• Structural Engineering and Mechanics
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• 제53권6호
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• pp.1215-1240
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• 2015

In this work, a novel simple first-order shear deformation plate theory based on neutral surface position is developed for bending and free vibration analysis of functionally graded plates and supported by either Winkler or Pasternak elastic foundations. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Numerical results of present theory are compared with results of the traditional first-order and the other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.

• Interaction and multiscale mechanics
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• 제3권1호
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• pp.95-110
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• 2010

In recent years, study of the static response of pavements to moving vehicle and aircraft loads has received significant attention because of its relevance to the design of pavements and airport runways. The static response of beams resting on an elastic foundation and subjected to moving loads was studied by several researchers in the past. However, most of these studies were limited to steady-state analytical solutions for infinitely long beams resting on Winkler-type elastic foundations. Although the modelling of subgrade as a continuum is more accurate, such an approach can hardly be incorporated in analysis due to its complexity. In contrast, the two-parameter foundation model provides a better way for simulating the underlying soil medium and is conceptually more appealing than the one-parameter (Winkler) foundation model. The finite element method is one of the most suitable mathematical tools for analysing rigid pavements under moving loads. This paper presents an improved solution algorithm based on the finite element method for the static analysis of rigid pavements under moving vehicular or aircraft loads. The concrete pavement is discretized by finite and infinite beam elements, with the latter for modelling the infinity boundary conditions. The underlying soil medium is modelled by the Pasternak model allowing the shear interaction to exist between the spring elements. This can be accomplished by connecting the spring elements to a layer of incompressible vertical elements that can deform in transverse shear only. The deformations and forces maintaining equilibrium in the shear layer are considered by assuming the shear layer to be isotropic. A parametric study is conducted to investigate the effect of the position of moving loads on the response of pavement.

• Smart Structures and Systems
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• 제20권6호
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• pp.709-728
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• 2017

This disquisition proposes a nonlocal strain gradient beam theory for thermo-mechanical dynamic characteristics of embedded smart shear deformable curved piezoelectric nanobeams made of porous electro-elastic functionally graded materials by using an analytical method. Electro-elastic properties of embedded curved porous FG nanobeam are assumed to be temperature-dependent and vary through the thickness direction of beam according to the power-law which is modified to approximate material properties for even distributions of porosities. It is perceived that during manufacturing of functionally graded materials (FGMs) porosities and micro-voids can be occurred inside the material. Since variation of pores along the thickness direction influences the mechanical and physical properties, so in this study thermo-mechanical vibration analysis of curve FG piezoelectric nanobeam by considering the effect of these imperfections is performed. Nonlocal strain gradient elasticity theory is utilized to consider the size effects in which the stress for not only the nonlocal stress field but also the strain gradients stress field. The governing equations and related boundary condition of embedded smart curved porous FG nanobeam subjected to thermal and electric field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is utilized to achieve the natural frequencies of porous FG curved piezoelectric nanobeam resting on Winkler and Pasternak foundation. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality parameter, electric voltage, coefficient of porosity, elastic foundation parameters, thermal effect, gradient index, strain gradient, elastic opening angle and slenderness ratio on the natural frequency of embedded curved FG porous piezoelectric nanobeam are successfully discussed. It is concluded that these parameters play important roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.

• Structural Engineering and Mechanics
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• 제71권2호
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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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• 제32권2호
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• pp.157-171
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• 2019

In this research, the dynamic instability region (DIR) of the sandwich nano-beams are investigated based on nonlocal strain gradient elasticity theory (NSGET) and various higher order shear deformation beam theories (HSDBTs). The sandwich piezoelectric nano-beam is including a homogenous core and face-sheets reinforced with functionally graded (FG) carbon nanotubes (CNTs). In present study, three patterns of CNTs are employed in order to reinforce the top and bottom face-sheets of the beam. In addition, different higher-order shear deformation beam theories such as trigonometric shear deformation beam theory (TSDBT), exponential shear deformation beam theory (ESDBT), hyperbolic shear deformation beam theory (HSDBT), and Aydogdu shear deformation beam theory (ASDBT) are considered to extract the governing equations for different boundary conditions. The beam is subjected to thermal and electrical loads while is resting on Visco-Pasternak foundation. Hamilton principle is used to derive the governing equations of motion based on various shear deformation theories. In order to analysis of the dynamic instability behaviors, the linear governing equations of motion are solved using differential quadrature method (DQM). After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various shear deformation theories, nonlocal parameter, strain gradient parameter, the volume fraction of the CNTs, various distributions of the CNTs, different boundary conditions, dimensionless geometric parameters, Visco-Pasternak foundation parameters, applied voltage and temperature change on the dynamic instability characteristics of sandwich piezoelectric nano-beam.

• Steel and Composite Structures
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• 제30권1호
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• pp.13-29
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• 2019

This work presents the buckling investigation of functionally graded plates resting on two parameter elastic foundations by using a new hyperbolic plate theory. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only four unknowns and which is even less than the first order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT) by introducing undetermined integral terms, hence it is unnecessary to use shear correction factors. The governing equations are derived using Hamilton's principle and solved using Navier's steps. The validation of the proposed theoretical model is performed to demonstrate the efficacy of the model. The effects of various parameters like the Winkler and Pasternak modulus coefficients, inhomogeneity parameter, aspect ratio and thickness ratio on the behaviour of the functionally graded plates are studied. It can be concluded that the present theory is not only accurate but also simple in predicting the critical buckling loads of functionally graded plates on elastic foundation.

• Steel and Composite Structures
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• 제39권5호
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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.

• Steel and Composite Structures
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• 제43권6호
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• pp.821-837
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• 2022

This research is devoted to study the effects of humidity and temperature on the bending behavior of functionally graded (FG) ceramic-metal porous plates resting on Pasternak elastic foundation using a quasi-3D hyperbolic shear deformation theory developed recently. The present plate theory with only four unknowns, takes into account both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the functionally graded plate without using shear correction factors. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. The governing differential equations are obtained using the "principle of virtual work". Analytically, the Navier method is used to solve the equations that govern a simply supported FG porous plate. The obtained results are checked by comparing the results determined for the perfect and imperfect FG plates with those available in the scientific literature. Effects due to material index, porosity factors, moisture and thermal loads, foundation rigidities, geometric ratios on the FG porous plate are all examined. Finally, this research will help us to design advanced functionally graded materials to ensure better durability and efficiency for hygro-thermal environments.

• 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.

• Structural Engineering and Mechanics
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• 제89권2호
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• pp.103-119
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• 2024

The present research investigates the thermodynamically bending behavior of FG sandwich plates, laying on the Winkler/Pasternak/Kerr foundation with various boundary conditions, subjected to harmonic thermal load varying through thickness. The supposed FG sandwich plate has three layers with a ceramic core. The constituents' volume fractions of the lower and upper faces vary gradually in the direction of the FG sandwich plate thickness. This variation is performed according to various models: a Power law, Trigonometric, Viola-Tornabene, and the Exponential model, while the core is constantly homogeneous. The displacement field considered in the current work contains integral terms and fewer unknowns than other theories in the literature. The corresponding equations of motion are derived based on Hamilton's principle. The impact of the distribution model, scheme, aspect ratio, side-to-thickness ratio, boundary conditions, and elastic foundations on thermodynamic bending are examined in this study. The deflections obtained for the sandwich plate without elastic foundations have the lowest values for all boundary conditions. In addition, the minimum deflection values are obtained for the exponential volume fraction law model. The sandwich plate's non-dimensional deflection increases as the aspect ratio increases for all distribution models.