis, such as provided by the nonlinear models, is emphasised. It is shown, however, that the linear elastic model does not necessarily over-predict borehole stresses and the opposite case can be true, depending on rock type and test interpretation.

• Structural Engineering and Mechanics
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• 제61권2호
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• pp.209-220
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• 2017

The purpose of this paper is to study the geometrically nonlinear free vibration of functionally graded nano/micro beams (FGNBs) based on the modified couple stress theory. For practical applications, some analytical expressions of nonlinear frequencies for FGNBs on a nonlinear Pasternak foundation are developed. Hamilton's principle is employed to obtain nonlinear governing differential equations in the context of both Euler-Bernoulli and Timoshenko beam theories for a comprehensive investigation. The modified continuum theory contains one material length scale parameter to capture the size effect. The variation of two-constituent material along the thickness is modeled using Reddy's power-law. Also, the Mori-Tanaka method as an accurate homogenization technique is implemented to estimate the effective material properties of the FGNBs. The results are presented for both hinged-hinged and clamped-clamped boundary conditions. The nonlinear partial differential equations are reduced to ordinary differential equations using Galerkin method and then the powerful method of homotopy analysis is utilized to obtain the semi-analytical solutions. Eventually, the presented analytical expressions are used to examine the influences of the length scale parameter, material gradient index, and elastic foundation on the nonlinear free vibration of FGNBs.

• Smart Structures and Systems
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• 제18권5호
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• pp.1029-1062
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• 2016

In this research, the nonlinear free vibration analysis of boron-nitride micro ribbon (BNMR) on the Pasternak elastic foundation under electrical, mechanical and thermal loadings using modified strain gradient theory (MSGT) is studied. Employing the von $K{\acute{a}}rm{\acute{a}}n$ nonlinear geometry theory, the nonlinear equations of motion for the graphene micro ribbon (GMR) using Euler-Bernoulli beam model with considering attached mass and size effects based on Hamilton's principle is obtained. These equations are converted into the nonlinear ordinary differential equations by elimination of the time variable using Kantorovich time-averaging method. To determine nonlinear frequency of GMR under various boundary conditions, and considering mass effect, differential quadrature element method (DQEM) is used. Based on modified strain MSGT, the results of the current model are compared with the obtained results by classical and modified couple stress theories (CT and MCST). Furthermore, the effect of various parameters such as material length scale parameter, attached mass, temperature change, piezoelectric coefficient, two parameters of elastic foundations on the natural frequencies of BNMR is investigated. The results show that for all boundary conditions, by increasing the mass intensity in a fixed position, the linear and nonlinear natural frequency of the GMR reduces. In addition, with increasing of material length scale parameter, the frequency ratio decreases. This results can be used to design and control nano/micro devices and nano electronics to avoid resonance phenomenon.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2000년도 가을 학술발표회논문집(I)
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• pp.291-296
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• 2000

In this paper a relatively simple and reliable wall models are investigated, which are suitable to be efficiently incorporated in a practical nonlinear seismic analysis of reinforced concrete shear wall structural systems. Four types of analogous frames have been selected for the elastic stress analysis. Three types of macro-elements model which include wide-column model, truss model and Kabeyasawa model, are chosen for the use in nonlinear analysis. A numerical analysis is carried out for six stories plane coupled wall structure. Analysis results indicate that macro-elements wall model is effective and suitable for simulating stress in elastic analysis. In inelastic analysis, the yielding strength have little effect on different wall model, and the effect on post-yielding stiffness in story shear-drift relationship depend on force-deformation properties of macro-elements.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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• pp.300-306
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• 2004

This paper is concerned with the application of perturbation method to the dynamic analysis of free-free beam. In general, the rigid-body motions and elastic vibrations are analyzed separately. However, the rigid-body motions cause vibrations and elastic vibrations also affect rigid-body motions in turn, which indicates that the rigid-body motions and elastic vibrations are coupled in nature. The resulting equations of motion are hybrid and nonlinear. We can discretize the equations of motion by means of admissible functions but still we have to cope with nonlinear equations. In this paper, we propose the use of .perturbation method to the coupled equations of motion. The resulting equations consist of zero-order equations of motion which depict the rigid-body motions and first-order equations of motion which depict the perturbed rigid-body motions and elastic vibrations. Numerical results show the efficacy of the proposed method.

• Earthquakes and Structures
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• 제1권1호
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• pp.21-41
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• 2010

Multi-span steel-concrete composite (SCC) bridges are very sensitive to earthquake loading. Extensive damage may occur not only in the substructures (piers), which are expected to yield, but also in the other components (e.g., deck, abutments) involved in carrying the seismic loads. Current seismic codes allow the design of regular bridges by means of linear elastic analysis based on inelastic design spectra. In bridges with superstructure transverse motion restrained at the abutments, a dual load path behavior is observed. The sequential yielding of the piers can lead to a substantial change in the stiffness distribution. Thus, force distributions and displacement demand can significantly differ from linear elastic analysis predictions. The objectives of this study are assessing the influence of piers-deck stiffness ratio and of soil-structure interaction effects on the seismic behavior of continuous SCC bridges with dual load path, and evaluating the suitability of linear elastic analysis in predicting the actual seismic behavior of these bridges. Parametric analysis results are presented and discussed for a common bridge typology. The response dependence on the parameters is studied by nonlinear multi-record incremental dynamic analysis (IDA). Comparisons are made with linear time history analysis results. The results presented suggest that simplified linear elastic analysis based on inelastic design spectra could produce very inaccurate estimates of the structural behavior of SCC bridges with dual load path.