• Advances in nano research
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• v.10 no.5
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• pp.423-435
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• 2021

This paper examines the thermal post-buckling behaviors of graphene-reinforced metal matrix composite (GRMMC) laminated cylindrical panels which possess in-plane negative Poisson's ratio (NPR) and rest on an elastic foundation. A panel consists of GRMMC layers of piece-wise varying graphene volume fractions to obtain functionally graded (FG) patterns. Based on the MD simulation results, the GRMMCs exhibit in-plane NPR as well as temperature-dependent material properties. The governing equations for the thermal post-buckling of panels are based on the Reddy's third order shear deformation shell theory. The von Karman nonlinear strain-displacement relationship and the elastic foundation are also included. The nonlinear partial differential equations for GRMMC laminated cylindrical panels are solved by means of a singular perturbation technique in associate with a two-step perturbation approach and in the solution process the boundary layer effect is considered. The results of numerical investigations reveal that the thermal post-buckling strength for (0/90)_5T GRMMC laminated cylindrical panels can be enhanced with an FG-X pattern. The thermal post-buckling load-deflection curve of 6-layer (0/90/0)_S and (0/90)_3T panels of FG-X pattern are higher than those of 10-layer (0/90/0/90/0)_S and (0/90)_5T panels of FG-X pattern.

• Computers and Concrete
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• v.33 no.3
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• pp.241-250
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• 2024

This article investigates the thermal and post-buckling problems of graphene platelets reinforced metal foams (GPLRMF) beams with initial geometric imperfection. Three distribution forms of graphene platelet (GPLs) and foam are employed. This article utilizes the mixing law Halpin Tsai model to estimate the physical parameters of materials. Considering three different boundary conditions, we used the Euler beam theory to establish the governing equations. Afterwards, the Galerkin method is applied to discretize these equations. The correctness of this article is verified through data analysis and comparison with the existing articles. The influences of geometric imperfection, GPL distribution modes, boundary conditions, GPLs weight fraction, foam distribution pattern and foam coefficient on thermal post-buckling are analyzed. The results indicate that, perfect GPLRMF beams do not undergo bifurcation buckling before reaching a certain temperature, and the critical buckling temperature is the highest when both ends are fixed. At the same time, the structural stiffness of the beam under the GPL-A model is the highest, and the buckling response of the beam under the Foam-II mode is the lowest, and the presence of GPLs can effectively improve the buckling strength.

• Advances in nano research
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• v.6 no.4
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• pp.377-397
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• 2018

In the present investigation, thermal buckling and free vibration characteristics of functionally graded (FG) Timoshenko nanobeams subjected to nonlinear thermal loading are carried out by presenting a Navier type solution. The thermal load is assumed to be nonlinear distribution through the thickness of FG nanobeam. Thermo-mechanical properties of FG nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model and the material properties are assumed to be temperature-dependent. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the thermal buckling and vibration analysis of graded nanobeams including size effect. Moreover, in following a parametric study is accompanied to examine the effects of the several parameters such as nonlocal parameter, thermal effect, power law index and aspect ratio on the critical buckling temperatures and natural frequencies of the size-dependent FG nanobeams in detail. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared some cases in the literature. Also, it is found that the small scale effects and nonlinear thermal loading have a significant effect on thermal stability and vibration characteristics of FG nanobeams.

• Earthquakes and Structures
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• v.26 no.4
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• pp.251-259
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• 2024

In this paper, the thermal post-buckling behavior of graphene platelets reinforced metal foams (GPLRMFs) plate with initial geometric imperfections on nonlinear elastic foundations are studied. First, the governing equation is derived based on the first-order shear deformation theory (FSDT) of plate. To obtain a single equation that only contains deflection, the Galerkin principle is employed to solve the governing equation. Subsequently, a comparative analysis was conducted with existing literature, thereby verifying the correctness and reliability of this paper. Finally, considering three GPLs distribution types (GPL-A, GPL-B, and GPL-C) of plates, the effects of initial geometric imperfections, foam distribution types, foam coefficients, GPLs weight fraction, temperature changes, and elastic foundation stiffness on the thermal post-buckling characteristics of the plates were investigated. The results show that the GPL-A distribution pattern exhibits the best buckling resistance. And with the foam coefficient (GPLs weight fraction, elastic foundation stiffness) increases, the deflection change of the plate under thermal load becomes smaller. On the contrary, when the initial geometric imperfection (temperature change) increases, the thermal buckling deflection increases. According to the current research situation, the results of this article can play an important role in the thermal stability analysis of GPLRMFs plates.

• Steel and Composite Structures
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• v.22 no.6
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• pp.1359-1389
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• 2016

Buckling and free vibration behavior of a laminated cylindrical panel exposed to non-uniform thermal load is addressed in the present study. The approach comprises of three portions, in the first portion, heat transfer analysis is carried out to compute the non-uniform temperature fields, whereas second portion consists of static analysis wherein stress fields due to thermal load is obtained, and the last portion consists of buckling and prestressed modal analyzes to capture the critical buckling temperature as well as first five natural frequencies and associated mode shapes. Finite element is used to perform the numerical investigation. The detailed parametric study is carried out to analyze the effect of nature of temperature variation across the panel, laminate sequence and structural boundary constraints on the buckling and free vibration behavior. The relation between the buckling temperature of the panel under uniform temperature field and non-uniform temperature field is established using magnification factor. Among four cases considered in this study for position of heat sources, highest magnification factor is observed at the forefront curved edge of the panel where heat source is placed. It is also observed that thermal buckling strength and buckling mode shapes are highly sensitive to nature of temperature field and the effect is significant for the above-mentioned temperature field. Furthermore, it is also observed that the panel with antisymmetric laminate has better buckling strength. Free vibration frequencies and the associated mode shapes are significantly influenced by the non-uniform temperature variations.

• Advances in aircraft and spacecraft science
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• v.7 no.4
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• pp.335-351
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• 2020

Thermal buckling of functionally graded sandwich cylindrical shells is presented in this study. Material properties and thermal expansion coefficient of FGM layers are assumed to vary continuously through the thickness according to a sigmoid function and simple power-law distribution in terms of the volume fractions of the constituents. Equilibrium and stability equations of FGM sandwich cylindrical shells with simply supported boundary conditions are derived according to the Donnell theory. The influences of cylindrical shell geometry and the gradient index on the critical buckling temperature of several kinds of FGM sandwich cylindrical shells are investigated. The thermal loads are assumed to be uniform, linear and nonlinear distribution across the thickness direction. An exact simple form of nonlinear temperature rise through its thickness taking into account the thermal conductivity and the inhomogeneity parameter is presented.

• Steel and Composite Structures
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• v.27 no.6
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• pp.777-788
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• 2018

An investigation on the thermal buckling resistance of simply supported FGM beams having parabolic-concave thickness variation and temperature dependent material properties is presented in this paper. An analytical formulation based on the first order beam theory is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. a function of thickness variation is introduced which controls the parabolic variation intensity of the beam thickness without changing its original material volume. The results showed the high importance of taking into account the temperature-dependent material properties in the thermal buckling analysis of such critical beam sections. Different Influencing parametric on the thermal stability are studied which may help in design guidelines of such complex structures.

• Advances in nano research
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• v.7 no.3
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• pp.181-190
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• 2019

The thermal buckling temperature values of the graded carbon nanotube reinforced composite shell structure is explored using higher-order mid-plane kinematics and multiscale constituent modeling under two different thermal fields. The critical values of buckling temperature including the effect of in-plane thermal loading are computed numerically by minimizing the final energy expression through a linear isoparametric finite element technique. The governing equation of the multiscale nanocomposite is derived via the variational principle including the geometrical distortion through Green-Lagrange strain. Additionally, the model includes different grading patterns of nanotube through the panel thickness to improve the structural strength. The reliability and accuracy of the developed finite element model are varified by comparison and convergence studies. Finally, the applicability of present developed model was highlight by enlighten several numerical examples for various type shell geometries and design parameters.

• Advances in nano research
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• v.14 no.3
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• pp.261-271
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• 2023

The present study follows three main goals. First, an analytical solution with high accuracy is developed to assess the effects of embedding pre-strained shape memory alloy (SMA) wires on the critical buckling temperatures of rectangular sandwich plates made of soft core and graphite fiber/epoxy (GF/EP) face sheets based on piecewise low-order shear deformation theory (PLSDT) using Brinson's model. As the second goal, this study compares the effects of SMAs on the thermal buckling of sandwich plates with those of carbon nanotubes (CNTs). The glass transition temperature is considered as a limiting factor. For each material, the effective ranges of operating temperature and thickness ratio are determined for real situations. The results indicate that depending on the geometric parameters and thermal conditions, one of the SMAs and CNTs may outperform the other. The third purpose is to study the thermal buckling of sandwich plates with advanced hybrid SMA/CNT/GF/EP composite face sheets. It is shown that in some circumstances, the co-incorporation of SMAs and CNTs leads to an astonishing enhancement in the critical buckling temperatures of sandwich plates.

• Advances in nano research
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• v.1 no.1
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• pp.1-11
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• 2013

The thermal buckling properties of double-walled carbon nanotubes (DWCNTs) are studied using nonlocal Timoshenko beam model, including the effects of transverse shear deformation and rotary inertia. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. The geometric nonlinearity is taken into account, which arises from the mid-plane stretching. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling temperatures under uniform temperature rise are obtained. The results show that the critical buckling temperature can be overestimated by the local beam model if the nonlocal effect is overlooked for long nanotubes. In addition, the effect of shear deformation and rotary inertia on the buckling temperature is more obvious for the higher-order modes. The investigation of the thermal buckling properties of DWCNTs may be used as a useful reference for the application and the design of nanostructures in which DWCNTs act as basic elements.