In this paper, free vibration behavior of carbon nanotube (CNT) reinforced functionally graded thick laminated composite plates utilizing Reddy’s higher-order shear deformation theory (HSDT) is ...studied. To the best of authors’ knowledge, this paper is the first to incorporate HSDT with one of the element-free approaches to investigate this issue. The element-free IMLS-Ritz method is employed and four types of CNT distributions are considered. The resulting effective material properties of the CNT-reinforced composite are estimated by a detailed and straightforward Mori–Tanaka approach. The numerical results have been compared with the literature showing excellent agreement. Considering various CNT orientation angles, a parametric study showing the effects of CNT volume fraction, plate aspect ratio, plate width-to-thickness ratio and number of plate’s layers on the non-dimensional natural frequencies is investigated. Finally, the influence of boundary conditions on the sequence of the first six mode shapes for various lamination arrangements is presented.
This paper presents the free vibration behavior of carbon nanotube (CNT) reinforced functionally graded composite plates in a thermal environment based on Reddy’s higher-order shear deformation ...theory (HSDT). The element-free kp-Ritz method is used in this study. Four different types of CNT distributions are considered. The literature reveals that there is a research gap in investigating the mechanical behaviors of CNT reinforced functionally graded composite plates using Reddy’s HSDT in association with any of the mesh-free methods. To the authors’ knowledge, this paper is the first to use this approach to investigate the vibration behavior of CNT reinforced functionally graded composite plates in a thermal environment. The rule of mixture is used to estimate the resulting effective material properties. To verify the reliability of the present model, the obtained numerical results based on a conversion study have been compared with those found in the literature with evident agreement. Moreover, parametric studies have been conducted on the effects of CNT distribution, boundary conditions, plate aspect ratio, plate thickness-to-width ratio and CNT volume fraction on the non-dimensional natural frequencies. Furthermore, the effects of plate aspect ratio and plate thickness-to-width ratio on the sequence of the first six mode shapes have been investigated.
This paper mainly presents bending and free vibration analyses of thin-to-moderately thick composite plates reinforced by single-walled carbon nanotubes using the finite element method based on the ...first order shear deformation plate theory. Four types of distributions of the uniaxially aligned reinforcement material are considered, that is, uniform and three kinds of functionally graded distributions of carbon nanotubes along the thickness direction of plates. The effective material properties of the nanocomposite plates are estimated according to the rule of mixture. Detailed parametric studies have been carried out to reveal the influences of the volume fractions of carbon nanotubes and the edge-to-thickness ratios on the bending responses, natural frequencies and mode shapes of the plates. In addition, the effects of different boundary conditions are also examined. Numerical examples are computed by an in-house finite element code and the results show good agreement with the solutions obtained by the FE commercial package ANSYS.
Abstract
Progress in research of dragon rolled thick plates are summarized in this paper. Basic characteristics, reduction and gap supplement, plate bending, rolling force and energy parameters, ...shear deformation at the center of the thick plates and the materials and methods in current research were introduced. Although the potential of the application of dragon rolling in thick plate production is obvious, there are still many unsolved problems, especially that the experimental data is still less, therefore there is still a lot of work to do from the practical application.
This study brings to readers the generalized formulation of three-variable plate theory and an efficient computational approach for analyzing plates. The theory not only has three degree of freedoms ...(DOFs) per node, which complies with three dimensional space of full plate model as classical plate theory (CPT) but also accounts for the effect of shear deformation without any requirement of shear correction factors (SCF). A complete set of strong forms, weak form as well as classical and non-classical boundary conditions (BCs) for linear and geometrically nonlinear analysis are consistently derived in this paper through a variational approach. The strong forms are sixth order differential equations, resulting in the symmetrical fourth order differential weak form. It is known that Isogeometric Analysis (IGA) arguably outweighs classical finite element method in terms of high continuity and high order differentiability. Thanks to its advantage, an IGA framework for the generalized three-variable plate theory is formulated with completely locking-free and only three DOFs per node. The classical BCs are strongly enforced to system equations as usual whilst the non-classical BCs are weakly imposed by a penalty approach. The new plate theory with only three-variable is thereafter used for static linear and nonlinear analysis of isotropic and functionally graded material (FGM) plates to demonstrate its ability. The reliability and accuracy of the present approach are ascertained by comparing the obtained results with other existing ones. Based on a robust formulation devoted in the paper, the proposed approach can be further extended for numerous problems related to the shear deformable effect in the literature.
•We propose a novel theory and isogeometric implementation for linear and nonlinear analysis of isotropic and FG plates.•The new theory has three variables and captures well shear deformable effect.•Strong form of new theory is of sixth order leading to a fourth order differential weak form.•Isogeometric analysis can effectively handle the high order differentiability of the proposed theory.•The numerical results show the reliability and efficiency of the present method.
An investigation into the postbuckling and geometrically nonlinear behaviors of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shells is carried out in this study. The discrete ...nonlinear equation system is established based on non-uniform rational B-Spline (NURBS) basis functions and the first-order shear deformation shell theory (FSDT). The nonlinearity of shells is formed in the Total Lagrangian approach considering the von Karman assumption. The incremental solutions are obtained by using a modified Riks method. In the present formulation, the rule of mixture is used to estimate the effective material properties of FG-CNTRC shells. Effects of CNTs distribution, volume fraction and CNTs orientation on the postbuckling behavior of FG-CNTRC shells are particularly investigated. Exact geometries of shells are modeled by using NURBS interpolation. Several verifications are given to show the high reliability of the proposed formulation. Especially, some complex postbuckling curves of FG-CNTRC panels and cylinders are first provided that could be useful for future references.
•NURBS-based postbuckling analysis of functionally graded carbon nanotube-reinforced composite shells is performed in this paper.•The discrete nonlinear equation system is established based on non-uniform rational B-Spline (NURBS) basis functions and the first-order shear deformation shell theory (FSDT).•The nonlinearity of shells is formed in the Total Lagrangian approach considering the von Karman assumption.•Effects of CNTs distribution, volume fraction and CNTs orientation on the postbuckling behavior of FG-CNTRC shells are particularly investigated.•Some complex postbuckling curves of FG-CNTRC panels and cylinders are first provided that could be useful for future references.
Literature researching the active vibration control of functionally graded material (FGM) plates with piezoelectric layers using Reddy’s higher-order shear deformation theory (HSDT) using any of the ...element-free methods does not exist. To the best of the authors’ knowledge, this paper is the first to use Reddy’s HSDT with the element-free IMLS-Ritz method to investigate this problem. In this study, seven mechanical degrees of freedom (DOF) and one additional electrical DOF are considered for each node of the discretized domain. The natural frequency results of two FGM plates with top and bottom piezoelectric layers are compared with the literature in terms of various electrical and mechanical boundary conditions, volume fraction exponent (n) and dimension ratios, with obvious agreement. Furthermore, parametric studies are performed, for the first time, to study the effects of mechanical boundary conditions, n value, FGM plate thickness-to-width ratio and piezoelectric layer thickness to FGM plate thickness ratio on the natural frequency increment between open and closed circuit conditions. For the purpose of active vibration control, a constant velocity feedback approach is utilized. The effectiveness of two proposed positions, of piezoelectric sensor and actuator layers, to control the vibration of FGM plates is investigated.
In present paper, a unified size-dependent high-order beam model which contains various higher-order shear deformation beam models as well as Euler–Bernoulli and Timoshenko beam models is developed ...to study the simultaneous effects of nonlocal stress and strain gradient on the bending and buckling behaviors of nanobeams by using the nonlocal strain gradient theory. For this objective, a nonlocal parameter is introduced to capture the nonlocal effect and a material length scale parameter is involved to evaluate the strain gradient effect. The governing equations and the associated boundary conditions are formulated by using Hamilton's principle. Navier's method is utilized to obtain the analytical solutions for bending and buckling of a simply supported nanobeam. The present model is validated by comparing the obtained results with those available in literature. The influences of nonlocal parameter, material length scale parameter, slenderness ratio and shear deformation on the bending and buckling behaviors of the nanobeam are examined in detail. Results reveal that within the framework of nonlocal strain gradient theory, results predicted by Timoshenko beam model and various higher-order beam models are almost same with some negligible differences. Moreover, it is found that the nanobeam could exhibit either stiffness-softening effect or stiffness-hardening effect, which depends on the relative magnitude of the nonlocal parameter and the material length scale parameter.
The static bending and buckling behaviors of bi-directional functionally graded (BFG) plates with porosity are investigated in this paper. An improved first-order shear deformation theory with an ...assuming parabolic distribution shear stresses is developed to describe the displacement, strain, and stress fields of the plates. The significant novelty of the proposed theory is that the transverse shear stresses equal to zero at two free surfaces of the BFG plates. Therefore, no shear correction factor is required as in other first-order shear deformation theory. A four-node quadrilateral plate element (IMQ4) is developed based on the improved first-order shear deformation theory, mixed finite element method (FEM) and Hamilton's principle for analysis of BFG plates. Several comparison studies are provided to demonstrate the precision and robustness of the proposed plate element IMQ4. Then the proposed plate element, IMQ4, is employed to analyze the bending and buckling responses of the BFG plates. Some new numerical results on the flexural and buckling behaviors of BFG plates are achieved via a deep parametric study.
•A new mixed four-node quadrilateral plate element based on first-order shear deformation theory is established.•The proposed element is accuracy, robustness and good convergence.•The proposed element does not need any shear correction factors.•The bending and buckling behaviors of the bi-directional functionally graded with porosity are investigated.
A size-dependent sinusoidal shear deformation beam model is developed to investigate the free vibration of nanobeams based on the nonlocal strain gradient theory. The new model contains a nonlocal ...parameter and a material length scale parameter which can capture the size effect. The governing equations and boundary conditions are derived by employing Hamilton's principle. Navier's method is utilized to obtain analytical solutions for natural frequencies of simply supported nanobeams. The results are compared with other beam models and other classical and non-classical theories. Several numerical examples are presented to illustrate the effects of nonlocal parameter, material length scale parameter, slenderness ratio and shear deformation on the free vibration of nanobeams. It is found that natural frequencies predicted by the nonlocal strain gradient theory are higher than those predicted by nonlocal theory and lower than those obtained by strain gradient theory. When the length scale parameter is smaller than the nonlocal parameter, the nanobeam exerts a stiffness-softening effect. When the length scale parameter is larger than the nonlocal parameter, the nanobeam exerts a stiffness-hardening effect. Moreover, it is observed that the effect of shear deformation becomes more significant for nanobeams with lower values of slenderness ratios and for higher modes.
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