• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.2
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• pp.113-125
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• 2007

Improved numerical method to obtain the exact stiffness matrices is newly proposed to perform the spatially coupled elastic and stability analyses of non-symmetric and open/closed thin-walled beam on elastic foundation. This method overcomes drawbacks of the previous method to evaluate the exact stiffness matrix for the spatially coupled stability analysis of thin-walled beam-column This numerical technique is accomplished via a generalized eigenproblem associated with 14 displacement parameters by transforming equilibrium equations to a set of first order simultaneous ordinary differential equations. Next polynomial expressions as trial solutions are assumed for displacement parameters corresponding to zero eigenvalues and the eigenmodes containing undetermined parameters equal to the number of zero eigenvalues are determined by invoking the identity condition. And then the exact displacement functions are constructed by combining eigensolutions and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently an exact stiffness matrix is evaluated by applying the member force-deformation relationships to these displacement functions. In order to illustrate the accuracy and the practical usefulness of this study, the numerical solutions are compared with results obtained from the thin-walled beam and shell elements.

• Smart Structures and Systems
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• v.20 no.3
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• pp.329-342
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• 2017

In this paper, the dispersion characteristics of elastic waves propagation in sandwich nano-beams with functionally graded (FG) face-sheets reinforced with carbon nanotubes (CNTs) is investigated based on various high order shear deformation beam theories (HOSDBTs) as well as nonlocal strain gradient theory (NSGT). In order to align CNTs as symmetric and asymmetric in top and bottom face-sheets with respect to neutral geometric axis of the sandwich nano-beam, various patterns are employed in this analysis. The sandwich nano-beam resting on Pasternak foundation is subjected to thermal, magnetic and electrical fields. In order to involve small scale parameter in governing equations, the NSGT is employed for this analysis. The governing equations of motion are derived using Hamilton's principle based on various HSDBTs. Then the governing equations are solved using analytical method. A detailed parametric study is conducted to study the effects of length scale parameter, different HSDBTs, the nonlocal parameter, various aligning of CNTs in thickness direction of face-sheets, different volume fraction of CNTs, foundation stiffness, applied voltage, magnetic intensity field and temperature change on the wave propagation characteristics of sandwich nano-beam. Also cut-off frequency and phase velocity are investigated in detail. According to results obtained, UU and VA patterns have the same cut-off frequency value but AV pattern has the lower value with respect to them.

• Geomechanics and Engineering
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• v.38 no.4
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• pp.381-395
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• 2024

With the wide application of urban subway tunnels, the foundation pits of new stations and existing subway tunnels are becoming increasingly close, and even zero-distance close-fitting construction has taken place. To optimize the construction support scheme, the existing tunnel's vertical displacement is theoretically analyzed using the two-stage analysis method to understand the action mechanism of the construction of zero-distance deep large foundation pits on both sides of the existing stations; a three-dimensional numerical calculation is also performed for further analysis. First, the additional stress field on the existing tunnel caused by the unloading of zero-distance foundation pits on both sides of the tunnel is derived based on the Mindlin stress solution of a semi-infinite elastic body under internal load. Then, considering the existing subway tunnel's joints, shear stiffness, and shear soil deformation effect, the tunnel is regarded as a Timoshenko beam placed on the Kerr foundation; a sixth-order differential control equation of the tunnel under the action of additional stress is subsequently established for solving the vertical displacement of the tunnel. These theoretical calculation results are then compared with the numerical simulation results and monitoring data. Finally, an optimized foundation pit support scheme is obtained considering the pit corner effect and external corner failure mode. The research shows a high consistency between the monitoring data,analytical and numerical solution, and the closer the tunnel is to the foundation pit, the more uplift deformation will occur. The internal corner of the foundation pit can restrain the deformation of the tunnel and the retaining structure, while the external corner can cause local stress concentration on the diaphragm wall. The proposed optimization scheme can effectively reduce construction costs while meeting the safety requirements of foundation pit support structures.

• Geomechanics and Engineering
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• v.32 no.5
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• pp.541-551
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• 2023

Snap-buckling is one of the main failure modes of structures, because it will lead to the reduction of structural bearing capacity, durability loss and even structural damage. Boundary condition plays an important role in the research of engineering mechanics. Further discussion on the boundary conditions problems will help to analyze the dynamic and static behavior of structures more accurately. Therefore, in order to understand the dynamic and static behavior of curved beams more comprehensively, this paper mainly studies the nonlinear snap-through buckling and forced vibration characteristics of functionally graded graphene reinforced composites (FG-GPLRCs) curved beams with two different boundary conditions (including clamped-hinged and hinged-hinged) using Euler-Bernoulli beam theory (E-BBT). In addition, the effects of the curved beam radius, the GLPs distributions, number of GLPs layers, the mass fraction of GLPs and elastic foundation parameters on the nonlinear snap-through buckling and forced vibration behavior are discussed respectively.

• Structural Engineering and Mechanics
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• v.54 no.6
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• pp.1061-1073
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• 2015

This paper presents a nonlocal sinusoidal shear deformation beam theory (SDBT) for the nonlinear vibration of single walled carbon nanotubes (CNTs). The present model is capable of capturing both small scale effect and transverse shear deformation effects of CNTs, and does not require shear correction factors. The surrounding elastic medium is simulated based on Pasternak foundation. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the CNTs are derived using Hamilton's principle. Differential quadrature method (DQM) for the natural frequency is presented for different boundary conditions, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory (TBT). The effects of nonlocal parameter, boundary condition, aspect ratio on the frequency of CNTs are considered. The comparison firmly establishes that the present beam theory can accurately predict the vibration responses of CNTs.

• Advances in nano research
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• v.10 no.3
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• pp.235-251
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• 2021

In the current study, the free vibrational behavior of a Porous Micro (PM) beam which is integrated with Functionally Graded Piezoelectric (FGP) layers with initial curvature is considered based on the two trigonometric shear deformation theories namely SSDBT and Tan-SDBT. The structure's mechanical properties are varied through its thicknesses following the given functions. The curved microbeam is exposed to electro-mechanical preload and also is rested on a Pasternak type of elastic foundation. Hamilton's principle is used to extract the motion equations and the MCST is used to capture the size effect. Navier's solution method is selected as an analytical method to solve the motion equations for a simply supported ends case and by validating the results for a simpler state with previously published works, effects of different important parameters on the behavior of the structure are considered. It is found that although increasing the porosity reduces the natural frequency, but enhancing the volume fraction of CNTs increasing it. Also, by increasing the central angle of the curved beam the vibrations of the structure increases. Designing and manufacturing more efficient smart structures such as sensors and actuators are of the aims of this study.

• Journal of Ocean Engineering and Technology
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• v.23 no.1
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• pp.54-59
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• 2009

In this paper, the effect of the position and size of a lumped mass on the structural stability of a high speed underwater vehicle is presented. For simplicity, a real vehicle was modeled as a follower force subjected beam that was resting on an elastic foundation, and the lumped mass effect was simplified as an elastic intermediate support. The stability of the simplified model was numerically analyzed based on the Finite element method (FEM). This numerical simulation revealed that flutter type instability or divergence type instability occurs, depending on the position and stiffness of the elastic intermediate support, which implies that the instability of the real model is affected by the position and size of the lumped mass.

• Smart Structures and Systems
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• v.18 no.5
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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.

• Computers and Concrete
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• v.33 no.1
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• pp.91-102
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• 2024

Beam-shaped components commonly rotate along a fixed axis when massive mechanical structures like rotors, jet engine blades, motor turbines, and rotating railway crossings perform their functions. For these structures to be useful in real life, their mechanical behavior is essential. Therefore, this is the first article to use the modified shear deformation theory type hyperbolic sine functions theory and the FEM to study the static bending response of rotating functionally graded GPL-reinforced composite (FG-GPLRC) beams with initial geometrical deficiencies in thermal media. Graphene platelets (GPLs) in three different configurations are woven into the beam's composition to increase its strength. By comparing the numerical results with those of previously published studies, we can assess the robustness of the theory and mechanical model employed in this study. Parameter studies are performed to determine the effect of various geometric and physical variables, such as rotation speed and temperature, on the bending reactions of structures.

• Journal of Industrial Technology
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• v.17
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• pp.191-197
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• 1997

For each construction material used, there is certain theoretical limit in sizes. For tall building construction, the reduction in slab weight is the first step to take in order to break such size limits. In this paper, the feasibility of such objective is proven and given by numerical analysis result. For a typical building slab, both concrete and advanced composite sandwich panels are considered. The concrete slab is treated as a special orthotropic plate to obtain more accurate result. Any method may be used to obtain the deflection influence surfaces needed for this vibration analysis. Finite difference method is used for this purpose, in this paper. The influence of the modulus of the foundation on the natural frequency is thoroughly studied.