• Structural Engineering and Mechanics
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• v.71 no.2
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• pp.185-196
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• 2019

In this investigation, study of the static and dynamic behaviors of functionally graded beams (FGB) is presented using a hyperbolic shear deformation theory (HySDT). The simply supported FG-beam is resting on the elastic foundation (Winkler-Pasternak types). The properties of the FG-beam vary according to exponential (E-FGB) and power-law (P-FGB) distributions. The governing equations are determined via Hamilton's principle and solved by using Navier's method. To show the accuracy of this model (HySDT), the current results are compared with those available in the literature. Also, various numerical results are discussed to show the influence of the variation of the volume fraction of the materials, the power index, the slenderness ratio and the effect of Winkler spring constant on the fundamental frequency, center deflection, normal and shear stress of FG-beam.

• Steel and Composite Structures
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• v.39 no.5
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• pp.631-643
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• 2021

The aim of this work is to study the hygro-thermo-mechanical bending responses of simply supported FG plate resting on a Winkler-Pasternak elastic foundation. The effect transverse shear strains is taken into account in which the zero transverse shear stress condition on the top and bottom surfaces of the plate is ensured without using any shear correction factors. The developed model contains only four unknowns variable which is reduced compared to other HSDTs models. The material properties of FG-plate are supposed to vary across the thickness of the plate according to power-law mixture. The differential governing equations are derived based on the virtual working principle. Numerical outcomes of bending analysis of FG plates under hygro-thermo-mechanical loads are performed and compared with those available in the literature. The effects of the temperature, moisture concentration, elastic foundation parameters, shear deformation, geometrical parameters, and power-law-index on the dimensionless deflections, axial and transverse shear stresses of the FG-plate are presented and discussed.

• Geomechanics and Engineering
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• v.13 no.4
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• pp.685-699
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• 2017

In order to determine the rate of penetrability, water pressure test is used before the grouting. One of the parameters which have the highest effect is pressure. Mathematical modeling is used for the first time in this study to determine the optimum pressure. Thus, the joints that exist in the rock mass are simulated using cylindrical shell model. The joint surroundings are also modeled through Pasternak environment. In order to validate the modeling, pressure values obtained by the model were used in the sites of Seymareh and Aghbolagh dams and the relative error rates were measured considering the differences between calculated and actual pressures recorded in these operations. In water pressure test, in Seymareh dam, the error values were equal to 4.75, 3.93, 4.8 percent and in the Aghbolagh dam, were 22.43, 5.22, 2.6 percent and in grouting operation in Seymareh dam were equal to 9.09, 32.50, 21.98, 5.57, 29.61 percent and in the Aghbolagh dam were 2.96, 5.40, 4.32 percent. Due to differences in rheological properties of water and grout and based on the overall results, modeling in water pressure test is more accurate than grouting and this error in water pressure test is 7.28 percent and in grouting is 13.92 percent.

• Computers and Concrete
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• v.19 no.2
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• pp.171-177
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• 2017

Water pressure test operation is used before the grouting to determine the rate of penetrability, the necessity and estimations related to grouting, by the penetration of water into the borehole. One of the parameters which have the highest effect is pressure of water penetration since the application of excessive pressure causes the hydraulic fracture to occur in the rock mass, and on the other hand, it must not be so small that prevents from seeing mechanical weaknesses and the rate of permeability. Mathematical modeling is used for the first time in this study to determine the optimum pressure. Thus, the joints that exist in the rock mass are simulated using cylindrical shell model. The joint surroundings are also modeled through Pasternak environment. To obtain equations governing the joints and the surroundings, energy method is used accompanied by Hamilton principle and an analytical solution method is used to obtain the maximum pressure. In order to validate the modeling, the pressure values obtained by the model were used in the sites of Seymareh and Aghbolagh dams and the relative error rates were measured considering the differences between calculated and actual pressures. Modeling in the sections of Seymareh dam showed 4.75, 3.93, 4.8 percent error rates and in the sections of Aghbolagh dam it rendered the values of 22.43, 5.22, 2.6 percent. The results indicate that this modeling can be used to estimate the amount of pressure for hydraulic fracture in water pressure test, to predict it and to prevent it.

• Steel and Composite Structures
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• v.34 no.1
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• pp.75-89
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• 2020

The current paper illustrates the effect of in-plane varying compressive force on critical buckling loads and buckling modes of sandwich composite laminated beam rested on elastic foundation. To generalize a proposed model, unified higher order shear deformation beam theories are exploited through analysis; those satisfy the parabolic variation of shear across the thickness. Therefore, there is no need for shear correction factor. Winkler and Pasternak elastic foundations are presented to consider the effect of any elastic medium surrounding beam structure. The Hamilton's principle is proposed to derive the equilibrium equations of unified sandwich composite laminated beams. Differential quadrature numerical method (DQNM) is used to discretize the differential equilibrium equations in spatial direction. After that, eigenvalue problem is solved to obtain the buckling loads and associated mode shapes. The proposed model is validated with previous published works and good matching is observed. The numerical results are carried out to show effects of axial load functions, lamination thicknesses, orthotropy and elastic foundation constants on the buckling loads and mode shapes of sandwich composite beam. This model is important in designing of aircrafts and ships when non-uniform compressive load and shear loading is dominated.

• Steel and Composite Structures
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• v.24 no.6
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• pp.711-726
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• 2017

In the present work, by considering the agglomeration effect of single-walled carbon nanotubes, free vibration characteristics of functionally graded (FG) nanocomposite sandwich plates resting on Pasternak foundation are presented. The volume fractions of randomly oriented agglomerated single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. To determine the effect of CNT agglomeration on the elastic properties of CNT-reinforced composites, a two-parameter micromechanical model of agglomeration is employed. In this research work, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented straight CNTs. The 2-D generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric and asymmetric profiles. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the laminated FG nanocomposite plates are investigated. It is shown that the natural frequencies of structure are seriously affected by the influence of CNTs agglomeration. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated plates.

• Steel and Composite Structures
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• v.48 no.3
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• pp.335-351
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• 2023

This research studies the primary resonance and nonlinear vibratory responses of multilayer functionally graded shallow (MFGS) shells under external excitations. The shells considered with functionally graded porous (FGP) core and resting on two types of nonlinear viscoelastic foundations (NVEF) governed by either a linear model with two parameters of Winkler and Pasternak foundations or a nonlinear model of hardening/softening cubic stiffness augmented by a Kelvin-Voigt viscoelastic model. The shells considered have three layers, sandwiched by functionally graded (FG), FGP, and FG materials. To investigate the influence of various porosity distributions, two types of FGP middle layer cores are considered. With the first-order shear deformation theory (FSDT), Hooke's law, and von-Kármán equation, the stress-strain relations for the MFGS shells with FGP core are developed. The governing equations of the shells are consequently derived. For the sake of higher accuracy and reliability, the P-T method is implemented in numerically analyzing the vibration, and the method of multiple scales (MMS) as one of the perturbation methods is used to investigate the primary resonance. The results of the present research are verified with the results available in the literature. The analytical results are compared with the P-T method. The influences of material, geometry, and nonlinear viscoelastic foundation parameters on the responses of the shells are illustrated.

• Structural Engineering and Mechanics
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• v.75 no.1
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• pp.87-100
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• 2020

The present paper investigates the combination resonance behavior of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells with internal and external functionally graded stiffeners under two-term large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation, which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness, to account for the vibration hardening/softening phenomena and damping considerations. With regard to classical plate theory of shells, von-Kármán equation and Hook law, the relations of stress-strain are derived for shell and stiffeners. The spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. According to the Galerkin method, the discretized motion equation is obtained. The combination resonance is obtained by using the multiple scales method. Finally, the influences of the stiffeners angles, foundation type, the nonlinear elastic foundation coefficients, material distribution, and excitation amplitude on the system resonances are investigated comprehensively.

• Computers and Concrete
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• v.21 no.5
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• pp.569-582
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• 2018

In this study, nonlinear vibration and stability of a polymeric pipe reinforced by single-walled carbon naotubes (SWCNTs) conveying fluid-nanoparticles mixture flow is investigated. The Characteristics of the equivalent composite are determined using Mori-Tanaka model considering agglomeration effects. The surrounding elastic medium is simulated by orthotropic visco-Pasternak medium. Employing nonlinear strains-displacements, stress-strain energy method the governing equations were derived using Hamilton's principal. Differential quadrature method (DQM) is used for obtaining the frequency and critical fluid velocity. The influence of volume percent of SWCNTs, agglomeration, geometrical parameters of pipe, viscoelastic foundation and fluid velocity are shown on the frequency and critical fluid velocity of pipe. Results showed the increasing volume percent of SWCNTs leads to higher frequency and critical fluid velocity.

• Geomechanics and Engineering
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• v.2 no.4
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• pp.281-302
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• 2010

An extended model for the response of a rigid footing on a reinforced foundation bed on super soft soil is proposed by incorporating the rough membrane element into the granular bed. The super soft soil, the granular bed and the reinforcement are modeled as non-linear Winkler springs, non-linear Pasternak layer and rough membrane respectively. The hyperbolic stress-displacement response of the super soft soil and the hyperbolic shear stress-shear strain response of the granular fill are considered. The finite deformation theory is used since large settlements are expected to develop due to deformation of the super-soft soil. Parametric studies quantify the effect of each parameter on the stress-settlement response of the reinforced foundation bed, the settlement and tension profiles.