Types Of Thermal Loading Research Articles

A PROBLEM IN FRACTIONAL ORDER THERMO-VISCOELASTICITY THEORY FOR A POLYMER MICRO-ROD WITH AND WITHOUT ENERGY DISSIPATION

A new study has been developed that considers the size-dependent interaction between viscoelastic deformation and thermal fields, incorporating the fractional heat conduction law with and without energy dissipation. The model is used for a particular one-dimensional problem involving a polymer micro-rod of arbitrary length experiencing three different types of thermal loading without the presence of any heat source. The study uses Laplace transforms and numerical inversion to examine how fractional order, nonlocal elasticity, and nonlocal thermal conduction impact thermal dispersion and thermo-viscoelastic response. Comparative numbers demonstrate the effects of various parameters. Findings demonstrate that nonlocal thermal and viscoelastic characteristics have a significant impact on all recorded field values, offering possible suggestions for the creation and assessment of thermal-mechanical attributes in nanoscale devices.

Coupled influences of magnetic field and several thermal loads on vibration of thermoelastic nano-ceramic (Si3N4) beam

Our study investigates the vibration of a thermoelastic nano-ceramic (Si3N4) beam exposed to a magnetic field under the effect of a moving heat source and different types of thermal loads. These nanobeams are modeled as non-Fourier heat conduction. In our formulation, the equation of motion and the principle of energy conservation from two coupled partial differential equations have been driven. A direct approach has been used to find the solutions to the governing equations using the Laplace transform definition. Numerical Laplace transform inversion was calculated using Hoing's approximation approach. Solutions have been applied to silicon nitride (Si3N4) nanobeam ceramics. Figures show the distribution of temperature increment, lateral deflection, and stress with different values of magnetic field and several thermal load parameters. In all the studied nanobeam functions, the magnetic field and several thermal loads’s parameters have significant effects. They could be used as tuners to control the vibration and temperature increment. In the present study, a moving heat source, and different thermal loads have been applied to a non-Fourier nanobeam exposed to a magnetic field. The results have been compared with those obtained in the thermoelastic cases.

Analyzing free vibration and buckling of heated laminated plate with cutouts: A Nitsche-based isogeometric approach

In this research, a comprehensive Nitsche-based isogeometric analysis framework is presented for studying the free vibration and buckling characteristics of laminated plates with cutouts under uniform and non-uniform thermal loads. The approach utilizes non-overlapping non-uniform rational B-Splines patches to discretize the perforated plate and seamlessly connects them using the Nitsche method. The technique is then applied to investigate the free vibration and buckling behaviors of laminated plates with cutouts under varying thermal conditions. Three tests with different element sizes are used to analyze composite plate under uniform thermal load, demonstrating good convergence and accuracy of the present method. Rectangular laminated plates without cutouts, considering various boundary conditions, fiber orientations, and temperature variations under uniform or non-uniform thermal loads are analyzed. The natural frequencies and critical buckling temperatures are found to be in excellent agreement with existing literature. Additionally, the analysis is expanded for laminated plates with cutouts under diverse boundary conditions, considering variations in fiber orientations, cutout shapes and numbers, and types of thermal loads. Thorough investigations are carried out to understand the influence of these factors on the vibrational and buckling behaviors of the plates. Moreover, numerical study with non-conforming mesh demonstrates strong capability of the proposed method.

Investigating hygrothermal bending behavior of FG nanobeams via local/nonlocal stress gradient theory of elasticity with general boundary conditions

The bending response of functionally graded (FG) nanobeams under hygrothermal loading was investigated to emphasize the different scenarios that arise when using simplified and original boundary conditions. The governing equations were derived by using the principle of virtual work on the basis of the local/nonlocal stress gradient theory of elasticity. A Wolfram language code in Mathematica was written by the authors to develop a numerical investigation for different values of the material gradient index, the gradient length parameter, the nonlocal parameter, and considering two distinct types of thermal loading, that is, uniform temperature rise and heat conduction across the thickness of FG nanobeam cross-section.

Nonlinear large-amplitude vibration analysis of annular sector plates made of FGMs subjected to cooling shock

A numerical approach is developed in the present article to study the geometrically nonlinear vibrations of annular sector plates made of functionally graded materials (FGMs) due to being exposed to cooling shock. The first-order shear deformation plate theory (FSDT) is used in the modeling of plate, and the governing equations of motion are derived based on Hamilton's principle considering von Kármán nonlinear kinematic relations. It is also considered that the properties of FGMs are dependent on temperature and distribution of materials. According to the uncoupled thermoelasticity theory, the temperature distribution is obtained via 1D Fourier-type transient heat conduction equation. To numerically solve the problem, the generalized differential quadrature (GDQ) method and Newmark-beta integration scheme are utilized. Considering two different types of thermal loading as cooling shock, the effects of various parameters including thermal load rapidity time, geometry, magnitude of thermal load and material properties on the large-amplitude vibrations of annular sector plates are investigated.

Symplectic Method-Based Analytical Solutions of Thermal Buckling for Shear Deformable Circular Functionally Graded Plates

Thermal buckling of a shear deformable circular plate made of functionally graded materials (FGM) is studied using an exact analytical method in the Hamiltonian system. Fundamental equations for the thermal buckling of the plate under transversely nonuniform temperature rising are established based on the first-order shear deformation theory. Subsequently, by introducing the symplectic method, the differential equations are converted into canonical equations in the Hamiltonian system. Buckling loads and buckling modes correspond to symplectic eigenvalues and eigen solutions, respectively. The expressions of complete buckling modes in the form of special functions are achieved by solving canonical equations and boundary conditions analytically and exactly. The symplectic eigenvalues are obtained simultaneously and the buckling temperature increments are calculated using the inverse solution. Finally, the influences of the gradient characteristics, geometric parameters, boundary conditions, and type of thermal loading on the buckling temperature increments are discussed through parameter research.

Nonlinear large amplitude vibrations of higher-order functionally graded beams under cooling shock

In this paper, thermally induced vibrations of beams made of functionally graded materials (FGMs) subjected to cooling shocks are investigated. It is considered that the beam has been made of a mixture of stainless steel (SUS 304) and low-carbon steel (AISI 1020). To model the displacement field, the third-order beam theory, known as the Reddy beam theory (RBT), is used. Material properties depend on temperature and distribution of materials, and this dependence is modeled through the temperature and the location of materials along the thickness direction. Considering the uncoupled thermoelasticity theory, the temperature distribution is obtained using a one-dimensional Fourier-type transient heat conduction equation, and the equations of motion governing the higher-order beam are derived utilizing Hamilton's principle. Solving the equations is done numerically; the generalized differential quadrature method (GDQM) is employed to approximate the spatial derivatives, and the Newton-Raphson scheme is applied to linearize the equations. In addition, for approximation of the time derivatives, the Newmark method is utilized. Subsequently, the effects of various parameters on the non-dimensional lateral deflection of the higher-order beam considering two different types of thermal loading are investigated. A comprehensive parametric study is conducted to study the effects of important parameters including beam thickness, thermal load rapidity time, the amount of applied load, and the FG parameter.

Three-dimensional convection regimes in a two-layer system with evaporation for different types of thermal loads on a substrate

Three-dimensional convection regimes in a two-layer system with evaporation for different types of thermal loads on a substrate

Thermal analysis of thermal barrier coating systems under transient and time harmonic thermal loads

In this study, the temperature fields in a thermal barrier coating system (TBC) under various types of thermal loadings, including steady and transient thermal loads, is investigated. TBCs are exposed to a variety of harsh thermal loadings, including thermal shock and periodic thermal loads. Therefore, the need to achieve the temperature distribution in different positions of the TBCs, especially in the protective coating is very crucial. Non-uniform Thermal boundary conditions are considered for both external temperature and heat flux distributions. The coating and substrate are not stationary at the onset of transient thermal load. Using the solution of steady-state problem as initial condition, the transient temperature fields within the coating-substrate system is obtained. The dual-phase lag (DPL) heat conduction is utilized to scrutinize the transient response of the TBC system. Fourier and Laplace integral transforms have been used to solve the temperature field equations. The effect of concentrated thermal shock and steady harmonic thermal load on the temperature fields of coating and substrate is investigated. The results demonstrate that the steady state and transient temperature fields strongly depend on the type of thermal load, the thickness and thermal properties of the coating, and the loading parameters. The results indicate that the effect of concentrated thermal shock is felt after at least 8.33 s at distance 1.2 cm far from the top surface of ceramic coating. The effect of concentrated thermal shock is eminent adjacent to point (x=0,y=0) of the free boundary of coating, but after a longitudinal distance of 2 cm drastically reduced. The ceramic coating is able to relieve the amplitude of temperature oscillations up to 1280C at a vertical distance of 3mm from the free boundary of coating.

Closed form solutions for thermo-mechanical buckling analysis of shallow piezo-laminated spherical shells

Thermo-mechanical buckling analysis of laminated spherical shells bounded with the piezoelectric actuator layers has been presented in this article. Applied loads are a combination of thermal, mechanical and electrical loads. Derivations of equilibrium and stability equations are based on the classical laminated shell theory and Sanders’s nonlinear kinematic relations. The analysis employs the Galerkin method to achieve closed-form formulas for the buckling loads of the piezo-laminated spherical shell. Effects of applied actuator voltage, voltage sign, geometrical parameters of the shell (length, diameter, and thickness), material properties, and layout of composite layers on the buckling strength are investigated. Analytical solutions are obtained for three types of thermal loading, and one thermo-mechanical loading condition. The results are validated by the known data in the literature.

An investigation of aero-thermo-elastic flutter and divergence of functionally graded porous skew plates

Aero-thermo-elastic flutter and divergence analyses of functionally graded (FG) porous skew plates subjected to supersonic airflow are investigated in this study. The material properties of skew plates vary across the thickness based on the modified power-law model. Three types of thermal loading as constant, linear and nonlinear temperature distributions in the thickness direction of the plate are considered. Applying the Hamilton’s principle, the coupled partial differential equations of motion and the associated boundary conditions based on the first-order shear deformation theory and linear piston theory are derived in the Cartesian coordinates. Also, the principle of minimum total potential energy and adjacent equilibrium criterion are used to obtain the stability equations. Using a mapping, the partial differential equations of motion and stability equations are converted from Cartesian coordinate system to a skew coordinate. The partial differential equations in the skew coordinate are discretized by generalized differential quadrature method (GDQM) and solved using the state space method. Consequently, the effects of geometrical, mechanical and thermal parameters such as thermal loading types, angle of skew, power-law index, porosity, and boundary conditions on the flutter and divergence boundaries of skew plate are studied in detail.

Effect of Porosity on the Thermal Buckling Analysis of Power and Sigmoid Law Functionally Graded Material Sandwich Plates Based on Sinusoidal Shear Deformation Theory

This work examines the effect of porosity distributions on thermal buckling analysis of functionally graded material (FGM) sandwich plates. To consider the porosity effect, five different types of distribution models, even, uneven, logarithmic uneven, linear uneven, and sinusoidal uneven are considered. It is assumed that the FGM faces of the sandwich plate are porous while the ceramic core is nonporous. To investigate the thermal buckling behavior of porous FGM sandwich plates, four different types of thermal loads, such as uniform, linear, nonlinear, and sinusoidal temperature rise along the thickness direction are considered. Effective material properties and thermal expansion coefficients of FGM sandwich plates are evaluated based on Voigt’s micromechanical model considering power law FGM (P-FGM) and sigmoid function FGM (S-FGM). The analytical solution is carried out using Hamilton’s variational principle considering the von Karman nonlinearity. The equilibrium and stability equations are derived based on sinusoidal shear deformation theory (SSDT). Numerical results are obtained to observe the influence of different porosity distributions, porosity coefficients, thermal loadings, and geometrical parameters over critical thermal buckling temperature.

A Bayesian approach for site-specific extreme load prediction of large scale bridges

To measure uncertainties of site-specific extreme loads for a signature bridge, a probabilistic method is developed based on structural health monitoring data in the Bayesian context. Compared with respective design loads, the probability of the predicted extreme load exceeding the design one is used to determine whether the design load is sufficient. The generalized Pareto distribution was first employed to model extreme value information. Then, Bayesian estimation was applied to predict probabilistic distributions of extreme loads, accounting for uncertainties within the prediction process. Finally, the effectiveness of the proposed method was validated through wind speed and temperature measurements from the Nanjing Dashengguan Yangtze River Bridge. The extreme wind speed and four types of thermal loads were predicted based on site-specific monitored loading data by using Bayesian estimation of the generalized Pareto distribution. As a result, the design wind speed and design change in uniform temperature are sufficient for the signature bridge. However, the probability that the predicted extreme vertical girder temperature difference exceeds the design one is 99.96%, and the probabilities subject to the transverse girder temperature difference and tower temperature difference are almost 100%.

Thermal buckling behavior of power and sigmoid functionally graded material sandwich plates using nonpolynomial shear deformation theories

PurposeThe purpose of this article is to carry out the thermal buckling analysis of power and sigmoid functionally graded material Sandwich plate (P-FGM and S-FGM) under uniform, linear, nonlinear and sinusoidal temperature rise.Design/methodology/approachThermal buckling of FGM Sandwich plates namely, FGM face with ceramic core (Type-A) and homogeneous face layers with FGM core (Type-B), incorporated with nonpolynomial shear deformation theories are considered for an analytical solution in this investigation. Effective material properties and thermal expansion coefficients of FGM Sandwich plates are evaluated based on Voigt's micromechanical model considering power and sigmoid law. The governing equilibrium and stability equations for the thermal buckling analysis are derived based on sinusoidal shear deformation theory (SSDT) and inverse trigonometric shear deformation theory (ITSDT) along with Von Karman nonlinearity. Analytical solutions for thermal buckling are carried out using the principle of minimum potential energy and Navier's solution technique.FindingsCritical buckling temperature of P-FGM and S-FGM Sandwich plates Type-A and B under uniform, linear, non-linear, and sinusoidal temperature rise are obtained and analyzed based on SSDT and ITSDT. Influence of power law, sigmoid law, span to thickness ratio, aspect ratio, volume fraction index, different types of thermal loadings and Sandwich plate types over critical buckling temperature are investigated. An analytical method of solution for thermal buckling of power and sigmoid FGM Sandwich plates with efficient shear deformation theories has been successfully analyzed and validated.Originality/valueThe temperature distribution across FGM plate under a high thermal environment may be uniform, linear, nonlinear, etc. In practice, temperature variation is an unpredictable phenomenon; therefore, it is essential to have a temperature distribution model which can address a sinusoidal temperature variation too. In the present work, a new sinusoidal temperature rise is proposed to describe the effect of sinusoidal temperature variation over critical buckling temperature for P-FGM and S-FGM Sandwich plates. For the first time, the FGM Sandwich plate is modeled using the sigmoid function to investigate the thermal buckling behavior under the uniform, linear, nonlinear and sinusoidal temperature rise. Nonpolynomial shear deformation theories are utilized to obtain the equilibrium and stability equations for thermal buckling analysis of P-FGM and S-FGM Sandwich plates.

Thermo-vibrational analyses of skin tissue subjected to laser heating source in thermal therapy

Laser-induced thermal therapy, due to its applications in various clinical treatments, has become an efficient alternative, especially for skin ablation. In this work, the two-dimensional thermomechanical response of skin tissue subjected to different types of thermal loading is investigated. Considering the thermoelastic coupling term, the two-dimensional differential equation of heat conduction in the skin tissue based on the Cattaneo–Vernotte heat conduction law is presented. The two-dimensional differential equation of the tissue displacement coupled with the two-dimensional hyperbolic heat conduction equation in the tissue is solved simultaneously to analyze the thermal and mechanical response of the skin tissue. The existence of mixed complicated boundary conditions makes the problem so complex and intricate. The Galerkin-based reduced-order model has been utilized to solve the two-sided coupled differential equations of vibration and heat transfer in the tissue with accompanying complicated boundary conditions. The effect of various types of heating sources such as thermal shock, single and repetitive pulses, repeating sequence stairs, ramp-type, and harmonic-type heating, on the thermomechanical response of the tissue is investigated. The temperature distribution in the tissue along depth and radial direction is also presented. The transient temperature and displacement response of tissue considering different relaxation times are studied, and the results are discussed in detail.

Guided wave propagation of porous functionally graded plates: The effect of thermal loadings

Because there is no literature on the effect of thermal loadings on guided wave propagation in FG plates, the present paper is to fill the gap. In the present paper, the wave propagation analysis of porous FG plates with clamped ends in thermal environments based on first order shear deformation theory are presented. The plates are exposed to various types of thermal loading including uniform and non-uniform temperature changes, the material properties of FG plates are temperature- and porosity-dependent. Using the Galerkin method, we obtain the dispersion relation of thermoelastic waves in porous functionally graded plates. Compared with the previous results, the correctness of the present work is verified. In the end, the effects of the temperature changes, porosity as well as power law index on the phase velocity and group velocity of the guided wave are investigated.

The effects of thermal loadings on wave propagation analysis of multi-scale hybrid composite beams

This research is concerned with the analysis of wave propagation of multi-scale hybrid composite beams subjected to various types of thermal loading. Carbon fiber (CF) and carbon nanotube (CNT) are assumed as reinforcements that are distributed in the matrix. The homogenization process is performed exerting the Halpin–Tsai model and the rule of mixture. Different types of temperature rise, namely, uniform, linear and sinusoidal temperature rise are presumed to present a more trustworthy thermal analysis. The beam is rested on Winkler–Pasternak foundation. A refined trigonometric shear deformable beam theory is used to compute the kinetic relations without any external shear correction coefficient. Governing equations are derived implementing Hamilton’s principle and then solved analytically. Eventually, the effects of different parameters, such as CNT’s weight fraction, the volume fraction of CF, elastic foundation, different types of temperature rise, etc., on wave frequency and phase velocity. are provided numerically in the framework of a set of illustrations.

Heat Transfer in Periodically Laminated Structures – Third Type Boundary Conditions

This work is about a heat transfer phenomenon in relation to the periodically laminated composite. The specific type of thermal loading, analyzed in this paper, require formulation of Robin boundary conditions. To consider a layered structure of analyzed composite, the tolerance averaging technique is used. This method allows to take into account a thickness of the layers and obtain the equations with continuous coefficients. To solve these equations, the finite difference method is used, because an analytical solution is not available in this case (in contrast to the analogous issue in relation to a homogeneous layer).

Investigation of thermal preloading and porosity effects on the nonlocal nonlinear instability of FG nanobeams with geometrical imperfection

The aim of the present research is twofold. The first is to present a study on nonlinear thermo-mechanical bending and thermal postbuckling analysis of functionally graded (FG) porous perfect/imperfect nanobeam according to the nonlocal elasticity theory. The second, concurrent aim is to address the snap-through phenomenon in the thermally preloaded graded porous nanobeams due to lateral mechanical load. Two types of thermal loading including, uniform temperature rise and heat conduction through the thickness as well as two cases of porosity distribution, including uniform and uneven, are considered. Geometrically imperfect FG porous nanobeam with four different types of immovable boundary conditions is also taken into account. Thermo-mechanical material properties of the porous nanobeam are assumed to be position-dependent according to the modified rule of mixture. The nonlinear equilibrium equations are constructed using the Euler–Bernoulli beam model and von-Kármán type of geometrical nonlinearity. Chebyshev polynomial based Ritz method is utilized into the principle of virtual displacement to obtain the matrix representation of the nonlocal governing equations. Two different strategies, including the Newton–Raphson technique and direct displacement control scheme, are first proposed to extract the nonlinear bending and postbuckling curves of the graded nanobeam. Afterwards, to capture the snapping behavior and trace the path beyond the limit loads of the thermally preloaded nanobeam, the cylindrical arch-length technique is adopted. Numerical results are provided to explore the effect of different parameters such as the power-law index, nonlocal parameter, boundary conditions, porosity distribution, thermal loading, and imperfection amplitude on the nonlinear thermo-mechanical bending and instability of the FG nanobeam.

Nonlinear thermal buckling and postbuckling analysis of bidirectional functionally graded tapered microbeams based on Reddy beam theory

In the present study, the nonlinear thermal buckling, postbuckling, and snap-through phenomenon of higher-order shear deformable tapered bidirectional functionally graded (BDFG) microbeams are comprehensively investigated under different types of thermal loading, for the first time. The thermomechanical properties of the BDFG microbeam are assumed to be functions of temperature, axial, and thickness directions. Reddy’s parabolic shear deformation beam theory with the von Karman nonlinearity is employed to derive the variable coefficient governing nonlinear differential equations on the basis the physical neutral surface concept. Size-dependent effect is captured in the formulation employing the modified couple stress theory. The generalized differential quadrature method (GDQM) is used to discretize the motion equations considering different boundary conditions. The resulting system of nonlinear algebraic equations is solved iteratively using Newton’s method. Theoretical analysis and numerical results indicate that, depending on the shear deformation beam theory, boundary conditions, and the type of thermal load, the response of the BDFG microbeam may be of the bifurcation or snap-through buckling type of instability. Numerical parametric studies are conducted to explore the influences of thermal load type, material property gradient indexes, boundary conditions, material temperature dependency, taperness ratio, and microstructural length scale on critical thermal buckling load, thermal postbuckling, and equilibrium paths of the BDFG microbeam.