Loads In Thermal Environments Research Articles

Lateral-torsional buckling of arches under an arbitrary radial point load in a thermal environment incorporating shear deformations

This paper presents an analytical investigation of the thermoelastic lateral-torsional buckling of circular arches under an arbitrary radial point load in a uniform thermal environment accounting for shear deformations, which has not been reported in the literature. The interaction of thermal environment with the arbitrary load and elastic end restraints produces complex non-uniform compressive, bending, and shearing actions in the arch. The theoretical solutions of the critical load and temperature field for the elastic lateral-torsional buckling of arches accounting for shear deformations are derived. Comparisons of theoretical solutions with finite element results show that their agreements are excellent. Effects of various factors on the lateral-torsional buckling are investigated. An increase of the temperature field reduces the buckling load, while an increase of the radial load reduced the critical temperature field for buckling. The effect of shear deformations on the lateral-torsional buckling load is also explored. It is shown that the neglect of shear deformations causes errors in the prediction of the critical buckling load. When shear deformations are considered, the buckling load for arches with a small and intermediate lateral slenderness ratio under the radial point load alone is shown to be lower than that without consideration of shear deformations. However, under the uniform temperature field alone, the critical temperature field for lateral-torsional buckling of the arches considering shear deformations is higher than that neglecting shear deformations.

Postbuckling behavior of CNT-reinforced composite cylindrical shell surrounded by an elastic medium and subjected to combined mechanical loads in thermal environments

Cylindrical shells are usually buckled under complex and combined loading conditions. This article presents an analytical approach to investigate the buckling and postbuckling behaviors of cylindrical shells reinforced by single-walled carbon nanotubes, surrounded by an elastic medium, exposed to thermal environments, and subjected to combined axial compression and lateral pressure loads. Carbon nanotubes (CNTs) are imbedded into matrix phase by uniform distribution or functionally graded distribution along the thickness direction. The properties of constituents are assumed to be temperature dependent, and effective properties of CNT-reinforced composite (CNTRC) are determined by an extended rule of mixture. Governing equations are based on the classical shell theory (CST) taking von Karman–Donnell nonlinearity and surrounding elastic foundations into consideration. Three-term form of deflection is assumed to satisfy simply supported boundary conditions, and Galerkin method is applied to obtain nonlinear load–deflection relations from which buckling loads and postbuckling equilibrium paths are determined. Numerical examples are carried out to show the effects of CNT volume fraction, distribution types, thermal environments, preexisting nondestabilizing lateral pressure and axial compression loads, and elastic medium on the buckling and postbuckling behaviors of CNTRC cylindrical shells.

Large deflection of thermo-mechanical loaded bilayer orthotropic graphene sheet in/on polymer matrix based on nonlocal elasticity theory

In this paper, large deflection behavior of a bilayer graphene sheet (BLGS) is investigated under uniformly transverse load in thermal environment with various boundary conditions. Using the principle of virtual work, the non-linear formulations are derived based on first-order shear deformation plate theory (FSDT) and large deflection von Kármán equations that includes the thermal effects. Differential quadrature (DQ) method and the Newton–Raphson iterative technique is employed to solve the system of nonlinear algebraic equations. To study the effect of elastic foundation on the results, two types of embedded in polymer matrix (EIPM) and resting on polymer matrix (ROPM) are considered. Besides, the influences of temperature rise, material properties, boundary conditions, small scale effect, thickness-to-length ratio, aspect ratio and polymer matrix properties are studied in detail.

Stability of a half-sine shallow arch under sinusoidal and step loads in thermal environment

Abstract The complex structural behavior of shallow arches can be remarkably affected by many parameters. In this paper, the structural responses of a half-sine pin-ended shallow arch under sinusoidal and step loadings are accurately calculated. Additionally, the effects of environmental temperature changes are considered. Three types of sinusoidal loadings are separately investigated. Displacements, load-bearing capacity, the magnitude of the axial force and the locus of critical points (including limit and bifurcation points) are directly obtained without tracing the corresponding equilibrium path. Furthermore, the boundaries identifying the number of critical points are investigated. All mentioned structural responses are formulized based on the rise of the arch and the environmental temperature change, which are introduced in a dimensionless form. The proposed formulation is also developed for generalized sinusoidal loadings. Additionally, the structural behavior of the shallow arch under two types of step loadings is investigated. Finally, the accuracy of the suggested approach is examined by a non-linear finite element method.

Nonlinear transient isogeometric analysis of FG-CNTRC nanoplates in thermal environments

This paper presents size-dependency effects on nonlinear transient dynamic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates under a transverse uniform load in thermal environments. To consider the length scale and size-dependency effect of nanostructures, a nonlocal continuum theory of Eringen is adopted. The nonlocal governing equations for nanoplate theory are derived from the Hamilton’s principle and approximated by using isogeometric analysis associated with the higher-order shear deformation theory. A numerical model based on the von Kármán strains and Newmark time integration scheme is employed to solve geometrically nonlinear transient problems. The material properties of the FG-CNTRC nanoplate are assumed to be graded and temperature-dependent in the thickness direction, which are expressed through a micromechanical model. Effects of nonlocal parameter, carbon nanotube volume fraction, length-to-thickness ratio, distributions of carbon nanotubes and temperatures through thickness are investigated in detail. Several numerical results show the reliability of the present method.

Nonlinear bending analysis of a 3D braided composite cylindrical panel subjected to transverse loads in thermal environments

The aim of this study is to investigate nonlinear bending for a 3-Dimensional (3D) braided composite cylindrical panel which has transverse loads on its finite length. By refining a micro-macro-mechanical model, the 3D braided composite can be treated as a representative average cell system. The geometric structural properties of its components deeply depend on their positions in the section of the cylindrical panel. The embedded elastic medium of the panel can be described by a Pasternak elastic foundation. Via using the shell theory of the von Kármán-Donnell type of kinematic nonlinearity, governing equations can be established to get higher-order shear deformation. The mixed Galerkin-perturbation method is applied to get the nonlinear bending behavior of the 3D braided cylindrical panel with a simply supported boundary condition. Based on the analysis of the braided composite cylindrical panel with variable initial stress, geometric parameter, fiber volume fraction, and elastic foundation, serial numerical illustrations are archived to represent the appropriate nonlinear bending responses.

Nonlinear dynamic responses of an axially moving laminated beam subjected to both blast and thermal loads

The nonlinear dynamic responses of an axially moving laminated beam subjected to a blast load in thermal environment is studied considering large-displacement. Firstly, the nonlinear dynamic equilibrium equation is established based on the large-displacement theory and the constitutive relation of the single layer material in thermal environment. Based on the Galerkin method, a set of ordinary differential equations is obtained. Secondly, the multiple scales method is adopted to get the nonlinear free vibration frequency. Then, the stability region of the axial velocity and temperature is derived and the truncation order is approximated by the convergence calculation of the natural frequencies. Finally, numerical calculations are performed to discuss the effects of different kinds of blast loads, axial velocity and temperature on the nonlinear dynamic responses adopting the Runge–Kutta technique.

Large Amplitude Dynamic Analysis of FGM Cylindrical Shells on Nonlinear Elastic Foundation Under Thermomechanical Loads

Nonlinear dynamic characteristics of functionally graded material (FGM) cylindrical shells surrounded by nonlinear elastic foundation under axial static and lateral dynamic loads in thermal environment are investigated in the current paper. The main emphasis is on the simulation of the elastic foundation model and thermal loads. Nonlinear tri-parametric elastic foundation including linear and nonlinear parameters is used to model the reaction of the elastic foundation on the cylindrical shell. Different thermal loading scenarios are applied to the system to study the effects of thermal environment, including uniform, linear and nonlinear temperature distribution across the shell thickness. Governing equations are derived based on the Donnell’s thin shell theory. Material properties of the FGM are assumed to be variable through the shell thickness according to a power law function. Discretization of the obtained governing equations is performed using the Galerkin’s method. An averaging method and the Runge–Kutta method are applied to obtain the frequency–amplitude relation and time–deflection relation, respectively. Comprehensive numerical results are given for investigating the effects of thermo-mechanical loads, material and geometrical properties and nonlinear elastic foundation parameters on nonlinear dynamic characteristics of the functionally graded cylindrical shells (FGCSs). Present formulations are validated by comparing the results with the published data for some specific cases.

Uncertainty quantification in non-linear dynamic response of functionally graded materials plate

ABSTRACTThis study deals with the stochastic non-linear dynamic response of functionally graded materials (FGMs) plate with uncertain system properties subjected to time-dependent uniformly distributed transverse load in thermal environments. System properties, such as material properties of each constituent's material, volume fraction index, and transverse load, are taken as uncorrelated random input variables. Material properties are assumed as temperature dependent (TD). The formulation is based on higher-order shear deformation theory (HSDT) with von-Karman non-linear strain kinematics using modified C° continuity. A Newton–Raphson-based non-linear finite element method along with a first-order perturbation technique (FOPT) and Monte Carlo sampling (MCS) is outlined to examine the second-order statistics (mean, standard deviation (SD), and probability density function (PDF)) of the non-linear dynamic response of the FGM plate. The governing dynamic equation is solved by Newmark's time integration scheme. The effects of volume fraction index, load parameters, plate thickness ratios, and temperature changes with random system properties are examined through parametric studies. The present outlined approach is validated with the results available in the literature and by MCS.

Vibrational investigation of the spinning bi-dimensional functionally graded (2-FGM) micro plate subjected to thermal load in thermal environment

This article presented a numerical method for discovering the free vibration of a spinning bi-dimensional functionally graded materials (FGM) micro circular plate exposed to thermal load based on Winkler–Pasternak foundation for the first time. Thermomechanical properties of bi-dimensional FGM micro plate are supposed to change during the thickness and radius directions of the plate. The small effect is taken into consideration the modified couple stress theory. Linear temperature rise during thickness and radius direction is investigated. First-order shear deformation theory is employed to derive the governing equations and boundary conditions of the bi-dimensional FGM circular plate in the thermal environment via Hamilton’s principle. The differential quadrature method is used to achieve the frequency of bi-dimensional FGM micro circular plate exposed to the thermal environment. A parametric analysis is led to assess the efficacy of Winkler and Pasternak parameters, FG power index, coefficients of bi-dimensional FGM, size dependency, non-dimensional angular velocity, temperature changes and thermal loading on the natural frequencies of bi-dimensional FGM micro plate.

Nonlinear thermo-mechanical response of eccentrically stiffened Sigmoid FGM circular cylindrical shells subjected to compressive and uniform radial loads using the Reddy's third-order shear deformation shell theory

ABSTRACTBased on Reddy's third-order shear deformation shell theory, this paper presents an analytical approach to investigate the nonlinear thermo-mechanical response of imperfect Sigmoid FGM circular cylindrical shells surrounded on elastic foundations and reinforced by outside metal stiffeners. The eccentrically stiffened S-FGM shells are subjected to axial compressive load and uniform radial load in thermal environment. Using the stress function, Bubnov–Galerkin method, the paper proposes the formula for forces and moments taking into account the thermal stress in both the shells and stiffeners. The obtained results are validated by comparing with other results reported in the literature.

Finite element based nonlinear dynamic response of elastically supported piezoelectric functionally graded beam subjected to moving load in thermal environment with random system properties

The second order statistics in terms of mean and standard deviation (SD) of normalized nonlinear transverse dynamic central deflection (NTDCD) response of un-damped elastically supported functionally graded materials (FGMs) beam with surface-bonded piezoelectric layers under the action of moving load are investigated in this paper. The random system properties such as Young's modulus, Poisson's ratio, density, thermal expansion coefficients, piezoelectric materials, volume fraction exponent and external loading are modeled as uncorrelated random variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics combined with Newton–Raphson technique through Newmark's time integrating scheme using finite element method (FEM). The non-uniform temperature distribution with temperature dependent material properties is taken into consideration for consideration of thermal loading. The one parameter Pasternak elastic foundation with Winkler cubic nonlinearity is considered as an elastic foundation. The stochastic based second order perturbation technique (SOPT) and direct Monte Carlo simulation (MCS) are adopted for the solution of nonlinear dynamic governing equation. The influences of volume fraction exponents, temperature increments, moving loads and velocity, nonlinearity, slenderness ratios, foundation parameters and external loadings with random system properties on the NTDCD are examined. The capability of present stochastic model in predicting the NTDCD statistics are compared by studying their convergence with the existing results those available in the literature.

Experimental investigation on dynamic response of aircraft panels excited by high-intensity acoustic loads in thermal environment

Metallic and composite panels are the major components for thermal protection system of aircraft vehicles, which are exposed to a severe combination of aerodynamic, thermal and acoustic environments during hypersonic flights. A thermal-acoustic testing apparatus which simulates thermal and acoustic loads was used to validate the integrity and the reliability of these panels. Metallic and ceramic matrix composite flat panels were designed. Dynamic response tests of these panels were carried out using the thermal acoustic apparatus. The temperature of the metallic specimen was up to 400 °C, and the temperature of the composite specimen was up to 600 °C. Moreover, the acoustic load was over 160 dB. Acceleration responses of these testing panels were measured using high temperature instruments during the testing process. Results show that the acceleration root mean square values are dominated by sound pressure level of acoustic loads. Compared with testing data in room environment, the peaks of the acceleration dynamic response shifts obviously to the high frequency in thermal environment.

Nonlinear dynamic and vibration analysis of piezoelectric eccentrically stiffened FGM plates in thermal environment

In this paper, the nonlinear dynamic response and vibration of a plate made of piezoelectric functionally graded materials (FGM) and reinforced by eccentrically outside stiffeners with piezoelectric actuators resting on Pasternak type elastic foundations subjected to mechanical and electrical loads in thermal environment are investigated. One of the salient features of this work is the consideration of temperature on the piezoelectric layer, stiffeners and all of them (the plate, outside stiffeners, piezoelectric layers) are deformed under temperature. The material properties of the FGM plates are assumed to be temperature dependent. The governing equations for the plates are derived by using the first order shear deformation theory of plates, taking into account both the geometrical nonlinearity in the von Karman sense, initial geometrical imperfections and different types of boundary conditions. The effects of geometrical parameters; material properties; imperfections; elastic foundations; stiffeners and thermal stress in stiffeners; mechanical and electrical loads, temperature on the nonlinear dynamic response and vibration of the piezoelectric FGM plates are studied simultaneously for first time.

Nonlinear thermo-elastic bending behavior of graphene sheets embedded in an elastic medium based on nonlocal elasticity theory

This paper investigates the large deflection behavior of orthotropic single layered graphene sheet (SLGS) embedded in a Winkler–Pasternak elastic medium under a uniform transverse load in thermal environments. Using the nonlocal differential constitutive relations of Eringen, the SLGS is modeled as a nonlocal orthotropic plate. Using the principle of virtual work, the coupled nonlinear equilibrium equations are obtained based on first-order shear deformation theory (FSDT) and the von Kármán geometrical model. The differential quadrature (DQ) discretized form of the governing equations with clamped and simply supported boundary conditions is derived. The Newton–Raphson iterative scheme is used to solve the resulting system of nonlinear algebraic equations. Effects of small scale parameter, thermal environment, width-to-length elasticity ratio, aspect ratio, thickness, elastic foundation, load value and boundary conditions are considered in detail. The results show that, unlike the simply supported boundary conditions, increase of small scale parameter plays a decreasing role in effect of thermal environment on the deflections of nanoplates with clamped edges. It is also observed that increasing the plate thickness, thermal load effects decline noticeably and depending on the small scale value the thermal loads do not have any significant effect on the results beyond a specified thickness.

Nonlinear dynamic analysis of fiber metal laminated beams subjected to moving loads in thermal environment

The present study is concerned with the nonlinear dynamic behaviors of fiber metal laminated (FML) beams subjected to moving loads in thermal environments. Based on von Kármán geometric nonlinear theory and Euler–Bernoulli beam hypothesis, the nonlinear equations of motion for the fiber-metal laminated beams under moving loads are derived by using Hamilton’s principle. Galerkin method and Newmark method are employed to solve the dynamic responses of FML beam numerically. The dynamic responses at the midspan of the FML beam are obtained for various load velocity and temperature rise and the outcome results have been compared to the results with those obtained from linear solution. The influences of temperature, geometric nonlinearity, material parameters and velocity of the moving load on the dynamic responses of fiber-metal laminated beams are investigated. Numerical results indicate that the above-mentioned effects play a very important role on the dynamic responses of the beam.

Nonlinear vibration and dynamic response of imperfect eccentrically stiffened shear deformable sandwich plate with functionally graded material in thermal environment

This paper presents an analytical approach to investigate the nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened sandwich plate with functionally graded material (FGM) on elastic foundation using both of the first-order shear deformation plate theory and stress function with full motion equations (not using Volmir's assumptions). The thick sandwich plates are assumed to rest on elastic foundation and subjected to mechanical loads in thermal environment. Numerical results for dynamic response of the eccentrically stiffened thick sandwich plates are obtained by Runge–Kutta method. The results show the influences of geometrical parameters, material properties, imperfections, the elastic foundations, eccentric stiffeners, mechanical loads and temperature on the nonlinear dynamic response and nonlinear vibration of functionally graded sandwich plates. The numerical results in this paper are compared with the results reported in other publications.

Nonlinear bending and postbuckling of FGM cylindrical panels subjected to combined loadings and resting on elastic foundations in thermal environments

A nonlinear analysis is presented for FGM cylindrical panels resting on elastic foundations subjected to the combined actions of uniform lateral pressure and compressive edge loads in thermal environments. The two cases of postbuckling of initially pressurized FGM cylindrical panels and of nonlinear bending of initially compressed cylindrical panels are considered. Heat conduction and temperature-dependent material properties are both taken into account. Material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction based on Mori-Tanaka micromechanics model. The formulations are based on a higher order shear deformation theory and von Kármán strain displacement relationships. The panel-foundation interaction and thermal effects are also included. The governing equations are solved by a singular perturbation technique along with a two-step perturbation approach. The numerical illustrations concern the postbuckling behavior and the nonlinear bending response of FGM cylindrical panels with two constituent materials resting on Pasternak elastic foundations. The effects of volume fraction index, temperature variation, foundation stiffness as well as initial stress on the postbuckling behavior and the nonlinear bending response of FGM cylindrical panels are discussed in detail.

Nonlinear reduced order modeling of functionally graded plates subjected to random load in thermal environment

In this paper, large amplitude vibration of functionally graded material (FGM) plates subjected to combined random pressure and thermal load is studied using finite element modal reduction method. The material properties, which are depended on the temperature, vary in the thickness direction by a simple power law distribution in terms of the volume fraction of the constituents. The equations of motion in structural node degrees of freedom (DOF) are obtained based on von-Karman large deflection and first order shear deformation theory. The order of these equations is reduced using a novel approach for selection of the base vectors. Then the numerical results of the obtained reduced-order equations are compared with those of reduced-order equations obtained by other base vectors and also with those of full finite element method. It is shown that the proposed set of base vectors forms an excellent candidate for reducing the order of the equations of motion.

Dynamic response analysis of a HSLA steel circular plate subjected to mechanical load in thermal environments

Dynamic response analysis of a high strength low alloy (HSLA) steel circular plate subjected to mechanical load in thermal environments is investigated. Based on the von Karman equation and classical theory of thin plate, the nonlinear governing equations for the HSLA steel circular plate are obtained by using the kirchhoff hypothesis. The unknown variable functions are discrete in space and time domains by utilizing the finite difference method and Newmark method, the whole problem is solved by the iterative method. Numerical results indicate that some of the important geometrical and physical parameters are important factors affecting the dynamic response of the HSLA steel circular plate and the design of structures.