• Smart Structures and Systems
• /
• 제23권3호
• /
• pp.215-225
• /
• 2019

In the present paper, the nonlocal strain gradient refined model is used to study the thermal stability of sandwich nanoplates integrated with piezoelectric layers for the first time. The influence of Kerr elastic foundation is also studied. The present model incorporates two small-scale coefficients to examine the size-dependent thermal stability response. Elastic properties of nanoplate made of functionally graded materials (FGMs) are supposed to vary through the thickness direction and are estimated employing a modified power-law rule in which the porosity with even type of distribution is approximated. The governing differential equations of embedded sandwich piezoelectric porous nanoplates under hygrothermal loading are derived through Hamilton's principle where the Galerkin method is applied to solve the stability problem of the nanoplates with simply-supported edges. It is indicated that the thermal stability characteristics of the porous nanoplates are obviously influenced by the porosity volume fraction and material variation, nonlocal parameter, strain gradient parameter, geometry of the nanoplate, external voltage, temperature and humidity variations, and elastic foundation parameters.

• Advances in nano research
• /
• 제10권4호
• /
• pp.313-325
• /
• 2021

This paper is concerned with the buckling behavior of 2D and quasi-3D problem of functionally graded nanobeam founded on high order shear deformation beams theory and made by two different types of porous distribution materials in Nano- and micro-scales. The used Quasi-3D formulation takes into account the transverse shear effect and uses only three variables. Both formulations do not include the correction factor that is required in the first shear deformation theory proposed by Timoshenko. Governing equations are derived using the principle of virtual work. Analytical resolutions for buckling of FG nanobeam are introduced under tow different boundary conditions, and the results obtained are compared to those proposed in literatures.

• Structural Engineering and Mechanics
• /
• 제81권4호
• /
• pp.461-479
• /
• 2022

A finite element method analysis framework is introduced for the free vibration analyses of functionally graded porous beam structures by employing two variables trigonometric shear deformation theory. Both Young's modulus and material density of the FGP beam element are simultaneously considered as grading through the thickness of the beam. The finite element approach is developed using a nonlocal strain gradient theory. The governing equations derived here are solved introducing a 3-nodes beam element. A comprehensive parametric study is carried out, with a particular focus on the effects of various structural parameters such as the dispersion patterns of GPL reinforcements and porosity, thickness ratio, boundary conditions, nonlocal scale parameter and strain gradient parameters. The results indicate that porosity distribution and GPL pattern have significant effects on the response of the nanocomposite beams.

• Steel and Composite Structures
• /
• 제49권5호
• /
• pp.503-516
• /
• 2023

In the current examination, a trigonometric shear deformation theory is hired to govern natural frequencies of a functionally graded porous microplate which is covered by two nanocomposite layers. The properties of the structure are varied based on the specified patterns. Utilizing the modified form of couple stress theory for taking the scale effect into account in conjunction with Hamilton's principle, the motion equations are obtained. Then, they are solved via Fourier series functions as an analytical approach. After confirming the results' accuracy, various parameters' effect on the results is investigated. Designing and manufacturing more efficient structures, especially those that are subjected to multi-physical loads can be accounted as findings of this work.

• Structural Engineering and Mechanics
• /
• 제89권3호
• /
• pp.225-238
• /
• 2024

In this paper, a quasi-3D hyperbolic shear deformation theory for the bending responses of a functionally graded (FG) porous micro-beam is based on a modified couple stress theory requiring only one material length scale parameter that can capture the size influence. The model proposed accounts for both shear and normal deformation effects through an illustrative variation of all displacements across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the micro-beam. The effective material properties of the functionally graded micro-beam are assumed to vary in the thickness direction and are estimated using the homogenization method of power law distribution, which is modified to approximate the porous material properties with even and uneven distributions of porosity phases. The equilibrium equations are obtained using the virtual work principle and solved using Navier's technique. The validity of the derived formulation is established by comparing it with the ones available in the literature. Numerical examples are presented to investigate the influences of the power law index, material length scale parameter, beam thickness, and shear and normal deformation effects on the mechanical characteristics of the FG micro-beam. The results demonstrate that the inclusion of the size effects increases the microbeams stiffness, which consequently leads to a reduction in deflections. In contrast, the shear and normal deformation effects are just the opposite.

• Computers and Concrete
• /
• 제24권4호
• /
• pp.347-367
• /
• 2019

This work investigates the effect of Winkler/Pasternak/Kerr foundation and porosity on dynamic behavior of FG plates using a simple quasi-3D hyperbolic theory. Four different patterns of porosity variations are considered in this study. The used quasi-3D hyperbolic theory is simple and easy to apply because it considers only four-unknown variables to determine the four coupled vibration responses (axial-shear-flexion-stretching). A detailed parametric study is established to evaluate the influences of gradient index, porosity parameter, stiffness of foundation parameters, mode numbers, and geometry on the natural frequencies of imperfect FG plates.

• Coupled systems mechanics
• /
• 제9권6호
• /
• pp.499-519
• /
• 2020

The effect of porosity on the thermo-mechanical behavior of simply supported functionally graded plate reposed on the Winkler-Pasternak foundation is investigated analytically in the present paper using new refined hyperbolic shear deformation plate theory. Both even and uneven distribution of porosity are taken into account and the effective properties of FG plates with porosity are defined by theoretical formula with an additional term of porosity. The present formulation is based on a refined higher order shear deformation theory, which is based on four variables and it still accounts for parabolic distribution of the transverse shearing strains and stresses through the thickness of the FG plate and takes into account the various distribution shape of porosity. The elastic foundation is described by the Winkler-Pasternak model. Anew modified power-law formulation is used to describe the material properties of FGM plates in the thickness direction. The closed form solutions are obtained by using Navier technique. The present results are verified in comparison with the published ones in the literature. The results show that the dimensionless and stresses are affected by the porosity volume fraction, constituent volume fraction, and thermal load.

• Wind and Structures
• /
• 제21권3호
• /
• pp.273-287
• /
• 2015

In this paper, a free vibration analysis of functionally graded beam made of porous material is presented. The material properties are supposed to vary along the thickness direction of the beam according to the rule of mixture, which is modified to approximate the material properties with the porosity phases. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton's principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Coupled systems mechanics
• /
• 제9권6호
• /
• pp.575-597
• /
• 2020

Equilibrium equations of a porous FG plate resting on Winkler-Pasternak foundations with various boundary conditions are derived using a new refined shear deformation theory. Different types of porosity distribution rate are considered. Governing equations are obtained including the plate-foundation interaction. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The novel rule of mixture is proposed to describe and approximate material properties of the FG plates with different distribution case of porosity. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature. Effects of variation of porosity distribution rate, boundary conditions, foundation parameter, power law index, plate aspect ratio, side-to-thickness ratio on the deflections and stresses are all discussed.

• Steel and Composite Structures
• /
• 제42권5호
• /
• pp.599-615
• /
• 2022

In the present paper, the numerical dynamic analysis of a functionally graded nano-scale nonuniform tube was investigated according to the high-order beam theory coupled with the nonlocal gradient strain theory. The supposed cross-section is changed along the pipe length, and the material distribution, which combines both metal and ceramics, is smoothly changed in the pipe length direction, which is called axially functionally graded (AFG) pipe. Moreover, the porosity voids are dispersed in the cross-section and the radial pattern that the existence of both material distribution along the tube length and porosity voids make a two-dimensional functionally graded (2D-FG) truncated conical pipe. On the basis of the Hamilton principle, the governing equations and the associated boundary conditions equations are derived, and then a numerical approach is applied to solve the obtained equations.