• Structural Engineering and Mechanics
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• v.58 no.6
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• pp.949-966
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• 2016

The second order analysis taking place due to non-linear behavior of the structures under the mechanical and geometric factors through implementing exact and approximate methods is an indispensible issue in the analysis of such structures. Among the exact methods is the slope-deflection method that due to its simplicity and efficiency of its relationships has always been in consideration. By solving the differential equations of the modified slope-deflection method in which the effect of axial compressive force is considered, the stiffness matrix including trigonometric entries would be obtained. The complexity of computations with trigonometric functions causes replacement with their Maclaurin expansion. In most cases only the first two terms of this expansion are used but to obtain more accurate results, more elements are needed. In this paper, the effect of utilizing higher order terms of Maclaurin expansion on reducing the number of required elements and attaining more rapid convergence with less error is investigated for the Bernoulli beam with various boundary conditions. The results indicate that when using only one element along the beam length, utilizing higher order terms in Maclaurin expansion would reduce the relative error in determining the critical buckling load and kinematic parameters in the second order analysis.

• Steel and Composite Structures
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• v.22 no.6
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• pp.1281-1299
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• 2016

This paper deals with the analysis of vibration of antisymmetric angle-ply plates using spline method for higher order shear theory. Free vibration of laminated plates is addressed to show the capability of the present method in the vicinity of higher order shear deformation theory and simply supported edges of plates. The coupled differential equations are obtained in terms displacement and rotational functions. These displacement and rotational functions are approximated using cubic and quantic spline. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The antisymmetric angle-ply fiber orientation are taken as design variables. Numerical results enable us to examine the frequencies for various geometric and material parameters and accuracy and effectiveness of the proposed method is also verified by comparative study.

• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.573-585
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• 2018

This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.

• Smart Structures and Systems
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• v.16 no.1
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• pp.141-162
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• 2015

The magneto-rheological visco-elastomer (MRVE) is used as a smart core to control the stochastic micro-vibration of a sandwich plate with supported mass. The micro-vibration response of the sandwich plate with MRVE core and supported mass under stochastic support motion excitations is studied and compared to evaluate the vibration suppression capability. The effects of the supported mass and localized magnetic field on the stochastic micro-vibration response of the MRVE sandwich plate are taken into account. The dynamic characteristics of the MRVE core in micro-vibration are described by a non-homogeneous complex modulus dependent on vibration frequency and controllable by applied magnetic fields. The partial differential equations for the coupled transverse and longitudinal motions of the MRVE sandwich plate with supported mass are derived from the dynamic equilibrium, constitutive and geometric relations. The simplified ordinary differential equations are obtained for the transverse vibration of the MRVE sandwich plate under localized magnetic fields. A frequency-domain solution method for the stochastic micro-vibration response of sandwich plates with supported mass is developed based on the Galerkin method and random vibration theory. The expressions of frequency-response functions, response power spectral densities and root-mean-square velocity responses of the plate in terms of the one-third octave frequency band are obtained for micro-vibration evaluation. Finally, numerical results are given to illustrate the large response reduction capacity of the MRVE sandwich plate with supported mass under stochastic support motion excitations, and the influences of MRVE parameters, supported mass and localized magnetic field placement on the micro-vibration response.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.677-682
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• 2003

The non-linear dynamic characteristics of a semi-circular pipe conveying fluid are investigated when the pipe is clamped at both ends. To consider the geometric non-linearity for the radial and circumferential displacements, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived form the Galerkin method. The natural frequencies varying with the flow velocity are computed fen the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized- method. From these results, we should to describe the non-linear behavior to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

• Steel and Composite Structures
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• v.31 no.2
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• pp.201-216
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• 2019

This scientific paper provides a theoretical, numerical and experimental analysis of local stability of axially compressed columns made of thin-walled rectangular concrete-filled steel tubes (CFSTs), with the consideration of initial geometric imperfections. The work presented introduces the theory of elastic critical stresses in local buckling of rectangular wall members under uniform compression. Moreover, a numerical calculation method for the determination of the critical stress coefficient is presented, using a differential equation for a slender wall with a variety of boundary conditions. For comparison of the results of the numerical analysis with those collected by experiments, a new model is created to study the behaviour of the composite members in question by means of the ABAQUS computational-graphical software whose principles are based on the finite element method (FEM). In modelling the analysed members, the actual boundary and loading conditions and real material properties are taken into account, obtained from the experiments and material tests on these members. Finally, the results of experiments on such members are analysed and then compared with the numerical values. In conclusion, several recommendations for the design of axially compressed composite columns made of rectangular concrete-filled thin-walled steel tubes are suggested as a result of this comparison.

• Advances in nano research
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• v.17 no.1
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• pp.9-18
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• 2024

This paper presents the development of an educational management model for analyzing the dynamic instability of nanocomposite sandwich beams. The model aims to provide a comprehensive framework for understanding the behavior of sandwich micro beams with foam cores, featuring top and bottom layers made of smart and porous functionally graded materials (FGM) nanocomposites. The bottom layer is influenced by an external electric field, and the entire beam is supported by a visco-Pasternak foundation, accounting for spring, shear, and damping constants. Using the Kelvin-Voigt theory to model structural damping and incorporating size effects based on strain gradient theory, the model employs the parabolic shear deformation beam theory (PSDBT) to derive motion equations through Hamilton's principle. The differential quadrature method (DQM) is applied to solve these equations, accurately identifying the improvement in student understanding (ISU) of the beams. The impact of various parameters, including FGM properties, external voltage, geometric constants, and structural damping, on the DIR is thoroughly examined. The educational model is validated by comparing its outcomes with existing studies, highlighting the increase in ISU with the application of negative external voltage to the smart layer. This model serves as a valuable educational tool for engineering students and researchers studying the dynamic stability of advanced nanocomposite structures.

• Geomechanics and Engineering
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• v.8 no.6
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• pp.811-828
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• 2015

Proper modelling of the basal resistance terms is key in simulating the motion of fluidized granular flow. In this paper, standard depth-averaged governing equations of granular flow are used together with the classical Coulomb, Voellmy, and velocity dependent friction models (VDFM). A high-resolution modified TVDLF method is implemented to solve the partial differential equations without numerical oscillations. The effects of basal resistance terms on the motion of granular flows such as geometric shape evolution, travel times and final deposits are analyzed. Based on the numerical results, the predictions of the front and rear end positions and developing length of granular flow with Coulomb friction model show excellent agreements with experiment results reported by Hutter et al. (1995), and illustrate the validity of the numerical approach. For the Voellmy model, the higher value of turbulent coefficient than reality may obtain more reasonable predicted runout for the small-scale avalanche or granular flow. The energy exchange laws indicate that VDFM is different from the Coulomb and Voellmy models, although the flow characteristics of both three models fit the measurements and observations very well.

• Structural Engineering and Mechanics
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• v.53 no.3
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• pp.497-517
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• 2015

In this study, nonlocal nonlinear buckling analysis of embedded polymeric temperature-dependent microplates resting on an elastic matrix as orthotropic temperature-dependent elastomeric medium is investigated. The microplate is reinforced by single-walled carbon nanotubes (SWCNTs) in which the equivalent material properties nanocomposite are estimated based on the rule of mixture. For the carbon-nanotube reinforced composite (CNTRC) plate, both cases of uniform distribution (UD) and functionally graded (FG) distribution patterns of SWCNT reinforcements are considered. The small size effects of microplate are considered based on Eringen's nonlocal theory. Based on orthotropic Mindlin plate theory along with von K$\acute{a}$rm$\acute{a}$n geometric nonlinearity and Hamilton's principle, the governing equations are derived. Generalized differential quadrature method (GDQM) is applied for obtaining the buckling load of system. The effects of different parameters such as nonlocal parameters, volume fractions of SWCNTs, distribution type of SWCNTs in polymer, elastomeric medium, aspect ratio, boundary condition, orientation of foundation orthtotropy direction and temperature are considered on the nonlinear buckling of the microplate. Results indicate that CNT distribution close to top and bottom are more efficient than those distributed nearby the mid-plane for increasing the buckling load.

• Wind and Structures
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• v.26 no.1
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• pp.1-9
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• 2018

This research studies the dynamic analysis of a concrete column reinforced with titanium dioxide ($TiO_2$) nanoparticles under earthquake load. The effect of nanoparticles accumulation in a region of concrete column is examined using Mori-Tanaka model. The structure is simulated mathematically based on the theory of sinusoidal shear deformation theory (SSDT). By calculating strain-displacement and stress-strain relations, the system energies include potential energy, kinetic energy, and external works are derived. Then, using the Hamilton's principle, the governing equations for the structure are extracted. Using these equations, the response of the concrete column under earthquake load is investigated using the numerical methods of differential quadrature (DQ) and Newark. The purpose of this study is to study the effects of percentage of nanoparticles, nanoparticles agglomeration, geometric parameters and boundary conditions on the dynamic response of the structure. The results indicate that by increasing the volume percent of $TiO_2$ nanoparticles, the maximum dynamic deflection of the structure decreases.