• Geomechanics and Engineering
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• 제21권5호
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• pp.471-487
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• 2020

In this work, the buckling analysis of material sandwich plates based on a two-parameter elastic foundation under various boundary conditions is investigated on the basis of a new theory of refined trigonometric shear deformation. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Applying the principle of virtual displacements, the governing equations and boundary conditions are obtained. To solve the buckling problem for different boundary conditions, Galerkin's approach is utilized for symmetric EGM sandwich plates with six different boundary conditions. A detailed numerical study is carried out to examine the influence of plate aspect ratio, elastic foundation coefficients, ratio, side-to-thickness ratio and boundary conditions on the buckling response of FGM sandwich plates. A good agreement between the results obtained and the available solutions of existing shear deformation theories that have a greater number of unknowns proves to demonstrate the precision of the proposed theory.

• Structural Engineering and Mechanics
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• 제62권4호
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• pp.401-415
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• 2017

A new higher shear deformation theory (HSDT) is presented for the thermal buckling behavior of functionally graded (FG) sandwich plates. It uses only four unknowns, which is even less than the first shear deformation theory (FSDT) and the conventional HSDTs. The theory considers a hyperbolic variation of transverse shear stress, respects the traction free boundary conditions and contrary to the conventional HSDTs, the present one presents a new displacement field which includes undetermined integral terms. Material characteristics and thermal expansion coefficient of the sandwich plate faces are considered to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are supposed as uniform, linear and non-linear temperature rises within the thickness direction. An energy based variational principle is used to derive the governing equations as an eigenvalue problem. The validation of the present work is carried out with the available results in the literature. Numerical results are presented to demonstrate the influences of variations of volume fraction index, length-thickness ratio, loading type and functionally graded layers thickness on nondimensional thermal buckling loads.

• Steel and Composite Structures
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• 제36권1호
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• pp.47-62
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• 2020

In this study, free vibration behavior of trapezoidal sandwich plates with porous core and two graphene platelets (GPLs) reinforced nanocomposite outer layers are presented. The distribution of pores and GPLs are supposed to be functionally graded (FG) along the thickness of core and nanocomposite layers, respectively. The effective Young's modulus of the GPL-reinforced (GPLR) nanocomposite layers is determined using the modified Halpin-Tsai micromechanics model, while the Poisson's ratio and density are computed by the rule of mixtures. The FSDT plate theory is utilized to establish governing partial differential equations and boundary conditions (B.C.s) for trapezoidal plate. The governing equations together with related B.C.s are discretized using a mapping- generalized differential quadrature (GDQ) method in the spatial domain. Then natural frequencies of the trapezoidal sandwich plates are obtained by GDQ method. Validity of current study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns of two faces through the thickness, porosity coefficient and distribution of porosity on natural frequencies characteristics. New results show the importance of this permeates on vibrational characteristics of porous/GPLR nanocomposite plates. Finally, the influences of B.C.s and dimension as well as the plate geometry such as face to core thickness ratio on the vibration behaviors of the trapezoidal plates are discussed.

• Steel and Composite Structures
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• 제51권1호
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• pp.73-91
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• 2024

This paper has focused on presenting vibration analysis of trapezoidal sandwich plates with a damaged core and FG wavy CNT-reinforced face sheets. A damage model is introduced to provide an analytical description of an irreversible rheological process that causes the decay of the mechanical properties, in terms of engineering constants. An isotropic damage is considered for the core of the sandwich structure. The classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. The First-order shear deformation theory of plate is utilized to establish governing partial differential equations and boundary conditions for the trapezoidal plate. The governing equations together with related boundary conditions are discretized using a mapping-generalized differential quadrature (GDQ) method in spatial domain. Then natural frequencies of the trapezoidal sandwich plates are obtained using GDQ method. Validity of the current study is evaluated by comparing its numerical results with those available in the literature. After demonstrating the convergence and accuracy of the method, different parametric studies for laminated trapezoidal structure including carbon nanotubes waviness (0≤w≤1), CNT aspect ratio (0≤AR≤4000), face sheet to core thickness ratio (0.1 ≤ ${\frac{h_f}{h_c}}$ ≤ 0.5), trapezoidal side angles (30° ≤ α, β ≤ 90°) and damaged parameter (0 ≤ D < 1) are carried out. It is explicated that the damaged core and weight fraction, carbon nanotubes (CNTs) waviness and CNT aspect ratio can significantly affect the vibrational behavior of the sandwich structure. Results show that by increasing the values of waviness index (w), normalized natural frequency of the structure decreases, and the straight CNT (w=0) gives the highest frequency. For an overall comprehension on vibration of laminated trapezoidal plates, some selected vibration mode shapes were graphically represented in this study.

• Steel and Composite Structures
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• 제48권3호
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• pp.275-291
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• 2023

This paper has focused on presenting vibration analysis of trapezoidal sandwich plates with 3D-graphene foam reinforced polymer matrix composites (GrF-PMC) core and FG wavy CNT-reinforced face sheets. The porous graphene foam possessing 3D scaffold structures has been introduced into polymers for enhancing the overall stiffness of the composite structure. Also, 3D graphene foams can distribute uniformly or non-uniformly in the plate thickness direction. The effective Young's modulus, mass density and Poisson's ratio are predicted by the rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. The First-order shear deformation theory of plate is utilized to establish governing partial differential equations and boundary conditions for trapezoidal plate. The governing equations together with related boundary conditions are discretized using a mapping-generalized differential quadrature (GDQ) method in spatial domain. Then natural frequencies of the trapezoidal sandwich plates are obtained using GDQ method. Validity of the current study is evaluated by comparing its numerical results with those available in the literature. It is explicated that 3D-GrF skeleton type and weight fraction, carbon nanotubes (CNTs) waviness and CNT aspect ratio can significantly affect the vibrational behavior of the sandwich structure. The plate's normalized natural frequency decreased and the straight carbon nanotube (w=0) reached the highest frequency by increasing the values of the waviness index (w).

• Advances in nano research
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• 제15권2호
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• pp.175-189
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• 2023

The under-evaluation structure includes a functionally graded porous (FGP) core which is confined by two piezoelectric carbon nanotubes reinforced composite (CNTRC) layers. The whole structure rests on the Pasternak foundation. Using quasi-3D hyperbolic shear deformation theory, governing equations of a sandwich plate are driven. Moreover, face sheets are subjected to the electric field and the whole model is under thermal loading. The properties of all layers alter continuously along with thickness direction due to the CNTs and pores distributions. By conducting the current study, the results emerged in detail to assess the effects of different parameters on buckling of structure. As instance, it is revealed that highest and lowest critical buckling load and consequently stiffness, is due to the V-A and A-V CNTs dispersion type, respectively. Furthermore, it is revealed that by porosity coefficient enhancement, critical buckling load and consequently, stiffness reduces dramatically. Current paper results can be used in various high-tech industries as aerospace factories.

• Steel and Composite Structures
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• 제43권5호
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• pp.581-601
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• 2022

The main objective of this research work is to investigate the free vibration behavior of annular sandwich plates resting on the Kerr foundation at thermal conditions. This sandwich configuration is composed of two FGM face sheets as coating layer and a porous GPLRC (GPL reinforced composite) core. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the core thickness direction. To model closed-cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme is used, while the Poisson's ratio and density are computed by the rule of mixtures. Besides, the material properties of two FGM face sheets change continuously through the thickness according to the power-law distribution. To capture fundamental frequencies of the annular sandwich plate resting on the Kerr foundation in a thermal environment, the analysis procedure is with the aid of Reddy's shear-deformation plate theory based high-order shear deformation plate theory (HSDT) to derive and solve the equations of motion and boundary conditions. The governing equations together with related boundary conditions are discretized using the generalized differential quadrature (GDQ) method in the spatial domain. Numerical results are compared with those published in the literature to examine the accuracy and validity of the present approach. A parametric solution for temperature variation across the thickness of the sandwich plate is employed taking into account the thermal conductivity, the inhomogeneity parameter, and the sandwich schemes. The numerical results indicate the influence of volume fraction index, GPLs volume fraction, porosity coefficient, three independent coefficients of Kerr elastic foundation, and temperature difference on the free vibration behavior of annular sandwich plate. This study provides essential information to engineers seeking innovative ways to promote composite structures in a practical way.

• Steel and Composite Structures
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• 제37권2호
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• pp.253-258
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• 2020

Vibration response in a sandwich plate with a nanocompiste core covered by magnetic layer is presented. The core is armed by functionalyy graded-carbon nanotubes (FG-CNTs) where the Mori-Tanaka law is utilized assuming agglomeration effects. The structure plate is located on elastic medium simulated by Pasternak model. The governing equations are derived based on Mindlin theory and Hamilton's principle. Utilizing diffrential quadrature method (DQM), the frequency of the structure is calculated and the effects of magnetic layer, volume percent and agglomeration of CNTs, elastic medium and geometrical parameters of structure are shown on the frequency of system. Results indicate that with considering magnetic layer, the frequency of structure is increased.

• Steel and Composite Structures
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• 제48권1호
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• pp.1-17
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• 2023

The main goal of this paper is to study vibration of damaged core laminated sectorial plates with Functionally graded (FG) face sheets based on three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. Three complicated equations of motion for the sectorial plates under consideration are semi-analytically solved by using 2-D differential quadrature method. Using the 2-D differential quadrature method in the r- and z-directions, allows one to deal with sandwich annular sector plate with arbitrary thickness distribution of material properties and also to implement the effects of different boundary conditions of the structure efficiently and in an exact manner. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The sandwich annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution and boundary conditions.

• Structural Engineering and Mechanics
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• 제85권3호
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• pp.289-304
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• 2023

The main objective of this paper is to study the effect of porosity on the buckling behavior of thick functionally graded sandwich plate resting on various boundary conditions under different in-plane loads. The formulation is made for a newly developed sandwich plate using a functional gradient material based on a modified power law function of symmetric and asymmetric configuration. Four different porosity distribution are considered and varied in accordance with material propriety variation in the thickness direction of the face sheets of sandwich plate, metal foam also is considered in this study on the second model of sandwich which containing metal foam core and FGM face sheets. New quasi-3D high shear deformation theory is used here for this investigate; the present kinematic model introduces only six variables with stretching effect by adopting a new indeterminate integral variable in the displacement field. The stability equations are obtained by Hamilton's principle then solved by generalized solution. The effect of Pasternak and Winkler elastic foundations also including here. the present model validated with those found in the open literature, then the impact of different parameters: porosities index, foam cells distribution, boundary conditions, elastic foundation, power law index, ratio aspect, side-to-thickness ratio and different in-plane axial loads on the variation of the buckling behavior are demonstrated.