• Smart Structures and Systems
• /
• v.18 no.5
• /
• pp.1029-1062
• /
• 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.

• Coupled systems mechanics
• /
• v.1 no.1
• /
• pp.1-7
• /
• 2012

The problem of laterally loaded piles is particularly a complex soil-structure interaction problem. The flexural stresses developed due to the combined action of axial load and bending moment must be evaluated in a realistic and rational manner for safe and economical design of pile foundation. The paper reports the finite element analysis of pile groups. For this purpose simplified models along the lines similar to that suggested by Desai et al. (1981) are used for idealizing various elements of the foundation system. The pile is idealized one dimensional beam element, pile cap as two dimensional plate element and the soil as independent closely spaced linearly elastic springs. The analysis takes into consideration the effect of interaction between pile cap and soil underlying it. The pile group is considered to have been embedded in cohesive soil. The parametric study is carried out to examine the effect of pile spacing, pile diameter, number of piles and arrangement of pile on the responses of pile group. The responses considered include the displacement at top of pile group and bending moment in piles. The results obtained using the simplified approach of the F.E. analysis are further compared with the results of the complete 3-D F.E. analysis published earlier and fair agreement is observed in the either result.

• Steel and Composite Structures
• /
• v.46 no.3
• /
• pp.367-383
• /
• 2023

In this investigation, an improved integral trigonometric shear deformation theory is employed to examine the vibrational behavior of the functionally graded (FG) sandwich plates resting on visco-Pasternak foundations. The studied structure is modelled with only four unknowns' variables displacements functions. The simplicity of the developed model being in the reduced number of variables which was made with the help of the use of the indeterminate integral in the formulation. The current kinematic takes into consideration the shear deformation effect and does not require any shear correction factors as used in the first shear deformation theory. The equations of motion are determined from Hamilton's principle with including the effect of the reaction of the visco-Pasternak's foundation. A Galerkin technique is proposed to solve the differentials governing equations, which enables one to obtain the semi-analytical solutions of natural frequencies for various clamped and simply supported FG sandwich plates resting on visco-Pasternak foundations. The validity of proposed model is checked with others solutions found in the literature. Parametric studies are performed to illustrate the impact of various parameters as plate dimension, layer thickness ratio, inhomogeneity index, damping coefficient, vibrational mode and elastic foundation on the vibrational behavior of the FG sandwich plates.

• Advances in nano research
• /
• v.7 no.2
• /
• pp.77-88
• /
• 2019

This paper infer the transient vibration of piezoelectric sandwich nanobeams, In present work, the flexoelectric effect on the mechanical properties of vibration piezoelectric sandwich nanobeam with different boundary conditions is investigated. According to the Nonlocal elasticity theory in nanostructures, the flexoelectricity is believed to be authentic for such size-dependent properties. The governing equations are derived by Hamilton's principle and boundary condition solved by Galerkin-based solution. This research develops a nonlocal flexoelectric sandwich nanobeam supported by Winkler-Pasternak foundation. The results of this work indicate that natural frequencies of a sandwich nanobeam increase by increasing the Winkler and Pasternak elastic constant. Also, increasing the nonlocal parameter at a constant length decreases the natural frequencies. By increasing the length to thickness ratio (L/h) of nanobeam, the nonlocal frequencies reduce.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.28 no.5
• /
• pp.553-561
• /
• 2015

The exponential and power law functionally graded material(FGM) theory is reformulated considering the refined shear and normal deformation theory. This theory has ability to capture the both normal deformation effect and exponential and power law function in terms of the volume fraction of the constituents for material properties through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported plates on Pasternak elastic foundation. Numerical solutions of vibration analysis of FGM plates are presented using this theory to illustrate the effects of power law index and 3-D theory of exponential and power law function on natural frequency. The relations between 3-D and 2-D higher-order shear deformation theory are discussed by numerical results. Further, effects of (i) power law index, (ii) side-to-thickness ratio, and (iii) elastic foundation parameter on nondimensional natural frequency are studied. To validate the present solutions, the reference solutions are discussed.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.16 no.1
• /
• pp.1-12
• /
• 2012

In this paper, the reduction factors to calculate the site coefficients of an embedded foundation are estimated, considering the effect of a poor backfill for the seismic design of a building built on an embedded foundation. This is determined by utilizing in-house finite element software, P3DASS, which has the capability of horizontal pseudo 3D seismic analysis with nonlinear soil. The 30m thick soil on stiff rock was assumed to be homogeneous, elastic, viscous and isotropic, and equivalent circular rigid foundations with radii of 10-70m were assumed to be embedded 0, 10, 20, and 30 m in the soil. Seismic analyses were performed with 7 bedrock earthquake records de-convoluted from the outcrop records; the scaling of the peak ground accelerations were to 0.1 g. The study results show that the site coefficients of a poor-backfilled foundation are gradually reduced as the foundation embedment ratio increases, except in the case of a small foundation embedded deeply in the weak soft soil. In addition, it was found that the deviation of the site coefficients due to the foundation size was not significant. Therefore, the typical reduction factors of an embedded foundation with poor backfill are proposed in terms of the shear wave velocity and site class. This is in order to find the site coefficients of an embedded foundation by multiplying the reduction factor by a site coefficient of a surface foundation specified in the design code. They can then be interpolated to determine the intermediate shear wave velocity.

• Steel and Composite Structures
• /
• v.26 no.4
• /
• pp.513-531
• /
• 2018

In this article, static, buckling and free vibration analyses of a sinusoidal micro composite beam reinforced by single-walled carbon nanotubes (SWCNTs) with considering temperature-dependent material properties embedded in an elastic medium in the presence of magnetic field under transverse uniform load are presented. This system is used at micro or sub micro scales to enhance the stiffness of micro composite structures such as bar, beam, plate and shell. In the present work, the size dependent effects based on surface stress effect and modified strain gradient theory (MSGT) are considered. The generalized rule of mixture is employed to predict temperature-dependent mechanical and thermal properties of micro composite beam. Then, the governing equations of motions are derived using Hamilton's principle and energy method. Numerical results are presented to investigate the influences of material length scale parameters, elastic foundation, composite fiber angle, magnetic intensity, temperature changes and carbon nanotubes volume fraction on the bending, buckling and free vibration behaviors of micro composite beam. There is a good agreement between the obtained results by this research and the literature results. The obtained results of this study demonstrate that the magnetic intensity, temperature changes, and two parameters elastic foundations have important effects on micro composite stiffness, while the magnetic field has greater effects on the bending, buckling and free vibration responses of micro composite beams. Moreover, it is shown that the effects of surface layers are important, and observed that the changes of carbon nanotubes volume fraction, beam length-to-thickness ratio and material length scale parameter have noticeable effects on the maximum deflection, critical buckling load and natural frequencies of micro composite beams.

• Steel and Composite Structures
• /
• v.19 no.5
• /
• pp.1203-1219
• /
• 2015

'Distortional buckling' is one of the predominant buckling types that may occur in a steel-concrete composite box beam (SCCBB) under a negative moment. The key factors, which affect the buckling modes, are the torsional and lateral restraints of the bottom plate of a SCCBB. Therefore, this article investigates the equivalent lateral and torsional restraint rigidity of the bottom plate of a SCCBB under a negative moment; the results of which show a linear coupling relationship between the applied forces and the lateral and/or torsional restraint stiffness, which are not depended on the cross-sectional properties of a SCCBB completely. The mathematical formulas for calculating the lateral and torsional restraint rigidity of the bottom plate can be used to estimate: (1) the critical distortional buckling stress of SCCBBs under a negative moment; and (2) the critical distortional moment of SCCBBs. This article develops an improved calculation method for SCCBBs on an elastic foundation, which takes into account the coupling effect between the applied forces and the lateral and/or torsional restraint rigidity of the bottom plate. This article analyzes the accuracy of the following calculation methods by using 24 examples of SCCBBs: (1) the conventional energy method; (2) the improved calculation method, as it has been derived in this article; and (3) the ANSYS finite element method. The results verify that the improved calculation method, as it has been proved in this article, is more accurate and reliable than that of the current energy method, which has been noted in the references.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.32 no.3C
• /
• pp.105-111
• /
• 2012

Bucket foundations, which are used in the foundations of offshore wind turbines, should be able to withstand large amounts of horizontal and moment loads. Tripod bucket foundation, which combines three single buckets, has been used to increase horizontal and moment capacities. This study performed numerical analysis using ABAQUS (2010), to analyze the group effect and the bearing capacity of a tripod bucket in clay. Parametric studies were performed varying the bucket spacing ratio S/D (S=spacing between the centers of the bucket and the tower; D=diameter of the bucket) and depth ratio L/D (L=embedded length of skirt). The applied constitutive models were a linear elastic perfectly plastic model with Tresca yield criteria for normally consolidated clay and an elastic model for buckets. Loading in the vertical, horizontal, and moment directions was simulated with an increase in each movement at a reference point. The bearing behavior and the capacities of a single and a tripod bucket were compared. Capacity evaluation method of the tripod bucket was suggested using the capacity of a single bucket.

• International Journal of Highway Engineering
• /
• v.7 no.4 s.26
• /
• pp.141-150
• /
• 2005

The behavior of the concrete slabs-on-grade considering the horizontal resistance at the slab bottom, which exists due to the shear resistance of the foundation and the friction between the slab and the foundation, has been investigated when the slabs-on-grade are subjected to the vertical load. Analytical formulations have been developed to include the effect of the horizontal resistance at the slab bottom, and the solutions have been obtained in the transformed field domain using the Fourier transform. Finite element formulations have also been developed using the plate bending elements and the flat shell elements. The solutions from the analytical and numerical models have been compared and showed very good agreement. The sensitivity of the horizontal resistance to the stresses of the concrete slab has been investigated with various values of the slab thickness, elastic modulus, and vertical stiffness of the foundation. The analysis results show that the horizontal resistance at the plate bottom can significantly affect the stresses of the slab.