• Advances in nano research
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• v.6 no.2
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• pp.163-182
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• 2018

Based on the Reissner mixed variational theorem (RMVT), the authors present a nonlocal Timoshenko beam theory (TBT) for the nonlinear free vibration analysis of multi-walled carbon nanotubes (MWCNT) embedded in an elastic medium. In this formulation, four different edge conditions of the embedded MWCNT are considered, two different models with regard to the van der Waals interaction between each pair of walls constituting the MWCNT are considered, and the interaction between the MWCNT and its surrounding medium is simulated using the Pasternak-type foundation. The motion equations of an individual wall and the associated boundary conditions are derived using Hamilton's principle, in which the von $K{\acute{a}}rm{\acute{a}}n$ geometrical nonlinearity is considered. Eringen's nonlocal elasticity theory is used to account for the effects of the small length scale. Variations of the lowest frequency parameters with the maximum modal deflection of the embedded MWCNT are obtained using the differential quadrature method in conjunction with a direct iterative approach.

• Structural Engineering and Mechanics
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• v.49 no.1
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• pp.1-22
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• 2014

A seismic evaluation is made of the response to horizontal ground shaking of cantilever retaining walls using the finite element model in three dimensional space whose verification is provided analytically through the modal analysis technique in case of the assumptions of fixed base, complete bonding behavior at the wall-soil interface, and elastic behavior of soil. Thanks to the versatility of the finite element model, the retained medium is then idealized as a uniform, elastoplastic stratum of constant thickness and semi-infinite extent in the horizontal direction considering debonding behavior at the interface in order to perform comprehensive soil-structure interaction (SSI) analyses. The parameters varied include the flexibility of the wall, the properties of the soil medium, and the characteristics of the ground motion. Two different finite element models corresponding with flexible and rigid wall configurations are studied for six different soil types under the effects of two different ground motions. The response quantities examined incorporate the lateral displacements of the wall relative to the moving base and the stresses in the wall in all directions. The results show that the wall flexibility and soil properties have a major effect on seismic behavior of cantilever retaining walls and should be considered in design criteria of cantilever walls. Furthermore, the results of the numerical investigations are expected to be useful for the better understanding and the optimization of seismic design of this particular type of retaining structure.

• Steel and Composite Structures
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• v.24 no.4
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• pp.499-512
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• 2017

This paper deals with nonlinear dynamic stability of embedded piezoelectric nano-composite separators conveying pulsating fluid. For presenting a realistic model, the material properties of structure are assumed viscoelastic based on Kelvin-Voigt model. The separator is reinforced with single-walled carbon nanotubes (SWCNTs) which the equivalent material properties are obtained by mixture rule. The separator is surrounded by elastic medium modeled by nonlinear orthotropic visco Pasternak foundation. The separator is subjected to 3D electric and 2D magnetic fields. For mathematical modeling of structure, three theories of classical shell theory (CST), first order shear deformation theory (FSDT) and sinusoidal shear deformation theory (SSDT) are applied. The differential quadrature method (DQM) in conjunction with Bolotin method is employed for calculating the dynamic instability region (DIR). The detailed parametric study is conducted, focusing on the combined effects of the external voltage, magnetic field, visco-Pasternak foundation, structural damping and volume percent of SWCNTs on the dynamic instability of structure. The numerical results are validated with other published works as well as comparing results obtained by three theories. Numerical results indicate that the magnetic and electric fields as well as SWCNTs as reinforcer are very important in dynamic instability analysis of structure.

• Steel and Composite Structures
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• v.23 no.6
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• pp.691-714
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• 2017

Rotating fluid induced vibration and instability of embedded piezoelectric nano-composite separators subjected to magnetic and electric fields is the main contribution of present work. The separator is modeled with cylindrical shell element and the structural damping effects are considered by Kelvin-Voigt model. Single-walled carbon nanotubes (SWCNTs) are used as reinforcement and effective material properties are obtained by mixture rule. The perturbation velocity potential in conjunction with the linearized Bernoulli formula is used for describing the rotating fluid motion. The orthotropic surrounding elastic medium is considered by spring, damper and shear constants. The governing equations are derived on the bases of classical shell theory (CST), first order shear deformation theory (FSDT) and sinusoidal shear deformation theory (SSDT). The nonlinear frequency and critical angular fluid velocity are calculated by differential quadrature method (DQM). The detailed parametric study is conducted, focusing on the combined effects of the external voltage, magnetic field, visco-Pasternak foundation, structural damping and volume percent of SWCNTs on the stability of structure. The numerical results are validated with other published works as well as comparing results obtained by three theories. Numerical results indicate that with increasing volume fraction of SWCNTs, the frequency and critical angular fluid velocity are increased.

• Structural Engineering and Mechanics
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• v.7 no.6
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• pp.533-550
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• 1999

Optimal design of raft-pile foundations is examined by combining finite element technique and the optimization approach. The piles and soil medium are modeled by three dimensional solid elements while the raft is modelled by shell elements. Drucker-Prager criterion is adopted for the soil medium while the raft and the piles are assumed to be linear elastic. For the optimization process, the approximate semi-analytical method is used for calculating constraint sensitivities and a constraint approximation method which is a combination of the extended Bi-point approximation and Lagrangian polynomial approximation is used for predicting the behaviour of the constraints. The objective function of the problem is the volume of materials of the foundation while the design variables are raft thickness, pile length and pile spacing. The generalized reduced gradient algorithm is chosen for solving the optimization process. It is demonstrated that the method proposed in this study is promising for obtaining optimal design of raft-pile foundations without carrying out a large number of analyses. The results are also compared with those obtained from the previous study in which linear analysis was carried out.

• Structural Engineering and Mechanics
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• v.78 no.1
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• pp.23-30
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• 2021

In this paper, we established the generalized thermoelasticity phenomenon in an isotropic elastic medium considering the electromagnetic field, rotation and two-temperature. Three theories of generalized thermoelasticity have been applied: Lord-Shulman (one relaxation time), Green-Lindsay (two relaxation times), as well as the coupled theory. We discussed some particular cases in the context of the wave propagation phenomenon in thermoelasticity. From solving the fundamental equations, we arrived that there are three waves: P-, T- and SV-waves that we calculated their velocities. The boundary conditions for mechanical stress and Maxwell's stress and thermal insulated or isothermal have been applied to determine the amplitudes ratios (reflection coefficients) for P-, T - and SV waves. Some utilitarian aspects are obtained from the reflection coefficients, presented graphically, and the new conclusions have been presented. Comparisons are made for the results predicted by different theories (CT, LS, GL) in the absence and presence of the electro-magnetic field, rotation, as well as two-temperature on the reflection of generalized thermoelastic waves. The results obtained concluded that the external parameters as the angle of incidence, electromagnetic field, rotation as well as the theories parameters have strong effect on the phenomenon.

• Economic and Environmental Geology
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• v.27 no.3
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• pp.281-287
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• 1994

The present paper deals with numerical modeling of Love channel waves in transversely isotropic elastic medium. First, an explicit finite-difference scheme of second order approximation is formulated with the wave equation of SH particle displacement in transversely isotropic medium. Since it is a heterogeneous formulation, it should enable efficient modeling of complex model structures without additional treatment of the internal boundary matching. With a model of isotropic coal seam embedded in high velocity host rock, seismograms are synthesized and tutn out to be essentially identical with published ones of Korn and $St{\ddot{o}}ckl$. Next, anisotropic coal seams are investigated. It is found that the horizontal velocity of the seam appears to play a major role of determining the group velocity of Love channel waves. The group velocity increases with the increase of the horizontal velocity or vice versa. However, further study will be needed to exploit fully Love channel waves for the determination of lithology, stratification, fracture in sedimentary rocks, for instance, for hydrocarbon exploration and development.

• Structural Engineering and Mechanics
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• v.13 no.6
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• pp.615-638
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• 2002

This paper presents a method of seismic analysis for a cylindrical liquid storage structure considering the effects of the interior fluid and exterior soil medium in the frequency domain. The horizontal and rocking motions of the structure are included in this study. The fluid motion is expressed in terms of analytical velocity potential functions, which can be obtained by solving the boundary value problem including the deformed configuration of the structure as well as the sloshing behavior of the fluid. The effect of the fluid is included in the equation of motion as the impulsive added mass and the frequency-dependent convective added mass along the nodes on the wetted boundary of the structure. The structure and the near-field soil medium are represented using the axisymmetric finite elements, while the far-field soil is modeled using dynamic infinite elements. The present method can be applied to the structure embedded in ground as well as on ground, since it models both the soil medium and the structure directly. For the purpose of verification, earthquake response analyses are performed on several cases of liquid tanks on a rigid ground and on a homogeneous elastic half-space. Comparison of the present results with those by other methods shows good agreement. Finally, an application example of a reinforced concrete tank on a horizontally layered soil with a rigid bedrock is presented to demonstrate the importance of the soil-structure interaction effects in the seismic analysis for large liquid storage tanks.

• Earthquakes and Structures
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• v.11 no.5
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• pp.741-777
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• 2016

A simplified approach of assessing torsionally balanced (TB) and torsionally unbalanced (TU) low-medium rise buildings of up to 30 m in height is presented in this paper for regions of low-to-moderate seismicity. The Generalised Force Method of Analysis for TB buildings which is illustrated in the early part of the paper involves calculation of the deflection profile of the building in a 2D analysis in order that a capacity diagram can be constructed to intercept with the acceleration-displacement response spectrum diagram representing seismic actions. This approach of calculation on the planar model of a building which involves applying lateral forces to the building (waiving away the need of a dynamic analysis and yet obtaining similar results) has been adapted for determining the deflection behaviour of a TU building in the later part of the paper. Another key original contribution to knowledge is taking into account the strong dependence of the torsional response behaviour of the building on the periodic properties of the applied excitations in relation to the natural periods of vibration of the building. Many of the trends presented are not reflected in provisions of major codes of practices for the seismic design of buildings. The deflection behaviour of the building in response to displacement controlled (DC) excitations is in stark contrast to behaviour in acceleration controlled (AC), or velocity controlled (VC), conditions, and is much easier to generalise. Although DC conditions are rare with buildings not exceeding 30 m in height displacement estimates based on such conditions can be taken as upper bound estimates in order that a conservative prediction of the displacement profile at the edge of a TU building can be obtained conveniently by the use of a constant amplification factor to scale results from planar analysis.

• Tunnel and Underground Space
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• v.20 no.3
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• pp.153-168
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• 2010

A fifth equation is required to determine the five independent elastic constants of a transversely isotropic rock from compression test of a single specimen. As an approximation proposed by Saint-Venant has been used for long time, it may cause an erroneous result in some cases, especially for specimen with low angle of anisotropy. Three equations were suggested replacing this traditional equation and proved to be applicable by the model analysis in the previous studies. As Saint-Venant's approximation is turned out the same as the first one of them, it has the characteristics that the apparent Young's modulus is monotonously increasing according to the anisotropic angle. The methodology to analyze the elastic constants from four independent strain measurements by uniaxial compressive test of a single standard specimen is concisely described, and the necessity and compatibility of new suggested equations are discussed. Saint-Venant's approximation can determine the elastic constants close to true values and other equations may be unnecessary in specimens with medium to large angle. Nevertheless, they may become applicable because they can produce the almost same amount. For the specimens of small angle of anisotropy, Saint-Venant's approximation may result in out of general ranges or thermodynamic constraints, but other suggested equations can produce the almost true value. Thus they can be applied before other alternative equation is known. The guide map constructed by model study may decide the most compatible one of the three equations.