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This is a fundamental study on the buckling temperature and post-buckling analysis of functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) disk covered with a piezoelectric actuator and surrounded by the nonlinear elastic foundation. The matrix material is reinforced with graphene nanoplatelets (GPLs) at the nanoscale. The displacement–strain of thermal post-buckling of the FG-GPLRC disk via third-order shear deformation theory and using Von Karman nonlinear plate theory is obtained. The equations of the model are derived from Hamilton’s principle and solved by the generalized differential quadrature method. The direct iterative approach is presented for solving the set of equations that includes highly nonlinear parameters. Finally, the results show that the radius ratio of outer to the inner (Ro/Ri), the geometrical parameter of GPLs, nonlinear elastic foundation, externally applied voltage, and piezoelectric thickness play an essential impact on the thermal post-buckling response of the piezoelectrically FG-GPLRC disk surrounded by the nonlinear elastic foundation. Another important consequence is that, when the effect of the elastic foundation is considered, there is a sinusoidal effect from the Ro/Ri parameter on the thermal post-buckling of the disk and this matter is true for both boundary conditions.

A beam model for thermal buckling analysis of a bimetallic box beam is presented. The Euler–Bernoulli–Vlasov beam theory is employed considering large rotations but small strains. The nonlinear stability analysis is performed using an updated Lagrangian formulation. In order to account for the thermal effects of temperature-dependent (TD) and temperature-independent (TID) materials, a uniform temperature rise through beam wall thickness is considered. The numerical results for thin-walled box beams are presented to investigate the effects of different boundary conditions, beam lengths and material thickness ratios on the critical buckling temperature and post-buckling responses. The effectiveness and accuracy of the proposed model are verified by means of comparison with a shell model. It is revealed that all of the abovementioned effects are invaluable for buckling analysis of thin-walled beams under thermal load. Moreover, it is shown that the TD solutions give lower values than the TID one, emphasizing the importance of TD materials in beams.

For the first time, a modified two-dimensional Fourier series approach is proposed for new thermal buckling analysis of rectangular thin plates under various edge conditions. The solution form of plate deflection is considered to be in terms of a double Fourier Sine series (Navier-form solution) whose derivatives are determined via utilizing the Stoke’s transform technic. The present study exhibits the following significant merits: (a) the method adopted allows one to consider any possible combination of boundary conditions with no necessity to be satisfied in the Fourier series; (b) the given solution procedure is simple and straightforward since the complicated boundary value problem (BVP) of partial differential equation (PDE) can be changed into solving sets of linear algebra equations, which heavily decreases the complicated mathematical manipulations of plate thermal buckling problem; (c) all the results acquired converge rapidly because of using the sum function of series. Greeting agreements between the present analytical solutions with the numerical results provided by FEM testifies the accuracy of the approach proposed. The present results are believed to be severe as new benchmarks for validating other methods and providing better design for plate structures. The influences of the aspect ratio and boundary condition on the thermal buckling behaviors of plates are also investigated and discussed. Furthermore, it is capable to extend the present solution procedure to deal with problems of plates under more complex edge conditions by ways of utilizing other Fourier series.

In this article, thermal buckling analysis of multilayer functionally graded graphene platelets (FGGPL) strengthened piezoelectric beam subjected to external electric voltage as well as humid conditions is illustrated. The effective Young’s modulus of the nanocomposite beam is estimated within the framework of Halpin-Tsai model. While, Poisson’s ratio, mass density, and piezoelectric properties are calculated by the rule of the mixture. Four FGGPL distribution types are considered in this study. A refined two-unknown beam theory considering shear deformation as well as thickness stretching effect is employed to describe the displacement components. The principle of virtual work including thermal, moisture, and electric loads is used to derive the stability differential equations. To check the accuracy of the obtained buckling temperature, some comparison examples are performed. The impacts of the GPLs volume fraction, distribution type, length-to-depth ratio, humid conditions, external electric voltage, and piezoelectric properties on the critical buckling temperature are studied.

This study utilizes higher‐order shear deformation and non‐local strain gradient elasticity theories to analyze the thermo‐mechanical vibrations and buckling of smart sandwich plates featuring functionally graded ceramic (Si3N4) and metal (Ni) surface layers, along with a Ni tetrachiral auxetic core. The governing equations are established through Hamilton's principle, with the Navier approach incorporating thermal and viscoelastic effects. Critical parameters encompass the length‐to‐thickness ratio, temperature, non‐local effects, metal‐to‐ceramic ratio, and layer thickness. Results indicate that increased nickel content and material size parameter and decreased plate thickness augment stiffness, whereas elevated material gradation, temperature, thickness ratio, non‐local parameter, and core thickness diminish natural frequency. This study significantly contributes by offering a novel framework for optimizing tetrachiral core sandwich nanoplates, thereby advancing high‐performance nanoscale engineering. The study presented investigates the thermo‐mechanical behavior of a sandwich structure with a tetrachiral‐shaped auxetic core. The geometric configuration, unit cell architecture, and the influence of the material length scale on the effective stiffness under temperature variation are illustrated. Results indicate a clear dependency of λ11 on both temperature difference (ΔT) and microstructural parameters.

In the present research, finite element solutions of thermal post-buckling load-bearing strength of functionally graded (FG) sandwich shell structures are reported by adopting a higher-order shear deformation type kinematics. For the numerical calculation, nine nodes are considered for each element. A specialized MATLAB code is developed incorporating the present mathematical model to evaluate the numerical buckling temperature. The Green–Lagrange nonlinear strain is adopted for the formulation of the sandwich structure. The eigenvalue equation of the FG sandwich structure is solved to predict the post-buckling temperature values of the structure. Moreover, three kinds of temperature distributions across the panel thickness are assumed, viz., uniform, linear and nonlinear. In addition, the properties are described using the power law distributions. The numerical solutions are first validated and, subsequently, the impact of alterations of structural parameters, viz., the curvature ratios, core–face thickness ratios, support conditions and power law index (nZ) including the amplitude ratio on the thermal post-buckling response of FG sandwich curved panels have been studied in details. The investigation reveals different interesting outcomes, which may help for future references for the analysis and design of the graded sandwich structure.

A new dieless forming method is proposed to produce metal bellows induced by local thermal buckling. The thermal buckling forming process is realized according to the local deformation behavior of metal tubes under the action of high temperature softening and axial pressure. In this paper, a forming device is designed and it is capable to produce metal bellows in two forming modes of a discontinuous bellow forming process and a continuous bellow forming process. FEM simulations are used to analyze this thermal buckling forming process and its product performance. The results show that the presented process can increase wall thickness and improve the energy absorption performance of metal bellows. Meanwhile, some thermal buckling forming cases of metal bellows of different materials and different sizes are presented.

An asymptotic analytical method is proposed to study the thermal post-buckling behaviors of fiber-reinforced composite (FRC)-laminated beams with geometric imperfections employing a modified zig-zag beam model. The beam model satisfied the discontinuity of the shear deformation at the interlayer interfaces and the stress boundary conditions on the upper and lower surfaces. Each imperfection was assumed to possess the same shape as the buckling mode, and the in-plane boundary conditions were presumed to be immovable. A two-step perturbation method was used to solve the nonlinear governing equations and obtain the equilibrium path. Subsequently, the initial defect sensitivity of the post-buckling behaviors was analyzed. The existence of the bifurcation-type equilibrium path for perfect beams is discussed in depth. Load–deflection curves for beams with various boundary conditions and ply modes were plotted to illustrate these findings. The effects of the slenderness ratio, elastic modulus ratio, thermal expansion coefficient ratio, ply modes, and supported boundaries on the buckling and post-buckling behaviors were also investigated. The numerical results indicate that the slenderness ratio significantly influences the critical buckling temperature, with thicker beams exhibiting higher buckling resistance. The elastic modulus ratio also plays a crucial role, with higher ratios leading to increased buckling strength. Additionally, the thermal expansion coefficient ratio affects the post-buckling load-bearing capacity, with lower ratios resulting in greater stability.

To accurately capture size effect and geometrically nonlinear effect on thermal post-buckling of micro-beams, a new theoretical analysis model is presented. The model is based on modified gradient elasticity and von Kármán geometrically nonlinear theory. Considering the thermal effect, the governing equations of thermal post-buckling are derived by the principle of minimum total potential energy. The complete information including post-buckling bifurcation, configuration, amplitude of hinged–hinged and clamped–clamped micro-beams under different temperature rises is obtained by analytical solution. Comprehensive discussions are represented for size effect and geometrically nonlinear effect on thermal post-buckling of micro-beams. It confirms that taking into account the effect of geometric nonlinearity results in smaller post-buckling amplitude and the buckling resistance increase with the decrease in beam size. Both size effect of the critical buckling temperature rises and the post-buckling amplitude can be captured. Compared with other models, the ability of this model to predict the thermal buckling behaviors is improved.

Purpose Thermal buckling of double-layered piezoelectric nanoplates has been analyzed by applying an external electric voltage on the nanoplates. The paper aims to discuss this issue. Design/methodology/approach Double-layered nanoplates are connected to each other by considering linear van der Waals forces. Nanoplates are placed on a polymer matrix. A comprehensive thermal stress function is used for investigating thermal buckling. A linear electric function is used for taking external electric voltages into account. For considering the small-scale effect, the modified couple stress theory has been applied. An analytical solution has been used by taking various boundary conditions. Findings EEV has a considerable impacted on the results of various half-waves in all boundary conditions. By increasing EEV, the reduction of critical buckling temperature in higher half-waves is remarkably slower than lower half-waves. By considering long lengths, the effect of EEV on the critical temperature will be markedly decreased. Originality/value This paper uses electro-thermal stability analysis. Double-layered piezoelectric nanoplates are analyzed. A comprehensive thermal stress function is applied for taking into account critical temperature.