Types Of Thermal Loading Research Articles

Thermal buckling behaviour of unstiffened and stiffened fixed-roof tanks under non-uniform heating

The problem addressed in this paper is the thermal buckling behaviour of thin-walled steel cylindrical fixed-roof tanks under non-uniform loading, induced by an adjacent tank. This specific type of thermal loading can be triggered by a neighboring tank fire where heat is transferred mainly through radiation. Since the calculation of the temperature field of the heated tank lies in other scientific fields (e.g. Computational Fluid Dynamics), a thermal pattern, proposed in literature, is used for the simulation of the fire-induced load and the investigation of the structural response of the tank due to heating. The study is conducted numerically through the Finite Element method, using coupled thermo-mechanical analysis. The general purpose Finite Element code MSC Marc, is used for the simulation. Three-dimensional models are developed using shell elements. Firstly, a detailed study of the failure mechanisms that take place in case of non-uniform loading is carried out. Furthermore, tanks with different geometries are studied. The main objective is the calculation of the critical temperature i.e. the temperature where the failure appears and the determination of the failure modes. Finally, a parametric study is conducted for the evaluation of the effectiveness of stiffening methods that are commonly used at ambient temperature design (stiffeners and stepwise wall thickness), in the case of the non-uniform heating load. In this study, the heated tanks are considered to be empty, which is the most severe scenario, for their structural integrity.

Dynamic modeling of porous heterogeneous micro/nanobeams

In the present paper, the thermo-mechanical vibration characteristics of a functionally graded (FG) porous microbeam subjected to various types of thermal loadings are investigated based on modified couple stress theory and exact position of neutral axis. The FG micro/nanobeam is modeled via a refined hyperbolic beam theory in which the shear deformation effect is verified without the shear correction factor. A modified power-law distribution which contains porosity volume fraction is used to describe the graded material properties of the FG micro/nanobeam. The temperature field has uniform, linear and nonlinear distributions across the thickness. The governing equations and the related boundary conditions are derived by Hamilton’s principle and they are solved applying an analytical solution which satisfies various boundary conditions. A comparison study is performed to verify the present formulation with the known data in the literature and a good agreement is observed. The parametric study covered in this paper includes several parameters, such as thermal loadings, porosity volume fraction, power-law exponents, slenderness ratio, scale parameter and various boundary conditions on natural frequencies of porous FG micro/nanobeams in detail.

Thermo-mechanical vibration analysis of functionally graded micro/nanoscale beams with porosities based on modified couple stress theory

Thermo-mechanical vibration characteristics of in homogeneousporous functionally graded (FG) micro/nanobeam subjected to various types of thermal loadings are investigated in the present paper based on modified couple stress theory with consideration of the exact position of neutral axis. The FG micro/nanobeam is modeled via a refined hyperbolic beam theory in which shear deformation effect is verified needless of shear correction factor. A modified power-law distribution which contains porosity volume fraction is used to describe the graded material properties of FG micro/nanobeam. Temperature field has uniform, linear and nonlinear distributions across the thickness. The governing equations and the related boundary conditions are derived by Extended Hamilton\'s principle and they are solved applying an analytical solution which satisfies various boundary conditions. A comparison study is performed to verify the present formulation with the known data in the literature and a good agreement is observed. The parametric study covered in this paper includes several parameters such as thermal loadings, porosity volume fraction, power-law exponents, slenderness ratio, scale parameter and various boundary conditions on natural frequencies of porous FG micro/nanobeams in detail.

On boundary conditions for thermally loaded FG beams

As a functionally graded extensible beam is subjected to the in-plan thermal loading, distinct scenarios occur depending on the boundary conditions of system. Analyzing the thermo-mechanical behavior of system by employing the simplified boundary conditions (neglecting the influence of thermal moment at the original boundary conditions of system) leads to prediction of inaccurate trends and results. Although, the problem based on the original boundary conditions was solved by some researchers, there exist remarkable amount of linear and nonlinear studies from macro to small scale based on the classical and non-classical theories by implementation of the simplified boundary conditions. In the present work, the thermo-mechanical equilibrium paths and free flexural vibration of system based on the simplified and original boundary conditions are compared to show the inaccuracy of simplified boundary conditions-based analysis. In this study, two distinct types of thermal loading i.e., uniform temperature rise and heat conduction across the thickness are considered. In addition, it is indicated that the original boundary conditions-based linear analysis for evaluation of the equilibrium path of system yields inaccurate trend.

A four-variable refined shear-deformation beam theory for thermo-mechanical vibration analysis of temperature-dependent FGM beams with porosities

ABSTRACTThis article proposes a four-variable shear deformation refined beam theory for thermo-mechanical vibration characteristics of porous, functionally graded (FG) beams exposed to various kinds of thermal loadings by using an analytical method. Thermo-mechanical properties of functionally graded material (FGM) beams are supposed to vary through the thickness direction, and are estimated through the modified power-law rule in which the porosities with even and uneven types are approximated. The material properties of FGM beams are supposed to be temperature dependent. Porosities possibly occur inside FGMs during fabrication because of technical problems that lead to the creation of microvoids in these materials. The variation of pores along the thickness direction influences the mechanical properties. Thus, it is incumbent to predict the effect of porosities on the thermo-mechanical vibration behavior of FG beam in the present study. Four types of thermal loading, namely, uniform, linear, nonlinear, and sinusoidal temperature rises through the z-axis direction are discussed. The governing differential equations and boundary conditions of FG porous beams subjected to thermal loadings are formulated through Hamilton's principle, based on a four-variable refined theory that considers a constant transverse displacement and higher order variation of axial displacement through the depth of the beam without the need of any shear correction factors. An analytical solution procedure is used to achieve the natural frequencies of porous FG beams subjected to various temperature fields. The impact of several specific parameters such as power-law exponent, porosity volume fraction, different porosity distribution, and thermal effect on the vibration of the porous FG beams is perused and discussed in detail. It is deduced that these parameters play a notable role on the thermo-dynamic behavior of porous FG beams. Presented numerical results can serve as benchmarks for the future analyses of FG beams with porosity phases.

Nonlinear bending, postbuckling and snap-through of circular size-dependent functionally graded piezoelectric plates

In the present work, the nonlinear thermoelectrical stability of perfect/imperfect circular size-dependent functionally graded piezoelectric plates is studied according to modified couple stress theory. The second, concurrent aim is to address snap-through phenomenon in the thermally preloaded plates due to concentrated/uniform lateral loads. Ritz finite element method is implemented into virtual displacement principle to construct the matrix representation of nonlinear governing equations. Under certain circumstances, bifurcational instability may occur in which case a direct displacement control scheme is utilized. In other cases, the response is unique and stable to which any standard load control strategy seems appropriate and thus Newton-Raphson method is selected. Standard load control strategies, however, fail to trace nonlinear equilibrium paths through limit points and path following methods must be employed in snap-through problems. Being more popular among the existing path following solution methods, cylindrical arc-length method is adopted. Two types of thermal loading as well as two cases of boundary conditions are considered. Moreover, various parametric studies are conducted to assess the influence of involved parameters.

In-plane vibration of FG micro/nano-mass sensor based on nonlocal theory under various thermal loading via differential transformation method

In the present study, free vibration model of a cantilever functionally graded (FG) nanobeam with an attached mass at tip and under various thermal loading and two types of material distribution is introduced. The vibration performance is considered using nonlocal Euler-Bernoulli beam theory. Two types of thermal loading, namely, uniform and nonlinear temperature rises through the thickness direction are considered. Thermo-mechanical properties of FG nano mass sensor are supposed to vary smoothly and continuously throughout the thickness based on power-law and Mori Tanaka distributions of material properties. Eringen non-local elasticity theory is exploited to describe the size dependency of FG nanobeam. The governing equations of the system with both axial and transverse displacements are derived based on Hamilton's principle and solved utilizing the differential transformation method (DTM) to find the non-dimensional natural frequencies. The results have good agreements with those discussing in the literature. After validation of the present model, the effect of various parameters such as mass and position of the attached nano particle, FG power-law exponent, thermal load type, material distribution type and nonlocal parameter on the frequency of nano sensor are studied. It is shown that the present model produces results of high accuracy, and it can be used as a benchmark in future studies of the free vibration of FG Nano-Mass Sensors.

Size-dependent thermal stability analysis of embedded functionally graded annular nanoplates based on the nonlocal elasticity theory

In the present investigation, bifurcation-type buckling characteristics of heated functionally graded (FG) annular nanoplates resting on an elastic foundation and subjected to various types of thermal loading are carried out by presenting an exact analytical solution for the first time. Three kinds of frequently used thermal loading, i.e. uniform temperature rise, linear and nonlinear temperature distribution through the thickness direction are considered. Thermo-mechanical properties of FG nanoplate are supposed to vary smoothly and continuously throughout the thickness based on power law model whereas the Poisson's ratio is held constant. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanoplate. Using the principle of virtual displacements, the equilibrium equations together with corresponding boundary conditions are obtained for the thermal buckling analysis of FG annular nanoplates including size effects. The pre-buckling analysis is performed and the proper boundary conditions are chosen to assure the existence of bifurcation-type buckling. Also, the nonlocal stability equations of FG annular nanoplate are derived by using the adjacent equilibrium criterion and they are solved by applying an exact asymmetrical solution. Moreover, in following a parametric study is accompanied to examine the effects of the several parameters such as nonlocal parameter, various temperature distributions, thickness to outer radius ratio, power law index, inner to outer radius ratios and elastic medium parameters on the critical buckling temperatures of the size-dependent FG nanoplates in detail. It is found that the small scale effects and thermal loading have a significant effect on thermal stability characteristics of FG annular nanoplates.

Three-dimensional thermal buckling analysis of functionally graded cylindrical panels using differential quadrature method (DQM)

Thermal buckling analysis of functionally graded cylindrical panels subjected to various conditions is discussed in this paper. Buckling governing equations are solved using the differential quadrature method. It is assumed that the mechanical properties of the panel are graded through thickness according to a power function of the thickness variable. The panel is assumed to be under the action of three types of thermal loading including uniform temperature rise and variable temperature rise in the axial and radial direction. In the present study, the effects of power law index, panel angle, different thermal load conditions and geometric parameters on the buckling behavior of functionally graded curved panels are studied. The results obtained through the present method are compared to the finite element solutions and the reported results in the literature. A desirable compatibility is concluded.

Thermal Buckling Analysis of Size-Dependent FG Nanobeams Based on the Third-Order Shear Deformation Beam Theory

In this paper, the thermal effects on the buckling of functionally graded (FG) nanobeams subjected to various types of thermal loading including uniform, linear and non-linear temperature changes are investigated based on the nonlocal third-order shear deformation beam theory. The material properties of FG nanobeam are supposed to vary gradually along the thickness direction according to the power-law form. The governing equations are derived through Hamilton’s principle and solved analytically. Comparison examples are performed to verify the present results. Obtained results are presented for thermal buckling analysis of FG nanobeams such as the effects of the power-law index, nonlocal parameter, slenderness ratio and thermal loading in detail.

Thermal buckling analysis of nanoplates based on nonlocal elasticity theory with four-unknown shear deformation theory resting on Winkler–Pasternak elastic foundation

ABSTRACTThe thermal buckling analysis of nanoplates is based on nonlocal elasticity theory with four-unknown shear deformation theory resting on Winkler–Pasternak elastic foundation. The nanoplate is assumed to be under three types of thermal loadings, namely uniform temperature rise, linear temperature rise, and nonlinear temperature rise through the thickness. The theory involves four unknown variables with small-scale effects, as against five in the case of other higher-order theories and first-order shear deformation theory. Closed-form solution for theory was also presented. Results are presented to discuss the influences of the nonlocal parameter, aspect ratio, side-to-thickness ratio, and elastic foundation parameters on the thermal buckling characteristics of analytical rectangular nanoplates.

Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory

In this paper thermo-mechanical vibration analysis of a porous functionally graded (FG) Timoshenko beam in thermal environment with various boundary conditions are performed by employing a semi analytical differential transform method (DTM) and presenting a Navier type solution method for the first time. The temperature-dependent material properties of FG beam are supposed to vary through thickness direction of the constituents according to the power-law distribution which is modified to approximate the material properties with the porosity phases. Also the porous material properties vary through the thickness of the beam with even and uneven distribution. Two types of thermal loadings, namely, uniform and linear temperature rises through thickness direction are considered. Derivation of equations is based on the Timoshenko beam theory in order to consider the effect of both shear deformation and rotary inertia. Hamilton\'s principle is applied to obtain the governing differential equation of motion and boundary conditions. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of several parameters such as porosity distributions, porosity volume fraction, thermal effect, boundary conditions and power-low exponent on the natural frequencies of the FG beams in detail. It is explicitly shown that the vibration behavior of porous FG beams is significantly influenced by these effects. Numerical results are presented to serve benchmarks for future analyses of FG beams with porosity phases.

Thermomechanical buckling of hybrid cross-ply laminated rectangular plates

A thermomechanical buckling analysis is presented for simply supported rectangular symmetric cross-ply laminated composite plates that are integrated with surface-mounted piezoelectric actuators and are subjected to the combined action of in-plane compressive edge loads, two types of thermal loads, and constant applied actuator voltage. The formulation of equations is based on the classical laminated plate theory and the von-Karman non-linear kinematic relations. The analysis uses an exact method to obtain closed-form solutions for the buckling load. The effects of applied actuator voltage, thermal and mechanical loads, plate geometry, and lay-up configuration of the laminated plates are investigated. The novelty of the present work is to obtain closed-form solutions for electro-thermomechanical buckling of hybrid composite plates, and to cover non-uniform temperature distribution loading. The results for various states are verified with known data in the literature.

Buckling Analysis of Smart Size-Dependent Higher Order Magneto-Electro-Thermo-Elastic Functionally Graded Nanosize Beams

AbstractThe present paper examines the thermal buckling of nonlocal magneto-electro-thermo-elastic functionally graded (METE-FG) beams under various types of thermal loading namely uniform, linear and sinusoidal temperature rise and also heat conduction. The material properties of nanobeam are graded in the thickness direction according to the power-law distribution. Based on a higher order beam theory as well as Hamilton's principle, nonlocal governing equations for METE-FG nanobeam are derived and are solved using Navier type method. The small size effect is captured using Eringen's nonlocal elasticity theory. The most beneficial feature of the present beam model is to provide a parabolic variation of the transverse shear strains across the thickness direction and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. Various numerical examples are presented investigating the influences of thermo-mechanical loadings, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on thermal buckling behavior of nanobeams made of METE-FG materials.

Thermally induced buckling of thin annular FGM plates

This article discusses the instability of thin annular FG plates subjected to transversely distributed temperature loading. Based on the classical thin plate theory, equilibrium equations of an annular FG plate are obtained. Plate is assumed to be graded in the thickness direction whose material properties vary smoothly according to the power law form. Existence of bifurcation buckling for various boundary conditions are examined and stability equations are obtained by means of the adjacent equilibrium criterion. An analytical solution is presented to calculate the thermal buckling load by finding the exact eigenvalues of the stability equation. Three types of thermal loading, namely uniform temperature rise, transversely linear temperature and heat conduction across the thickness are studied. The effects of thickness, power law index and thermal loading type on the critical buckling temperature of FG plates are presented comprehensively. It is found that, while the temperature loading through the plate is symmetric, first buckled configuration of a fully clamped FGM plate is always asymmetric.

Nonlinear thermal stability and snap-through behavior of circular microstructure-dependent FGM plates

Abstract The aim of the present work is twofold. The First is to present a study on nonlinear thermal stability of perfect/imperfect circular size-dependent functionally graded plates according to modified couple stress theory. The second, concurrent aim is to address snap-through phenomenon in the thermally preloaded plates due to concentrated/uniform lateral loads. Ritz finite element method is implemented into generalized form of Hamilton’s principle to construct the matrix representation of nonlinear governing equations. Under certain circumstances, bifurcation type instability may occur in which case a direct displacement control scheme is utilized. In other cases, the response is unique and stable to which any standard load control strategy seems appropriate and thus Newton-Raphson method is selected. Standard load control strategies, however, fail to trace nonlinear equilibrium paths through limit points and path following methods must be employed in snap-through problems. Being more popular among the existing path following solution methods, cylindrical arc-length method is adopted. Two types of thermal loading as well as two cases of boundary conditions are considered. Moreover, various parametric studies are conducted to assess the influence of involved parameters.

Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams

ABSTRACTIn this article, the thermal effects on buckling and free vibrational characteristics of functionally graded (FG) size-dependent nanobeams subjected to various types of thermal loading are investigated by presenting a Navier-type solution for the first time. Temperature-dependent material properties of FG nanobeams vary continuously along the thickness according to the power-law form. The small-scale effect is taken into consideration based on Eringen's nonlocal elasticity theory. The nonlocal equations of motion are derived through Hamilton's principle and they are solved applying an analytical solution. It is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams.

Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment

ABSTRACTIn the present work, thermo-electro-mechanical buckling behavior of functionally graded piezoelectric (FGP) nanobeams is investigated based on higher-order shear deformation beam theory. The FGP nanobeam is subjected to four types of thermal loading including uniform, linear, and sinusoidal temperature rise as well as heat conduction through the beam thickness. Thermo-electro-mechanical properties of FGP nanobeam are supposed to change continuously in the thickness direction based on power-law model. To consider the influences of small-scale sizes, Eringen’s nonlocal elasticity theory is adopted. Applying Hamilton’s principle, the nonlocal governing equations of an FGP nanobeam in thermal environments are obtained and are solved using Navier-type analytical solution. The significance of various parameters, such as thermal loadings, external electric voltage, power-law index, nonlocal parameter, and slenderness ratio on thermal buckling response of size-dependent FGP nanobeams is investigated.

Dynamic modeling of a thermo–piezo-electrically actuated nanosize beam subjected to a magnetic field

In this article, free vibration behavior of magneto–electro–thermo-elastic functionally graded nanobeams is investigated based on a higher order shear deformation beam theory. Four types of thermal loading including uniform and linear temperature change as well as heat conduction and sinusoidal temperature rise through the thickness are assumed. Magneto–electro–thermo-elastic properties of FG nanobeam are supposed to change continuously throughout the thickness based on power-law model. Via nonlocal elasticity theory of Eringen, the small size effects are adopted. Based upon Hamilton’s principle, the coupled nonlocal governing equations for higher order shear deformable METE-FG nanobeams are obtained and they are solved applying analytical solution. It is shown that the vibrational behavior of METE-FG nanobeams is significantly affected by various temperature rises, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio.

A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities

In the present paper, thermomechanical vibration characteristics of functionally graded (FG) Reddy beams made of porous material subjected to various thermal loadings are investigated by utilizing a Navier solution method for the first time. Four types of thermal loadings, namely, uniform, linear, nonlinear, and sinusoidal temperature rises, through the thickness direction are considered. Thermomechanical material properties of FG beam are assumed to be temperature-dependent and supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM) which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. The governing differential equations of motion are derived based on higher order shear deformation beam theory. Hamilton’s principle is applied to obtain the governing differential equations of motion which are solved by employing an analytical technique called the Navier type solution method. Influences of several important parameters such as power-law exponents, porosity distributions, porosity volume fractions, thermal effects, and slenderness ratios on natural frequencies of the temperature-dependent FG beams with porosities are investigated and discussed in detail. It is concluded that these effects play significant role in the thermodynamic behavior of porous FG beams.