• Advances in nano research
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• 제14권3호
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• pp.211-224
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• 2023

This work presents a modified analytical model for the bending behavior of axially functionally graded (AFG) carbon nanotubes reinforced composite (CNTRC) nanobeams. New higher order shear deformation beam theory is exploited to satisfy parabolic variation of shear through thickness direction and zero shears at the bottom and top surfaces.A Modified continuum nonlocal strain gradient theoryis employed to include the microstructure and the geometrical nano-size length scales. The extended rule of the mixture and the molecular dynamics simulations are exploited to evaluate the equivalent mechanical properties of FG-CNTRC beams. Carbon nanotubes reinforcements are distributed axially through the beam length direction with a new power graded function with two parameters. The equilibrium equations are derived with associated nonclassical boundary conditions, and Navier's procedure are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear, or sinusoidal mechanical loadings. Numerical results are carried out to investigate the impact of inhomogeneity parameters, geometrical parameters, loadings type, nonlocal and length scale parameters on deflections and stresses of the AFG CNTRC nanobeams. The proposed model can be used in the design and analysis of MEMS and NEMS systems fabricated from carbon nanotubes reinforced composite nanobeam.

• Structural Engineering and Mechanics
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• 제43권2호
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• pp.253-271
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• 2012

To analyze the bending and transverse shear effects of laminated composite plates, a thirteen nodes triangular element will be presented. The suggested formulations consider a parabolic variation of the transverse shear strains through the thickness. As a result, there is no need to use shear correction coefficients in computing the shear stresses. The proposed element can model both thin and thick plates without any problems, such as shear locking and spurious modes. Moreover, the effectiveness of $w_{,n}$, as an independent degree of freedom, is concluded by the present study. To perform the accuracy tests, several examples will be solved. Numerical results for the orthotropic materials with different boundary conditions, shapes, number of layers, thickness ratios and fiber orientations will be presented. The suggested element calculates the deflections and stresses more accurate than those available in the literature.

• Steel and Composite Structures
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• 제33권5호
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• pp.699-716
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• 2019

In this paper, wave propagations in sigmoid functionally graded (S-FG) plates are studied using new Higher Shear Deformation Theory (HSDT) based on two-dimensional (2D) elasticity theory. The current higher order theory has only four unknowns, which mean that few numbers of unknowns, compared with first shear deformations and others higher shear deformations theories and without needing shear corrector. The material properties of sigmoid functionally graded are assumed to vary through thickness according sigmoid model. The S-FG plates are supposed to be imperfect, which means that they have a porous distribution (even and uneven) through the thickness of these plates. The governing equations of S-FG plates are derived employed Hamilton's principle. Using technique of Navier, differential equations of S-FG in terms displacements are solved. Extensive results are presented to check the efficient of present methods to predict wave dispersion and velocity wave in S-FG plates.

• Steel and Composite Structures
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• 제21권6호
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• pp.1287-1306
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• 2016

The current research presents a buckling analysis of isotropic and orthotropic plates by proposing a new four variable refined plate theory. Contrary to the existing higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed model uses a new displacement field which incorporates undetermined integral terms and involves only four variables. The governing equations for buckling analysis are deduced by utilizing the principle of virtual works. The analytical solution of a simply supported rectangular plate under the axial loading has been determined via the Navier method. Numerical investigations are performed by using the proposed model and the obtained results are compared with CPT solutions, FSDT solutions, and the existing exact solutions in the literature. It can be concluded that the developed four variable refined plate theory, which does not use shear correction coefficient, is not only simple but also comparable to the FSDT.

• Structural Engineering and Mechanics
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• 제69권2호
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• pp.231-241
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• 2019

In this paper, a new higher order shear deformation model is developed for static and free vibration analysis of functionally graded beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. Different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. In addition, the effect of different micromechanical models on the bending and free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present higher-order shear deformation model, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain displacement, stresses and frequencies, and the numerical results are compared with those available in the literature. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, micromechanical models, mode numbers, and geometry on the bending and natural frequencies of imperfect FG beams.

• Steel and Composite Structures
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• 제18권2호
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• pp.409-423
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• 2015

In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams. The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect (${\varepsilon}_Z{\neq}0$) is also included in the present theory. Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors. The neutral surface position for such beams in which the material properties vary in the thickness direction is determined. Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle. Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses.

• Earthquakes and Structures
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• 제10권5호
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• pp.1033-1048
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• 2016

An analytical solution based on the neutral surface concept is developed to study the free vibration behavior of simply supported functionally graded plate reposed on the elastic foundation by taking into account the effect of transverse shear deformations. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain obtained by using a new refined shear deformation theory. The foundation is described by the Winkler-Pasternak model. The Young's modulus of the plate is assumed to vary continuously through the thickness according to a power law formulation, and the Poisson ratio is held constant. The equation of motion for FG rectangular plates resting on elastic foundation is obtained through Hamilton's principle. Numerical examples are provided to show the effect of foundation stiffness parameters presented for thick to thin plates and for various values of the gradient index, aspect and side to thickness ratio. It was found that the proposed theory predicts the fundamental frequencies very well with the ones available in literature.

• Advances in materials Research
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• 제9권1호
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• pp.63-98
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• 2020

The novelty of this paper is the use of a simple higher order shear and normal deformation theory for bending and free vibration analysis of functionally graded material (FGM) beams on two-parameter elastic foundation. To this aim, a new shear strain shape function is considered. Moreover, the proposed theory considers a novel displacement field which includes undetermined integral terms and contains fewer unknowns with taking into account the effects of both transverse shear and thickness stretching. Different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. In addition, the effect of different micromechanical models on the bending and free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams for which properties vary continuously across the thickness according to a simple power law. Hamilton's principle is used to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio, foundation parameter, the volume fraction of porosity and micromechanical models on the displacements, stresses, and frequencies.

• 한국지진공학회논문집
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• 제19권5호
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• pp.239-246
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• 2015

Reinforced concrete shear walls are effective for resisting lateral loads imposed by wind or earthquakes. Observed damages of the shear wall in recent earthquakes in Chile(2010) and New Zealand(2011) exceeded expectations. Various analytical models have been proposed in order to incorporate such response features in predicting the inelastic response of RC shear walls. However, the model has not been implemented into widely available computer programs, and has not been sufficiently calibrated with and validated against extensive experimental data at both local and global response levels. In this study, reinforced concrete shear walls were modeled with fiber slices, where cross section and reinforcement details of shear walls can be arranged freely. Nonlinear analysis was performed by adding nonlinear shear spring elements that can represent shear deformation. This analysis result will be compared with the existing experiment results. To investigate the nonlinear behavior of reinforced concrete shear walls, reinforced concrete single shear walls with rectangular wall cross section were selected. The analysis results showed that the yield strength of the shear wall was approximately the same value as the experimental results. However, the yielding displacement of the shear wall was still higher in the experiment than the analysis. The analytical model used in this study is available for the analysis of shear wall subjected to high axial forces.

• Wind and Structures
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• 제27권6호
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• pp.369-380
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• 2018

In this research work, nonlinear thermal buckling behavior of functionally graded (FG) plates is explored based a new higher-order shear deformation theory (HSDT). The present model has just four unknowns, by using a new supposition of the displacement field which enforces undetermined integral variables. A shear correction factor is, thus, not necessary. A power law distribution is employed to express the disparity of volume fraction of material distributions. Three kinds of thermal loading, namely, uniform, linear, and nonlinear and temperature rises over z-axis direction are examined. The non-linear governing equations are resolved for plates subjected to simply supported boundary conditions at the edges. The results are approved with those existing in the literature. Impacts of various parameters such as aspect and thickness ratios, gradient index, type of thermal load rising, on the non-dimensional thermal buckling load are all examined.