Thermomechanical Buckling Research Articles

Nonlinear thermo-mechanical dynamic buckling and vibration of FG-GPLRC circular plates and shallow spherical shells resting on the nonlinear viscoelastic foundation

Nonlinear thermo-mechanical dynamic buckling and vibration of FG-GPLRC circular plates and shallow spherical shells resting on the nonlinear viscoelastic foundation

On thermo-mechanical buckling of porous bi-directional functionally graded plates using isogeometric analysis

The combined thermal and mechanical loads usually lead to buckling failure of key structures in various engineering fields. It is found that porous functionally graded structures can be used to reduce and evenly prevent potential impact on the stability of structures from extremely high temperature loads. In this paper, we employ the isogeometric analysis (IGA) method to investigate the thermo-mechanical coupling buckling behaviors of porous bi-directional functionally graded (PB-FGM) plates with porosity. The material properties such as Young's modulus, Poisson's ratio, and thermal expansion coefficient are assumed to be linearly dependent on the x-axial and z-axial coordinates. Such a gradient property can be easily realized by changing the porosity distribution. Based on the first-order shear deformation theory (FSDT), the thermo-mechanical buckling behaviors of PB-FGM rectangular and circular plates under combined thermal and mechanical loads are numerically studied. This paper elucidates the mechanical mechanism through which gradient indexes, aspect ratios, loading types, and boundary conditions influence the critical thermo-mechanical coupling-induced buckling temperature.

Thermomechanical buckling and vibration of composite sandwich doubly curved shells with carbon nanotube‐reinforced face layers

AbstractIn this paper, the thermomechanical buckling and vibration analysis are investigated for carbon nanotube‐reinforced composite sandwich doubly curved shells (CNCSDS) under the action of both thermal loads and in‐plane compressive loads. Based on the von‐Karman non‐linear kinematic relations, First Order Shear Theory, and Hamilton's principle, the vibration and stability equations for CNCSDS under thermomechanical loads are deduced. For obtaining the critical thermomechanical buckling load and vibration frequency, an exact method is adopted. Subsequently, the results are validated by comparing with the finding in published literature and simulation results. At last, the influence of system parameters on critical thermomechanical buckling load and vibration frequency is studied and displayed graphically. Meanwhile, some new results about thermomechanical buckling and vibration analysis of CNCSDS are proposed for the first time.Highlights Thermomechanical buckling and vibration of carbon nanotube‐reinforced composite sandwich doubly curved shells was studied. Vibration and stability equations under thermomechanical loads was deduced. The change rules of thermomechanical buckling load and frequency were obtained.

Temperature-dependent thermal buckling and free vibration behavior of smart sandwich nanoplates with auxetic core and magneto-electro-elastic face layers

This article addresses the thermomechanical thermal buckling and free vibration response of a novel smart sandwich nanoplate based on a sinusoidal higher-order shear deformation theory (SHSDT) with a stretching effect. In the proposed sandwich nanoplate, an auxetic core layer with a negative Poisson’s ratio made of Ti-6Al-4V is sandwiched between Ti-6Al-4V rim layers and magneto-electro-elastic (MEE) face layers. The MEE face layers are homogenous volumetric mixtures of cobalt ferrite (CoFe2O4) and barium titanate (BaTiO3). The mechanical and thermal material properties of the auxetic core and MEE face layers are temperature-dependent. Using Hamilton’s principle, governing equations are constructed. To characterize the size-dependent behavior of the nanoplate, governing equations are adapted with the nonlocal strain gradient theory (NSGT). By applying the principles of Navier’s technique, closed-form solutions are obtained. Parametric simulations are carried out to examine the effects of auxetic core parameters, temperature-dependent material properties, nonlocal parameters, electric, magnetic, and thermal loads on the free vibration and thermal buckling behavior of the nanoplate. According to the simulation results, it is determined that the auxetic core parameters, temperature-dependent material properties, and nonlocal factors significantly affect the thermomechanical behavior of the nanoplate. The outcomes of this investigation are expected to contribute to the advancement of smart nano-electromechanical systems, transducers, and nanosensors characterized by lightweight, exceptional structural integrity and temperature sensitivity. Also, the auxetic core with a negative Poisson’s ratio provides a metamaterial feature, and thanks to this feature, the proposed model has the potential to be used as an invisibility technology in sonar and radar-hiding applications.

A novel isogeometric model for dynamic buckling analysis of doubly curved two-directional functionally graded porous shallow microshells in thermal environments via variable length-scale parameters

In this study, the thermo-mechanical dynamic buckling analysis of two-directional functionally graded porous (2D-FGP) shallow microshells resting on elastic foundations with arbitrary boundary conditions is performed using the isogeometric approach. The isogeometric approach takes advantage of non-uniform rational B-spline basic functions to exactly represent the structure geometry models and the attainment of higher order approximation conditions. The characteristics of the material vary in both the thickness and axial x orientation. Especially, a new point in this material length-scale parameter of microshell is analyzed as a function of spatial coordinates and as a function of the material gradient parameters. Using Hamilton’s principle, the modified couple stress theory, and Kirchhoff-Love’s shell theory, the governing equations of a 2D-FGP microshell lying on a Pasternak medium are obtained. A computer program that employs an isogeometric analysis method to analyze the static and dynamic buckling of a 2D-FGP doubly curved shallow microshell with various boundary conditions. The numerical results for thin cylindrical, spherical, and hyperbolic paraboloidal shallow microshells with various planforms, such as rectangular and circular, are presented. Several special cases are used to demonstrate the accuracy and efficacy of the developed model by comparing the numerical results obtained by the proposed formulations with other published data. In addition, the effects of certain parameters, such as the length scale parameters, the power-law indexes, the thickness-to-sides ratio, and the radius ratio, on the dynamic thermo-mechanical buckling response of the 2D-FGP shallow microshells with double curvature are explored in depth.

The effect of the various porous layers on thermomechanical buckling of FGM sandwich plates

This study focuses on the thermal buckling behavior of sandwich porous plates made up of metal-ceramic functionally graded material (FGM) components using a new sinusoidal high order shear theory. The sandwich plate consists of a core plate made of either pure metal or pure ceramic, with face layers composed of a functional gradient of metal and ceramic constituents. This study examined the porosity and four porosity distribution functions in plates with FGM face layers and nonlinear temperature increase and material grading index of the face layers on the thermal buckling loads of sandwich plates.

The effects of the foam and FGM distributions on thermomechanical buckling response of sandwich plates

The effects of the foam and FGM distributions on thermomechanical buckling response of sandwich plates

Nonlinear thermo-mechanical stress-driven modeling of nano arches augmented by higher order double-scaled kernel

Modeling the nonlocal behavior of small-scale structures is almost controversial. The recently developed approach, known as the stress-driven nonlocal model, in which the stress is the input of nonlocal integral, has been proved to pose as a remedy for the ill-posing behavior of strain-driven solutions. Though it is still in its early stages, stress-driven modeling of the nonlinear behavior of nano-scaled problems needs further thought. The coupled displacement field, in particular, makes nano-arches more challenging. The stress-driven formulation, enhanced by constitutive boundary conditions, reveals the thermo-mechanical buckling and post-buckling features of shallow nano-arches for the first time in this research. Furthermore, the single-scaled Helmholtz kernel is replaced with the more appropriate double-scaled kernel known as the bi-Helmholtz averaging nonlocal kernel. Higher-order continuity of the bi-Helmholtz kernel and, hence, constitutive boundary conditions and higher-order differential equations corresponding to the stress-driven scheme hold the key to efficiency. The arch is subjected to uniform temperature and radial pressure at the same time. To demonstrate the response of the nano-arch during buckling and post-buckling, the nonlinear equilibrium path, whether for mechanical or thermal loading, is given for the first time by prevailing on the challenges of the higher-order problems. Moreover, it would be beneficial if one could have the chance to recognize how and when the arch buckles. These valuable data are available in this study to give the limiting parameters at the moment of buckling, including limiting temperature, nonlocal parameter, and geometry.

Effect of foam structure on thermo-mechanical buckling of foam core sandwich nanoplates with layered face plates made of functionally graded material (FGM)

Effect of foam structure on thermo-mechanical buckling of foam core sandwich nanoplates with layered face plates made of functionally graded material (FGM)

An analytical solution for thermomechanical buckling of variable angle tow composite laminates with elastically restrained edges

The inherent anisotropy and variable stiffness characteristics exhibited by Variable Angle Tow (VAT) composite materials offer significant possibilities for enhancing the performance of corresponding structures. Through appropriate selection of the curved fiber paths, it becomes feasible to design structures that are both lightweight and efficient. However, conducting mechanical analysis on VAT composite structures is of considerable challenges, particularly in seeking analytical solutions. In view of this, this paper aims to investigate the thermomechanical buckling behavior of VAT composite laminates with elastically restrained edges and presents an analytical solution for the studied problem. The analysis is based on the assumption that the fiber orientation angle of each lamina varies linearly or nonlinearly along the x direction, and the fundamental equations for thermomechanical buckling of VAT laminates are derived using the classical laminated plate theory. The analytical solution is obtained through the combined utilization of Taylor series and Frobenius series. Furthermore, a comprehensive parameter analysis is conducted to assess the impact of different factors, such as fiber paths and elastic support stiffness, on the critical thermomechanical buckling load and mode of VAT laminates. The resulting findings serve as a valuable reference for VAT laminate design, while the proposed analytical solution can be employed as a benchmark for validating other numerical results.

Thermomechanical vibration and buckling response of magneto-electro-elastic higher order laminated nanoplates

This study investigated the free vibration and buckling behavior of a magneto-electro-elastic (MEE) sandwich porous nanoplate under nonlinear thermal loads and electric and magnetic potentials. The equation of motion of the nanoplate consisting of barium-titanate and cobalt-ferrite components, with a functionally graded (FG) porous core and two face plates, was modeled by a sinusoidal higher-order shear (SHSDT) and the nonlocal strain gradient (NSGT) theories. Due to the significant effect of the temperature in the dynamics of the magneto-electro-elastic nanoplate, the temperature-dependent material properties of barium-titanate (BaTiO3) and cobalt ferrite (CoFe2O4) were defined and applied to the modeling for the first time in the literature. The laminated plate consists of upper and lower surface auxiliary plates and a main FG core plate. The core plate consists of functionally grading cobalt-ferrite and barium-titanate, while face plates can be in three different material compositions consisting of pure cobalt-ferrite, pure barium-titanate, or a combination of the two. It has been shown in this study that the dynamic behavior of the core plate, exposed to high temperatures, can be controlled through auxiliary surface plates. Especially in nanosensor applications, the disadvantage of thermal load can be reduced by the electric and magnetic field's strength applied to the surface plates. This study will make an essential contribution to the design and application of nanosensor or nanoelectromechanical systems, especially by controlling nanosensor responses in high-temperature applications.

Nonlinear thermo-mechanical axisymmetric stability of FG-GPLRC spherical shells and circular plates resting on nonlinear elastic medium

ABSTRACT An analytical approach for nonlinear thermo-mechanical buckling of functionally graded graphene platelet reinforced composite (FG-GPLRC) circular plates and shallow spherical shells resting on nonlinear elastic medium using the higher-order shear deformation theory (HSDT) and the nonlinearities of von Kármán is established in the present work. Assuming that the structures are axisymmetrically displaced for the central axis and external pressure and thermal loads are applied. The nonlinear elastic medium is used to model the behaviour of hardening or softening medium depending on the positive and negative values of the nonlinear parameter, respectively. By applying the Ritz energy method, the relation expressions of load-deflection are archived to investigate the postbuckling response and critical buckling load of the structures. Special effects on the nonlinear thermo-mechanical behaviour of plates and shells with different medium stiffnesses, different material parameters, and different geometrical dimensions are explored and discussed in numerical results.

On the influence of edge damage on thermally induced buckling of stepped circular bi-laminates

The influence of edge damage on thermo-mechanical buckling of stepped circular bi-laminates is examined analytically. The nonlinear equations of equilibrium, the associated boundary conditions and the transversality conditions for the propagating interior boundaries of a region of sliding contact are derived via the Principal of Stationary Potential Energy as a propagating boundary problem in the calculus of variations. The problem is ultimately recast in a mixed formulation expressed in terms of the membrane forces and the transverse displacements of the composite structure. A loading parameter is identified and closed form analytical solutions to the resulting non-linear problem are determined. In addition, a stability criterion is established based on the second variation of the total potential energy of the structure, and qualitative behavior concerning contact is deduced analytically. Results of numerical simulations based on the analytical solutions established herein are generated and the phenomenon of “sling-shot buckling” is observed, whereby the structure first deflects in one direction upon heating (or cooling) and then, when a critical temperature is achieved, dynamically “sling-shots” from the current equilibrium configuration to an alternate equilibrium configuration possessing deflections in the opposite sense. In addition, the phenomenon of “buckle-trapping” is observed for stepped circular bi-laminates with hinged-fixed supports, as well as for clamped-fixed structures with relatively large damaged area. A robust mixture of contact behavior, including propagating sliding contact, edge contact and no contact, and the transition from one form of contact to another, is exhibited for both pre-buckling and post-buckling configurations. The influence of edge damage on critical load and characteristic behavior is assessed.

Thermo-Mechanical Buckling and Non-Linear Free Oscillation of Functionally Graded Fiber-Reinforced Composite Laminated (FG-FRCL) Beams

We investigated the thermal buckling temperature and nonlinear free vibration of functionally graded fiber-reinforced composite laminated (FG-FRCL) beams. The governing nonlinear partial differential equations were derived from the Euler–Bernoulli beam theory, accounting for the von Kármán geometrical nonlinearity. Such equations were then reduced to a single equation by neglecting the axial inertia. Thus, the Galerkin method was applied to discretize the governing nonlinear partial differential equation in the form of a nonlinear ordinary differential equation, which was then solved analytically according to the He’s variational method. Three different boundary conditions were selected, namely simply, clamped and clamped-free supports. We also investigated the effect of power-index, lay-ups, and uniform temperature rise on the nonlinear natural frequency, phase trajectory and thermal buckling of FG-FRCL beams. The results showed that FG-FRCL beams featured the highest fundamental frequency, whereas composite laminated beams were characterized by the lowest fundamental frequency. Such nonlinear frequencies increase for an increased power index and a decreased temperature. Finally, it was found that FG-FRCL beams with [0/0/0] lay-ups featured the highest nonlinear natural frequency and the highest thermal buckling temperature, followed by [0/90/0] and [90/0/90] lay-ups, while a [90/90/90] lay-up featured the lowest nonlinear natural frequency and critical buckling temperature.

Re-examination of thermo-mechanical buckling and postbuckling responses of sandwich plates with porous FG-GPLRC core

The current study re-examines compressive postbuckling and thermal postbuckling responses of porous sandwich plates resting on an elastic foundation. The core of the sandwich plates is made of porous graphene platelets reinforced composite (GPLRC). Compressive postbuckling of the porous sandwich plates under uniaxial compression at elevated temperature and thermal postbuckling of the same plates under uniform thermal loading are studied. The GPLRC core is made of multilayers, and each layer may have different values of porosity coefficient to obtain a piecewise functionally graded (FG) pattern. The Young’s moduli along with the shear modulus of the porous GPLRC core are estimated through a generic Halpin–Tsai model in which the porous nature of the material is taken into consideration. The material properties of the metal face sheets and the porous GPLRC core are assumed to be temperature dependent. The governing equations for the postbuckling of the porous sandwich plates reinforced by GPLs are established based on the Reddy’s third order shear deformation theory (TSDT). In the modeling, we also consider the von Kármán nonlinear strain–displacement relationships, the plate-foundation interaction and the thermal effect. A two-step perturbation approach is utilized in solving the postbuckling problem. Numerical studies are performed to compare the results obtained from the present model and the equivalent isotropic model (EIM). The results confirm that the EIM is not suitable for analyzing buckling and postbuckling of porous plates.

A Novel Analytical Approach for Nonlinear Thermo-Mechanical Buckling of Higher-Order Shear Deformable Porous Circular Plates and Spherical Caps with FGM Face Sheets

A novel analytical approach for nonlinear thermo-mechanical buckling of higher-order shear deformable porous circular plates and spherical caps with functionally graded material (FGM) face sheets resting on Pasternak elastic foundation is presented in this paper. The circular plates and spherical caps are assumed to be subjected to uniformly distributed external pressure and/or uniformly distributed thermal loads, and the nonlinear higher-order shear deformation theory (HSDT) is used for largely thick plates and caps with the shell-foundation interaction modeled by Pasternak elastic foundation. The caps are assumed to be shallow with clamped boundary conditions. The total potential energy expression of structures is established and the Ritz energy method is used to solve the problem directly from the total potential energy expression. The expressions between external pressure–deflection, thermal load–deflection, and thermo-mechanical combined load–defection can be obtained using the iterative algorithms. The critical buckling loads and postbuckling behavior of plates/caps are investigated numerically. Significant effects of foundation, porosity, structure parameters on the nonlinear thermo-mechanical responses of circular plates and spherical caps are numerically investigated and discussed, and the complex tendencies of postbuckling strength of plates and caps are obtained.

Thermo-mechanical buckling analysis of non-uniformly heated rectangular plates with temperature-dependent material properties

This paper examines the thermo-mechanical buckling behavior of a rectangular plate with temperature-dependent (TD) material properties exposed to non-uniform heating. The buckling analysis was performed by using the differential quadrature (DQ) method, which mainly includes three steps: (i) a two-dimensional (2D) non-linear heat transfer equation was proposed to obtain the temperature distribution in the plate considering the convective–radiative conditions on the plate surface; (ii) the in-plane stress distribution of the plate was obtained by solving the thermoelastic equilibrium equation; (iii) the critical load was determined by solving the stability equation based on the stress distribution in the previous step. The comparison study shows that the present results were in good agreement with the finite element (FE) solutions and the results reported in the literature. The effects of the surrounding temperature fields and in-plane load cases on the thermo-mechanical behavior of the plate are analyzed in detail.

Nonlinear thermo-mechanical buckling and postbuckling of sandwich FG-GPLRC spherical caps and circular plates with porous core by using higher-order shear deformation theory

The main aim of this research is to establish the algorithm for nonlinear thermo-mechanical buckling of sandwich functionally graded graphene platelet reinforced composite (FG-GPLRC) shallow spherical caps and circular plates with porous core under external pressure and/or uniformly distributed thermal load according to the higher-order shear deformation theory considering the von Karman nonlinearities. Sandwich spherical caps and circular plates are made by the porous core and two FG-GPLRC coatings and are assumed to be rested on an elastic foundation modeled by the Pasternak model. The equilibrium equation system in the form of nonlinear algebra can be approximately obtained using the Ritz energy method. The critical buckling loads and postbuckling curves can be explicitly determined. The effects of material parameters, geometrical parameters, porous core, and elastic foundation on thermo-mechanical buckling of sandwich spherical caps and circular plates with porous core and FG-GPLRC coatings are investigated and discussed in detail in the numerical investigation section.

Thermomechanical buckling and wrinkling characteristics of softcore sandwich panels with CNT reinforced composite face sheets

This article explores the local and global stability of CNT reinforced composite (CNTRC) sandwich shell panels consist of softcore material. The shell panel's face sheets are reinforced with functionally graded nanotube particles. The effective properties of CNTRC face sheets are determined considering the extended rule of mixture technique, and a multi-layer approach is used to examine the local and global stability phenomena. The material properties of the face sheets are assumed to be temperature-dependent. The formulation account for the core compressibility effect by considering higher-order polynomial terms for transverse core displacement. The governing equations for each layer of the sandwich panel are derived by minimizing the total potential energy of the system. The Galerkin's technique is adopted to obtain a set of non-linear algebraic equations from the derived partial differential equations. Global buckling and wrinkling loads of sandwich shell panels under thermomechanical loadings are obtained by solving standard eigenvalue problem. The nonlinear responses for sandwich shell panels subjected to mechanical and thermal stresses are traced through the arc-length approach and iterative approach, respectively. The obtained responses elucidate the influence of CNT gradation, volume fractions and core thickness on the local and global stability behaviour of CNTRC sandwich shell panels.

Methodology and application to assess thermo-mechanical buckling in composite marine structures

This paper describes the research performed within the scope of H2020 project FIBRE4YARD in the development of a suitable thermo-mechanical framework to analyse composite structures under fire loads. The thermo-mechanical model uses the adiabatic temperature to obtain the through-thickness distribution of temperature of the triangular shell element, this formulation is able to predict phenomena such as pyrolysis, thermo-mechanical yielding and large displacements (non-linear buckling). An application case of a load-bearing section of a container ship is shown to demonstrate the correctness of the methodology, two type of materials are considered in the analysis, traditional materials such steel and advanced materials like fibre reinforced plastic (FRP) composites.