• Structural Engineering and Mechanics
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• 제43권5호
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• pp.637-655
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• 2012

In this study, stochastic responses of a cable-stayed bridge subjected to the spatially varying earthquake ground motion are investigated by the finite element method taking into account soil-structure interaction (SSI) effects. The considered bridge in the analysis is Quincy Bay-view Bridge built on the Mississippi River in between 1983-1987 in Illinois, USA. The bridge is composed of two H-shaped concrete towers, double plane fan type cables and a composite concrete-steel girder deck. In order to determine the stochastic response of the bridge, a two-dimensional lumped masses model is considered. Incoherence, wave-passage and site response effects are taken into account for the spatially varying earthquake ground motion. Depending on variation in the earthquake motion, the response values of the cable-stayed bridge supported on firm, medium and soft foundation soil are obtained, separately. The effects of SSI on the stochastic response of the cable-stayed bridge are also investigated including foundation as a rigidly capped vertical pile groups. In this approach, piles closely grouped together beneath the towers are viewed as a single equivalent upright beam. The soil-pile interaction is linearly idealized as an upright beam on Winkler foundation model which is commonly used to study the response of single piles. A sufficient number of springs on the beam should be used along the length of the piles. The springs near the surface are usually the most important to characterize the response of the piles surrounded by the soil; thus a closer spacing may be used in that region. However, in generally springs are evenly spaced at about half the diameter of the pile. The results of the stochastic analysis with and without the SSI are compared each other while the bridge is under the sway of the spatially varying earthquake ground motion. Specifically, in case of rigid towers and soft soil condition, it is pointed out that the SSI should be significantly taken into account for the design of such bridges.

• Structural Engineering and Mechanics
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• 제84권5호
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• pp.685-697
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• 2022

Nanotechnology has become one of the interesting technique used in material science and engineering. However, it is low used in civil engineering structures. The purpose of the present study is to investigate the static behavior of concrete plates reinforced with silica-nanoparticles. Due to agglomeration effect of silica-nanoparticles in concrete, Voigt's model is used for obtaining the equivalent nano-composite properties. Furthermore, the plate is simulated mathematically with higher order shear deformation theory. For a large use of this study, the concrete plate is assumed resting on a Pasternak elastic foundation, including a shear layer, and Winkler spring interconnected with a Kerr foundation. Using the principle of virtual work, the equilibrium equations are derived and by the mean of Hamilton's principle the energy equations are obtained. Finally, based on Navier's technique, closed-form solutions of simply supported plates have been obtained. Numerical results are presented considering the effect of different parameters such as volume percent of SiO₂ nanoparticles, mechanical loads, geometrical parameters, soil medium, on the static behavior of the plate. The most findings of this work indicate that the use of an optimum amount of SiO₂ nanoparticles on concretes increases better mechanical behavior. In addition, the elastic foundation has a significant impact on the bending of concrete slabs.

• Steel and Composite Structures
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• 제47권5호
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• pp.551-568
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• 2023

In this research, a new two-dimensional (2D) and quasi three-dimensional (quasi-3D) higher order shear deformation theory is devised to address the bending problem of functionally graded plates resting on an elastic foundation. The displacement field of the suggested theories takes into account a parabolic transverse shear deformation shape function and satisfies shear stress free boundary conditions on the plate surfaces. It is expressed as a combination of trigonometric and exponential shear shape functions. The Pasternak mathematical model is considered for the elastic foundation. The material properties vary constantly across the FG plate thickness using different distributions as power-law, exponential and Mori-Tanaka model. By using the virtual works principle and Navier's technique, the governing equations of FG plates exposed to sinusoidal and evenly distributed loads are developed. The effects of material composition, geometrical parameters, stretching effect and foundation parameters on deflection, axial displacements and stresses are discussed in detail in this work. The obtained results are compared with those reported in earlier works to show the precision and simplicity of the current formulations. A very good agreement is found between the predicted results and the available solutions of other higher order theories. Future mechanical analyses of three-dimensionally FG plate structures can use the study's findings as benchmarks.

• Steel and Composite Structures
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• 제47권6호
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• pp.693-707
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• 2023

This article investigates the static thermo-mechanical response of anisotropic thick laminated composite plates on Visco-Pasternak foundations under various thermal load conditions (linear, non-linear, and uniform) along the transverse direction (thickness) of the plate, while keeping the mechanical load constant. The governing equations, which represent the thermo-mechanical behavior of the composite plate, are derived from the principle of virtual displacements. Using Navier's type solution, these equations are solved for the composite plate with simply supported condition. The Visco-Pasternak foundation type is included by considering the impact of the damping on the classical foundation model, which is modeled by Winkler's linear modulus and Pasternak's shear modulus. The excellent accuracy of the present solution is confirmed by comparing the results with those available in the literature. The study investigates the impact of geometric ratios, thermal expansion coefficient ratio, damping coefficient and foundation parameters on the thermo-mechanical flexural response of the composite plate. Overall, this article provides insights into the behavior of composite plates on visco-Pasternak foundations and may be useful for designing and analyzing composite structures in practical applications.

• Computers and Concrete
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• 제32권1호
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• pp.75-85
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• 2023

This work utilizes simplified higher-order shear deformation beam theory (HSDBT) to investigate the vibration response for functionally graded carbon nanotube-reinforced composite (CNTRC) beam. Novel to this work, single-walled carbon nanotubes (SWCNTs) are distributed and aligned in a matrix of polymer throughout the beam, resting on a viscoelastic foundation. Four un-similar patterns of reinforcement distribution functions are investigated for the CNTRC beam. Porosity is another consideration taken into account due to its significant effect on functionally graded materials (FGMs) properties. Three types of uneven porosity distributions are studied in this study. The damping coefficient and Winkler's and Pasternak's parameters are considered in investigating the viscosity effect on the foundation. Moreover, the impact of different parameters on the vibration of the CNTRC beam supported by a viscoelastic foundation is discussed. A comparison to other works is made to validate numerical results in addition to analytical discussions. The findings indicate that incorporating a damping coefficient can improve the vibration performance, especially when the spring constant factors are raised. Additionally, it has been noted that the fundamental frequency of a beam increases as the porosity coefficient increases, indicating that porosity may have a significant impact on the vibrational characteristics of beams.

• Advances in nano research
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• 제15권4호
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• pp.339-353
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• 2023

This work aims to present a solution for the buckling behavior of perforated nano/microbeams with deformable boundary conditions using nonlocal strain gradient theory (NLSGT). For the first time, a solution that can provide buckling loads based on the non-local and strain gradient effects of perforated nanostructures on an elastic foundation, while taking into account both deformable and rigid boundary conditions. Stokes' transformation and Fourier series are used to realize this aim and determine the buckling loads under various boundary conditions. We employ the NLSGT to account for size-dependent effects and utilize the Winkler model to formulate the elastic foundation. The buckling behavior of the perforated nano/microbeams restrained with lateral springs at both ends is studied for various parameters such as the number of holes, the length and filling ratio of the perforated beam, the internal length, the nonlocal parameter and the dimensionless foundation parameter. Our results indicate that the number of holes and filling ratio significantly affect the buckling response of perforated nano/microbeams. Increasing the filling ratio increases buckling loads, while increasing the number of holes decreases buckling loads. The effects of the non-local and internal length parameters on the buckling behavior of the perforated nano/microbeams are also discussed. These material length parameters have opposite effects on the variation of buckling loads. This study presents an effective eigenvalue solution based on Stokes' transformation and Fourier series of the restrained nano/microbeams under the effects of elastic medium, perforation parameters, deformable boundaries and nonlocal strain gradient elasticity for the first time.

• Computers and Concrete
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• 제34권2호
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• pp.179-193
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• 2024

The bending and buckling effect for carbon nanotube-reinforced composite (CNTRC) beams can be evaluated by developing the theory of third shear deformation (TSDT). This study examines beams supported by viscoelastic foundations, where single-walled carbon nanotubes (SWCNTs) are dispersed and oriented within a polymer matrix. Four patterns of reinforcement are used for the CNTRC beams. The rule of mixtures is assessed for the material properties of CNTRC beams. The effective functionally graded materials (FGM) properties are studied by considering three different uneven distribution types of porosity. The damping coefficient is considered to investigate the viscosity effect on the foundation in addition to Winkler's and Pasternak's parameters. The accuracy of the current theory is inspected with multiple comparison works. Moreover, the effects of different beam parameters on the CNTRC beam bending and buckling over a viscoelastic foundation are discussed. The results demonstrated that the O-beam is the weakest type of CNTRC beam to resist buckling and flexure loads, whereas the X-beam is the strongest. Moreover, it is indicated that the presence of porosity in the beams decreases the stiffness and increases deflection. In comparison, the deflection was reduced in the presence of a viscoelastic foundation.

• Steel and Composite Structures
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• 제20권4호
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• pp.889-911
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• 2016

Using the hyperbolic shear deformation plate model and including plate-foundation interaction (Winkler and Pasternak model), an analytical method in order to determine the deflection and stress distributions in simply supported rectangular functionally graded plates (FGP) subjected to a sinusoidal load, a temperature and moisture fields. The present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain is given. Materials properties of the plate (elastic, thermal and moisture expansion coefficients) are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Numerical examples are presented and discussed for verifying the accuracy of the present theory in predicting the bending response of FGM plates under sinusoidal load and a temperature field as well as moisture concentration. The effects of material properties, temperature, moisture, plate aspect ratio, side-to-thickness ratio, ratio of elastic coefficients (ceramic-metal) and three distributions for both temperature and moisture on deflections and stresses are investigated.

• Coupled systems mechanics
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• 제5권3호
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• pp.269-283
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• 2016

A two new high-order shear deformation theory for bending analysis is presented for a simply supported, functionally graded plate with porosities resting on an elastic foundation. This porosities may possibly occur inside the functionally graded materials (FGMs) during their fabrication, while material properties varying to a simple power-law distribution along the thickness direction. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theories presented are variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. It is established that the volume fraction of porosity significantly affect the mechanical behavior of thick function ally graded plates. The validity of the two new theories is shown by comparing the present results with other higher-order theories. The influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

• Structural Engineering and Mechanics
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• 제61권6호
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• pp.721-736
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• 2017

In this paper, free vibration characteristics of functionally graded (FG) nanobeams embedded on elastic medium are investigated based on third order shear deformation (Reddy) beam theory by presenting a Navier type solution for the first time. The material properties of FG nanobeam are assumed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on third order shear deformation beam theory through Hamilton's principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared to some cases in the literature. The obtained results are presented for the vibration analysis of the FG nanobeams such as the influences of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.