• Steel and Composite Structures
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• 제17권5호
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• pp.753-776
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• 2014

In this paper, nonlinear vibration and post-buckling analysis of beams made of functionally graded materials (FGMs) resting on nonlinear elastic foundation subjected to thermo-mechanical loading are studied. The thermo-mechanical material properties of the beams are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and to be temperature-dependent. The assumption of a small strain, moderate deformation is used. Based on Euler-Bernoulli beam theory and von-Karman geometric nonlinearity, the integral partial differential equation of motion is derived. Then this PDE problem which has quadratic and cubic nonlinearities is simplified into an ODE problem by using the Galerkin method. Finally, the governing equation is solved analytically using the variational iteration method (VIM). Some new results for the nonlinear natural frequencies and buckling load of the FG beams such as the influences of thermal effect, the effect of vibration amplitude, elastic coefficients of foundation, axial force, end supports and material inhomogenity are presented for future references. Results show that the thermal loading has a significant effect on the vibration and post-buckling response of FG beams.

• Advances in nano research
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• 제17권2호
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• pp.95-107
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• 2024

In this article, the semi-analytical method was used to analyze the nonlinear dynamic stability and vibration analysis of sandwich shallow spherical shells (SSSS). The SSSS was considered as functionally graded carbon nanotube-reinforced composites (FG-CNTRC) with three new patterns of FG-CNTRC. The governing equation was obtained and discretized utilizing the Galerkin method by implementing the von Kármán-Donnell nonlinear strain-displacement relations. The nonlinear dynamic stability was analyzed by means of the fourth-order Runge-Kutta method. Then the Budiansky-Roth criterion was employed to obtain the critical load for the dynamic post-buckling. The approximate solution for the deflection was represented by suitable mode functions, which consisted of the three modes of transverse nonlinear oscillations, including one symmetrically and two asymmetrical mode shapes. The influences of various geometrical characteristics and material parameters were studied on the nonlinear dynamic stability and vibration response. The results showed that the order of layers had a significant influence on the amplitude of vibration and critical dynamic buckling load.

• 한국생산제조학회지
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• 제7권6호
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• pp.36-41
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• 1998

The objective of this study is to investigate effects of prebuckling on the buckling of laminated composite cylindrical shells. axial compression is considered for laminated composite cylindrical shells with length to radius ratios. The shell walls are made of a laminate with several symmetric ply orientations. This study was made using finite difference energy method, utilizing the nonlinear bifurcation branch with nonlinear prebuckling displacements. The results are compared to the buckling loads determined when membrane prebuckling displacements are considered.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2007년도 춘계학술대회 논문집
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• pp.1564-1570
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• 2007

There are normally two types of the energy absorbers used in the crashworthiness of trains. The first is a structure type, which mainly used in not only the primary structures of the train but also the crash energy absorbers at the accident. The second is a module type, which just absorbs the crash energy independent of the primary structures and attached to the structures of the train. The expansion and inversion tube are widely used as the module type crash energy absorbers, especially in the train. The tubes should not be buckled under the load acting on the end of the tube in longitudinal direction during absorbing the crash energy. The buckling stability of the tubes is affected by the boundary conditions, thickness and length of tube. In this study, the effects of the length and thickness of the tubes on the buckling load are studied by using the ABAQUS, a commercial finite element analysis program, and then presents the guideline to design the tube. The analysis processes to compute the buckling load consist of a linear buckling analysis and a nonlinear post-buckling analysis. The buckling modes are evaluated by the linear buckling analysis, as using these modes, the buckling loads are computed by the nonlinear post-buckling analysis.

• Steel and Composite Structures
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• 제36권3호
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• pp.307-319
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• 2020

The upper chords in half-through truss bridges are prone to buckling due to a lack of the upper transverse connections. Taking into account geometric and material nonlinearity, nonlinear finite-element analysis of a simple supported truss bridge was carried out to exhibit effects of different types of initial imperfections. A half-wave of initial imperfection was proved to be effective in the nonlinear buckling analysis. And a parameter analysis of initial imperfections was also conducted to reveal that the upper chords have the greatest impact on the buckling, followed by the bottom chords, vertical and diagonal web members. Yet initial imperfections of transverse beams have almost no effect on the buckling. Moreover, using influence surface method, the combinatorial effects of initial imperfections were compared to demonstrate that initial imperfections of the upper chords play a leading role. Furthermore, the equivalent effective length coefficients of the upper chord were derived to be 0.2~0.28 by different methods, which implies vertical and diagonal web members still provide effective constraints for the upper chord despite a lack of the upper transverse connections between the two upper chords. Therefore, the geometrical and material nonlinear finite-element method is effective in the buckling analysis due to its higher precision. Based on nonlinear analysis and installation deviations of members, initial imperfection of l/500 is recommended in the nonlinear analysis of half-through truss bridges without initial imperfection investigation.

• Structural Engineering and Mechanics
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• 제67권4호
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• pp.337-346
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• 2018

The purpose of this study is to investigate thermal post-buckling analysis of a laminated composite beam subjected under uniform temperature rising with temperature dependent physical properties. The beam is pinned at both ends and immovable ends. Under temperature rising, thermal buckling and post-buckling phenomena occurs with immovable ends of the beam. In the nonlinear kinematic model of the post-buckling problem, total Lagrangian approach is used in conjunction with the Timoshenko beam theory. Also, material properties of the laminated composite beam are temperature dependent: that is the coefficients of the governing equations are not constant. In the solution of the nonlinear problem, incremental displacement-based finite element method is used with Newton-Raphson iteration method. The effects of the fibber orientation angles, the stacking sequence of laminates and temperature rising on the post-buckling deflections, configurations and critical buckling temperatures of the composite laminated beam are illustrated and discussed in the numerical results. Also, the differences between temperature dependent and independent physical properties are investigated for post-buckling responses of laminated composite beams.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2007년도 춘계학술대회A
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• pp.774-779
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• 2007

The crash energy absorbers used in the trains normally are classified into two types. The first is the structure type, which mainly used in not only the primary structure of train but also the crash energy absorbers at the critical accidents. The second is the module type, which just absorbs the crash energy independently and attached onto the structures of the trains. The expansion tube is widely used as the module type of the crash energy absorbers, especially in the trains that have a heavy mass. Since the crash energy is absorbed by means of expanding the tube in the radial direction, the features of the expansion tube have the uniform load during the compression. As the uniform load remains in sudden impact, the expansion tube is effective to decrease acceleration of passengers when the train accident occur. The buckling instability of the expansion tubes is affected by the boundary conditions, thickness and length of tube. In this study, the effects of the length and thickness of the expansion tubes under the arbitrary load on the buckling are studied using the ABAQUS/standard and ABAQUS/explicit, a commercial finite element analysis program, and then presents the guideline to design the expansion tubes. The analysis processes to compute the buckling load consist of the linear buckling analysis and the nonlinear post-buckling analysis. To analysis the nonlinear post-buckling analysis, the geometry imperfections are introduced by applying the linear buckling modes to nonlinear post-buckling analysis.

• Structural Engineering and Mechanics
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• 제35권5호
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• pp.555-570
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• 2010

Shallow fixed arches have a nonlinear primary equilibrium path with limit points and an unstable postbuckling equilibrium path, and they may also have bifurcation points at which equilibrium bifurcates from the nonlinear primary path to an unstable secondary equilibrium path. When a shallow fixed arch is subjected to a central step load, the load imparts kinetic energy to the arch and causes the arch to oscillate. When the load is sufficiently large, the oscillation of the arch may reach its unstable equilibrium path and the arch experiences an escaping-motion type of dynamic buckling. Nonlinear dynamic buckling of a two degree-of-freedom arch model is used to establish energy criteria for dynamic buckling of the conservative systems that have unstable primary and/or secondary equilibrium paths and then the energy criteria are applied to the dynamic buckling analysis of shallow fixed arches. The energy approach allows the dynamic buckling load to be determined without needing to solve the equations of motion.

• Advances in aircraft and spacecraft science
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• 제11권1호
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• pp.55-81
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• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• Journal of Advanced Marine Engineering and Technology
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• 제23권4호
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• pp.565-573
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• 1999

Hihg Tensile Steel enables to reduce the plate thickness comparing to the case when Mild Steel is used. From the economical view points this is very preferable since the reduction in the hull weight. however to use the High Tensile Steel effectively the plate thickness may become thin so that the occurrence of buckling is inevitable and design allowing plate buckling may be necessary. If the inplane stiffness of the plating decreases due to buckling the flexural rigidity of the cross sect6ion of a ship's hull also decreases. This may lead to excessive deflection of the hull girder under longitudinal bending. In these cases a precise estimation of plate's behavior after buckling is necessary and nonliner analysis of isolated and stiffened plates is required for structural sys-tem analysis. In this connection this paper discusses nonlinear behaviour of thin plate under thrust. Based on the analytical method elastic large deflection analysis of isolated plate is perform and simple expression are derived to evaluated the inplane rigidity of plates subjected to uniaxial compression.