Vibrational behavior of sandwich plates with functionally graded wavy carbon nanotube-reinforced face sheets resting on Pasternak elastic foundation

2017 ◽  
Vol 24 (11) ◽  
pp. 2327-2343 ◽  
Author(s):  
Rasool Moradi-Dastjerdi ◽  
Hamed Momeni-Khabisi
Keyword(s):  
Carbon Nanotube ◽  
Aspect Ratio ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Forced Vibrations ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Free And Forced Vibrations ◽  
Mesh Free ◽  
Pasternak Elastic Foundation

In this paper, free and forced vibrations, and also resonance and pulse phenomena in sandwich plates with an isotropic core and composite reinforced by wavy carbon nanotube (CNT) face sheets are studied based on a mesh-free method and first order shear deformation theory (FSDT). The sandwich plates are resting on Pasternak elastic foundation and subjected to periodic loads. In the mesh-free analysis, moving least squares (MLS) shape functions are used for approximation of displacement field in the weak form of motion equation and the transformation method is used for imposition of essential boundary conditions. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak’s elastic foundation coefficients, sandwich plate thickness, face sheets thickness, plate aspect ratio and time depended force are investigated on the free and forced vibrations, and resonance behavior of the sandwich plates with wavy CNT-reinforced face sheets.

Free Vibration and Buckling Analysis of Functionally Graded Plates Resting on Elastic Foundation Using Higher Order Theory

2018 ◽  
Vol 18 (04) ◽  
pp. 1850049 ◽  
Author(s):  
Smita Parida ◽  
Sukesh Chandra Mohanty
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Higher Order ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Pasternak Elastic Foundation

This paper deals with the free vibration and buckling analysis of functionally graded material (FGM) plates, resting on the Winkler–Pasternak elastic foundation. The higher order shear deformation plate theory (HSPT) is adopted for the realistic variation of transverse displacement through the thickness, using the power law distribution to describe the variation of the material properties. Both the effects of shear deformation and rotary inertia are considered. In the present model, the plate is discretised into [Formula: see text] eight noded serendipity quadratic elements with seven nodal degrees of freedom (DOFs). The validation study is carried out by comparing the calculated values with those given in the literature. The effects of various parameters like the Winkler and Pasternak modulus coefficients, volume fraction index, aspect ratio, thickness ratio and different boundary conditions on the behaviour of the FGM plates are studied.

scholarly journals Big data in nanocomposites: ONN approach and mesh-free method for functionally graded carbon nanotube-reinforced composites

2018 ◽  
Vol 6 (2) ◽  
pp. 209-223 ◽  
Author(s):  
Mostafa Jalal ◽  
Rasool Moradi-Dastjerdi ◽  
Morteza Bidram
Keyword(s):  
Neural Network ◽  
Big Data ◽  
Carbon Nanotube ◽  
Vibrational Frequency ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Computational Time ◽  
Reinforced Composites ◽  
Mesh Free ◽  
Mesh Free Method

Abstract In this paper, the concept of big data in composite materials for design purpose with focus on functionally graded carbon nanotube reinforced composites (FG-CNTRC) has been addressed through mesh-free method and an optimized neural network (ONN) approach. With this regard, mesh-free method as a robust technique was used to analyze the FG-CNTRC for vibrational frequency. The applied nanocomposite is made of aggregated single-walled carbon nanotubes (CNTs) that are embedded in an isotropic polymer as matrix. The material properties are estimated based on the Eshelby–Mori–Tanaka approach. Then a new multi-step approach was used to find optimized neural network for accurate modeling of the nanocomposite which can be used for later goals of optimization and design. Computational time and accuracy of various algorithms were investigated and compared for big data modeling of nanocomposite to come up with the optimal model. Comparative study of the results was carried out to examine and compare the accuracy of the developed ONN model relative to mesh-free method. Furthermore, a comprehensive parametric study was also performed to investigate the effect of geometrical dimensions, CNT distribution and volume fraction on vibrational frequency of the nanocomposite. Highlights Big data in nanocomposites. Analysis of nanocomposite through mesh-free method. Optimized neural network (ONN) for big data mining. Multi-step approach for finding an optimized model. Efficiency of ONN to handle big data.

Exact Solution for Free Vibration and Buckling of Sandwich S-FGM Plates on Pasternak Elastic Foundation with Various Boundary Conditions

2019 ◽  
Vol 19 (03) ◽  
pp. 1950028 ◽  
Author(s):  
S. J. Singh ◽  
S. P. Harsha
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Load Parameter ◽  
Various Boundary Conditions ◽  
Pasternak Elastic Foundation ◽  
Parametric Studies

In the present study, free vibration and buckling characteristics of a sandwich functionally graded material (FGM) plate resting on the Pasternak elastic foundation have been investigated. The formulation is based on non-polynomial higher-order shear deformation theory with inverse hyperbolic shape function. A new modified sigmoid law is presented to compute the effective material properties of sandwich FGM plate. The governing equilibrium equations have been derived using Hamilton’s principle. Non-dimensional frequencies and critical buckling loads are evaluated by considering different boundary conditions based on admissible functions satisfying the desired primary and secondary variables. Comprehensive parametric studies have been performed to analyze the influence of geometric configuration, volume fraction exponent, elastic medium parameter, and non-dimensional load parameter on the non-dimensional frequency and critical buckling load. These parametric studies have been done for various boundary conditions and different configurations of the sandwich plate. The computed results can be used as a benchmark for future comparison of sandwich S-FGM plates.

scholarly journals Thermo-Mechanical Post Buckling Analysis of Multiwall Carbon Nanotube-Reinforced Composite Laminated Beam under Elastic Foundation

2019 ◽  
Vol 6 (1) ◽  
pp. 212-228 ◽  
Author(s):  
Achchhe Lal ◽  
Kanif Markad
Keyword(s):  
Carbon Nanotube ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Coefficient Of Thermal Expansion ◽  
Buckling Analysis ◽  
Multiwall Carbon Nanotube ◽  
Laminated Beam ◽  
Reinforced Composite ◽  
Multi Walled Carbon Nanotube ◽  
Pasternak Elastic Foundation

AbstractIn present paper, buckling analysis is performed over laminated composite beam incorporating multi walled carbon nanotube (MWCNT) polymer matrix and then reinforced with E-glass fiber in an orthotropic manner under inplane varying thermal and mechanical loads by finite element method (FEM). Aim of the study is to develop a model which accurately perform the buckling deterministic analysis of multi-walled carbon nanotube reinforced composite laminated beam (MWCNTRCLB) with the evaluation of material property by applying Halpin–Tsai model. Combined Higher order shear deformation theory and Pasternak elastic foundation based on von Karman nonlinear kinematics and Winkler cubic nonlinearity respectively, are successfully implemented. Through minimum potential energy principle, generalized static analysis is performed using FEM, based on interactive MATLAB coding. The critical buckling load and critical buckling temperature is presented under the action of inplane variable mechanical and thermal load, with different boundary conditions, beam thickness ratio and MWCNT aspect ratio, variation with MWCNT volume fraction and coefficient of thermal expansion, with and without foundation for linear and nonlinear cases.

scholarly journals THERMAL BUCKLING ANALYSIS OF FUNCTIONALLY GRADED CIRCULAR PLATE RESTING ON THE PASTERNAK ELASTIC FOUNDATION VIA THE DIFFERENTIAL TRANSFORM METHOD

2017 ◽  
Vol 15 (3) ◽  
pp. 545 ◽  
Author(s):  
Fatemeh Farhatnia ◽  
Mahsa Ghanbari-Mobarakeh ◽  
Saeid Rasouli-Jazi ◽  
Soheil Oveissi
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Temperature Rise ◽  
Volume Fraction ◽  
Thermal Buckling ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Transform Method ◽  
Pasternak Elastic Foundation ◽  
Differential Transform

In this paper, we propose a thermal buckling analysis of a functionally graded (FG) circular plate exhibiting polar orthotropic characteristics and resting on the Pasternak elastic foundation. The plate is assumed to be exposed to two kinds of thermal loads, namely, uniform temperature rise and linear temperature rise through thickness. The FG properties are assumed to vary continuously in the direction of thickness according to the simple power law model in terms of the volume fraction of two constituents. The governing equilibrium equations in buckling are based on the Von-Karman nonlinearity. To obtain the critical buckling temperature, we exploit a semi-numerical technique called differential transform method (DTM). This method provides fast accurate results and has a short computational calculation compared with the Taylor expansion method. Furthermore, some numerical examples are provided to consider the influence of various parameters such as volume fraction index, thickness-to-radius ratio, elastic foundation stiffness, modulus ratio of orthotropic materials and influence of boundary conditions. In order to predict the critical buckling temperature, it is observed that the critical temperature can be easily adjusted by appropriate variation of elastic foundation parameters and gradient index of FG material. Finally, the numerical results are compared with those available in the literature to confirm the accuracy and reliability of the DTM to determine the critical buckling temperature.

scholarly journals Geometrically nonlinear free and forced vibrations analysis of clamped-clamped functionally graded beams with multicracks

2018 ◽  
Vol 211 ◽  
pp. 02002 ◽  
Author(s):  
Mohcine Chajdi ◽  
Ahmed Adri ◽  
Khalid El bikri ◽  
Rhali Benamar
Keyword(s):  
Volume Fraction ◽  
Geometrical Nonlinearity ◽  
Beam Theory ◽  
Forced Vibrations ◽  
Functionally Graded ◽  
Geometrically Nonlinear ◽  
Cracked Beam ◽  
Free And Forced Vibrations ◽  
Wide Range ◽  
Rotational Spring Model

Geometrically nonlinear free and forced vibrations of clampedclamped Functionally Graded beams with multi-cracks, located at different positions, based on the equivalent rotational spring model of crack and the transfer matrix method for beams is investigated. The FG beam properties are supposed to vary continuously through the thickness direction. The theoretical model is based on the Euler-Bernoulli beam theory and the Von Karman geometrical nonlinearity assumptions. A homogenization procedure, taking into account the presence of the crack, is developed to reduce the problem examined to that of an equivalent isotropic homogeneous multi-cracked beam. Upon assuming harmonic motion, the discretized expressions for the total strain and kinetic energies of the beam are derived, and through application of Hamilton’s principle and spectral analysis, the problem is reduced to a nonlinear algebraic system solved using an approximate explicit method developed previously (second formulation) to obtain numerically the FG multi-cracked beam nonlinear fundamental mode and the corresponding backbone curves for a wide range of vibration amplitudes. The numerical results presented show the effect of the number of cracks, the crack depths and locations, and the volume fraction on the beam nonlinear dynamic response.

Geometrically nonlinear buckling analysis of functionally graded carbon nanotube reinforced cylindrical panels resting on Winkler–Pasternak elastic foundation

2018 ◽  
Vol 233 (2) ◽  
pp. 702-712
Author(s):  
Pham Toan Thang
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Elastic Foundation ◽  
Cylindrical Panel ◽  
Functionally Graded ◽  
Geometrically Nonlinear ◽  
Nonlinear Buckling ◽  
Pasternak Elastic Foundation ◽  
Cylindrical Panels ◽  
Nonlinear Buckling Analysis

This paper deals with geometrically nonlinear buckling analysis of functionally graded carbon nanotube reinforced (FG-CNTR) cylindrical panels. The FG-CNTR cylindrical panel is assumed to be rested on the Winkler–Pasternak elastic foundation and subjected to uniform pressure. In the FG-CNTR cylindrical panel model, uniform and three distributions of carbon nanotubes, which are graded in the thickness direction of the panel, are considered. Effective properties of materials of the panels reinforced by single-walled carbon nanotubes are estimated through a micromechanical model based on the extended rule of mixtures. Governing equilibrium equations of the FG-CNTRC cylindrical panel are obtained based on the classical shell theory and considering the von Karman geometrically nonlinearity and initial geometric imperfection. A closed form of the resulting stability equations is established via the Galekin procedure to obtain the buckling load–deflection relations in case of simply supported boundary condition. In the numerical results section, the exactness of formulation is validated by comparing the obtained results with those reported in the open database. Then, a comprehensive investigation into the influence of carbon nanotube volume fraction, carbon nanotube distribution rule, imperfection parameter, elastic foundation as well as the geometry parameters on the nonlinear buckling behaviors of the FG-CNTRC cylindrical panels is discussed in detail.

Thermal and mechanical buckling of sandwich plates with FGM face sheets resting on the Pasternak elastic foundation

2011 ◽  
Vol 226 (1) ◽  
pp. 32-41 ◽  
Author(s):  
Y Kiani ◽  
E Bagherizadeh ◽  
M R Eslami
Keyword(s):  
Elastic Foundation ◽  
Power Law ◽  
Plate Theory ◽  
Plate Thickness ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Closed Form Solutions ◽  
Winkler Model ◽  
Pasternak Elastic Foundation ◽  
Mechanical Buckling

Instability of sandwich plates with functionally graded material (FGM) face sheets, which are in contact with elastic foundation and subjected to thermal or mechanical loading, is considered. The derivation of equations is based on the first-order shear deformation plate theory. It is assumed that the thermo-mechanical non-homogeneous properties of FGM layers vary smoothly by distribution of power law across the plate thickness. Using the non-linear strain–displacement relations, the equilibrium and stability equations of sandwich plates are derived. The boundary conditions for the plate are assumed to be simply supported in all edges. The elastic foundation is modelled by the two parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. Closed-form solutions are presented to calculate the critical buckling load or temperature, which are useful for engineers in design. The effects of the foundation parameters, sandwich plate dimensions, and power law index of the FGM layers are presented comprehensively for the thermo-mechanical buckling of sandwich plates.

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