Foundations In Thermal Environments Research Articles

Thermoelastic response of CNT reinforced cylindrical panel resting on elastic foundation using theory of elasticity

Abstract Based on the three-dimensional elasticity theory, the investigation of the free vibration response of a carbon nanotube-reinforced cylindrical panel resting in elastic foundation in thermal environments is presented. The response of the elastic medium is formulated by the Winkler/Pasternak model. The cylindrical panel has been reinforced by carbon nanotube in the radial direction and the material properties are temperature dependent and estimated by the extended rule of mixture. Dynamic Young’s modulus of single-walled carbon nanotubes can be expressed a function of loading rate and environmental temperature. Differential quadrature method is being utilized and natural frequencies of cylindrical panel are obtained. An accuracy of the present solution is confirmed by comparing with some available results in the article. A detailed numerical study is conducted to examine the effects of temperature rise, carbon nanotube volume fraction, elastic foundations and the geometrical parameters on the deflection of the cylindrical panels.

Non-linear dynamic response and vibration of an imperfect three-phase laminated nanocomposite cylindrical panel resting on elastic foundations in thermal environments

Abstract This paper presents an analytical approach to investigate the non-linear dynamic response and vibration of an imperfect three-phase laminated nanocomposite cylindrical panel resting on elastic foundations in thermal environments. Based on the classical laminated shell theory and stress function, taking into account geometrical non-linearity, initial geometrical imperfection, Pasternak-type elastic foundation, and temperature, the governing equations of the three-phase laminated nanocomposite cylindrical panel are derived. The numerical results for the dynamic response and vibration of the polymer nanocomposite cylindrical panel are obtained by using the Runge-Kutta method. The influences of fibres and nanoparticles, different fibre angles, material and geometrical properties, imperfection, elastic foundations, and temperature on the non-linear dynamic response of the polymer nanocomposite cylindrical panel are discussed in detail.

Nonlinear dynamical analyses of eccentrically stiffened functionally graded toroidal shell segments surrounded by elastic foundation in thermal environment

Abstract In this study, the nonlinear vibration and dynamic buckling of eccentrically stiffened functionally graded toroidal shell segments surrounded by an elastic medium in thermal environment are presented. The governing equations of motion of eccentrically stiffened functionally graded toroidal shell segments are derived based on the classical shell theory with the geometrical nonlinear in von Karman-Donnell sense and the smeared stiffeners technique. Furthermore, the dynamical characteristics of shells as natural frequencies, nonlinear frequency–amplitude relation, nonlinear dynamic responses and the nonlinear dynamic critical buckling loads evaluated by Budiansky-Roth criterion are considered. The effects of characteristics of functionally graded materials, geometrical ratios, elastic foundation, pre-loaded axial compression and temperature on the dynamical behavior of shells are investigated.

Nonlinear bending and vibration of functionally graded tubes resting on elastic foundations in thermal environment based on a refined beam model

This paper studies the nonlinear bending and vibration problems of functionally graded tubes with temperature-dependent material properties based on a refined beam model. The tubes are exposed to a uniform distributed temperature field and are placed on elastic foundation. The refined beam model for tubes can satisfy the stress boundary conditions on inner and outer surfaces. The governing equations of nonlinear bending and vibration for the functionally graded tubes are derived by using Hamilton's principle and are solved by introducing a two-step perturbation technique. Some comparisons for bending and vibration are presented to valid the correctness of present beam model and solution method. In numerical results, the effects of transverse shear deformation, the volume fraction, inner radius and elastic foundation stiffness as well as the temperature on the natural frequency, amplitude–frequency responses and nonlinear bending responses are discussed.

Nonlinear vibration and dynamic response of shear deformable imperfect functionally graded double-curved shallow shells resting on elastic foundations in thermal environments

ABSTRACTIn this article, nonlinear vibration and dynamic response of imperfect functionally graded materials (FGM) thick double-curved shallow shells resting on elastic foundations are investigated using Reddy's third-order shear deformation shell theory in thermal environments. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The FGM shells are subjected to mechanical, damping, and thermal loads. The Galerkin method and fourth-order \\hboxRunge–Kutta method are used to calculate natural frequencies, nonlinear frequency–amplitude relation, and dynamic response of the shells. In numerical results, the effects of geometrical parameters, material properties, imperfections, shear deformation, the elastic foundations, mechanical, thermal and damping loads on the nonlinear dynamic response, and nonlinear vibration of FGM double-curved shallow shells are investigated. Accuracy of the present formulation is shown by comparing the results of numerical examples with the ones available in literature.

Dynamic response of acoustically excited plates resting on elastic foundations in thermal environments

In order to ensure integrity of thermal protection system for hypersonic vehicles, the random dynamic response induced by the combination of the thermal and acoustic loadings has been investigated for a composite thin skin panel resting on a two-parameter elastic foundation. A theoretical model is developed based on the first four symmetric plate modes through Galerkin method. The solutions of a set of the high-order coupled ODEs have been validated by comparison of the postbuckling deflection with the results obtained from FEM postbuckling analysis. A dynamic response evolution parameter deduced from the primary-mode modal equation is used to characterize a transition from linear vibration to fully nonlinear dynamic snap-through. The study demonstrates the combination of acoustic excitation, thermal effect and structural stiffness governs the dynamic response evolution. As the elastic foundation stiffness increases, the buckling temperature increases and the postbuckling deflection decreases, which promote the nonlinear dynamic snap-through response remarkably with reducing snap-through amplitude.

Postbuckling of pressure-loaded nanotube-reinforced composite doubly curved panels resting on elastic foundations in thermal environments

This paper presents an investigation on the postbuckling behavior of doubly curved nanocomposite panels reinforced by carbon nanotubes (CNTs) subjected to lateral pressure. The functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to have CNTs linearly graded in the thickness direction. The overall mechanical properties of the FG-CNTRCs, which include the thermal effect of CNTs and the matrix, are estimated through a micromechanical model. The panels may rest on elastic foundations. The governing differential equations for the doubly curved panels are based on a higher order shear deformation shell theory with von Kármán strain–displacement relationships and the panel–foundation interaction. The initial deflections caused by lateral pressure and thermal bending stresses are both taken into account. The governing equations are further deduced to a boundary layer type problem that includes nonlinear prebuckling deformations and initial geometric imperfections of the panels which are subsequently solved using a two-step perturbation approach. The influences of CNT volume fraction, temperature variation, panel geometric parameters, as well as foundation stiffness on the postbuckling behavior of FG-CNTRC doubly curved panels are investigated.

Nonlinear buckling of eccentrically stiffened functionally graded toroidal shell segments under torsional load surrounded by elastic foundation in thermal environment

The nonlinear buckling and post-buckling of functionally graded stiffened toroidal shell segment surrounded by elastic foundation in thermal environment and under torsional load are investigated in this paper. The functionally graded toroidal shell segments are reinforced by ring and stringer stiffeners system in which material properties of shell are assumed to be continuously graded in the thickness direction. The two-parameter elastic foundation proposed by Pasternak is studied. Theoretical formulations are derived basing on the classical shell theory with the geometrical nonlinearity in von Karman sense and the smeared stiffeners technique. The three-term approximate solution of deflection is chosen more correctly and the explicit expression for finding critical load and post-buckling torsional load-deflection curves are found. The effects of geometrical parameters, temperature, stiffeners and elastic foundation are investigated.

Nonlinear dynamics of matrix-cracked hybrid laminated plates containing carbon nanotube-reinforced composite layers resting on elastic foundations

This paper investigates the nonlinear dynamic response of hybrid laminated plates resting on elastic foundations in thermal environments. The plate consists of conventional fiber-reinforced composite (FRC) layers and carbon nanotube-reinforced composite (CNTRC) layers. Each layer may have matrix cracks, and the damage is described by a refined self-consistent model. The motion equations are based on a higher-order shear deformation theory with a von Karman type of kinematic nonlinearity. The thermal effects are included, and the material properties of both FRC and CNTRC are assumed to be temperature dependent. The plate–foundation interaction is also included. The motion equations are solved by a two-step perturbation technique to determine the dynamic response of matrix-cracked hybrid laminated plates. The boundary condition is assumed to be simply supported with in-plane displacements “movable” or “immovable.” The effects of stiffness reduction due to matrix cracks, the foundation stiffness, the temperature change, the percentage and distribution of carbon nanotubes in CNTRC layers are discussed in detail through a parametric study.

Postbuckling of pressure-loaded FGM doubly curved panels resting on elastic foundations in thermal environments

Modeling and analysis for the postbuckling of FGM doubly curved panels resting on elastic foundations and subjected to lateral pressure under heat conduction are presented. The initial deflections caused by lateral pressure and thermal bending stresses are both taken into account. The temperature-dependent 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 with von Kármán strain–displacement relationships. The panel-foundation interaction and thermal effects are also included. The governing equations are first deduced to a boundary layer type that includes nonlinear prebuckling deformations and initial geometric imperfections of the panel. These equations are then solved by means of a singular perturbation technique along with a two-step perturbation approach. The effects of volume fraction index, temperature variation, the panel geometric parameters as well as foundation stiffness on the postbuckling behavior of FGM doubly curved panels are discussed in detail.

Large amplitude free vibration of nanotube-reinforced composite doubly curved panels resting on elastic foundations in thermal environments

A large amplitude vibration analysis is presented for nanocomposite doubly curved panels resting on elastic foundations in thermal environments. The doubly curved nanocomposite panels are studied with the consideration of different types of distributions of uniaxial aligned single-walled carbon nanotubes (SWCNTs). The material properties of the functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction according to linear distributions of the volume fraction of CNTs and are estimated through a micromechanical model. The motion equations are based on a higher order shear deformation theory and von Kármán strain-displacement relationships. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. The motion equations are solved by a two-step perturbation approach to determine the nonlinear frequencies of the CNTRC doubly curved panel. The numerical illustrations cover small- and large-amplitude vibration characteristics of CNTRC doubly curved panels resting on Pasternak elastic foundations. The present solutions also highlight the effects of CNT volume fraction, temperature variation, foundation stiffness, panel curvature ratio as well as in-plane boundary conditions on the nonlinear free vibration behaviors of CNTRC doubly curved panels.

Nonlinear stability of thin FGM annular spherical segment in thermal environment

The nonlinear stability of functionally graded material (FGM) annular spherical segment resting on elastic foundations in thermal environment is studied analytically. Based on the classical thin shell theory, the governing equations are derived. Approximate solutions are assumed to satisfy the simply supported boundary condition and Galerkin method is applied to obtain closed-form relations of bifurcation type of buckling and post-buckling loads. In the present research an analysis is carried out to show the effects of material, geometrical properties, elastic foundations and combination of external pressure and temperature on the nonlinear stability of the shell.

Nonlinear vibration of FGM doubly curved panels resting on elastic foundations in thermal environments

A large amplitude vibration analysis is presented for a shear deformable doubly curved panel made of functionally graded materials (FGMs) resting on elastic foundations in thermal environments. The effective material properties are evaluated using the 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 temperature-dependent material properties of FGMs are assumed to be graded in the thickness direction according to a simple power law distribution. The motion equations are solved by a two-step perturbation approach to determine the nonlinear frequencies of the FGM doubly curved panel. The numerical illustrations cover small- and large-amplitude vibration characteristics of FGM doubly curved panels resting on elastic foundations of Pasternak-type. The results obtained from the Mori–Tanaka model are compared with those obtained from the Voigt model. The results confirm that in most cases Voigt model and Mori–Tanaka model have the same accuracy for predicting the vibration characteristics of FGM doubly curved panels. The effects of volume fraction index, temperature variation, foundation stiffness and panel curvature ratio on the nonlinear free vibration behaviors of FGM doubly curved panels are also discussed in detail.

Nonlinear bending and postbuckling analysis of matrix cracked hybrid laminated plates containing carbon nanotube reinforced composite layers in thermal environments

The nonlinear bending and postbuckling behaviors of a hybrid laminated plate resting on a Pasternak elastic foundation in thermal environments are investigated in this paper. The plate is composed of conventional fiber reinforced composite (FRC) layers and carbon nanotube reinforced composite (CNTRC) layers. The CNTRC layer consists of reinforcing carbon nanotubes either uniformly distributed (UD) or functionally graded (FG) along the thickness direction. Transverse matrix cracking is introduced in the FRC and UD CNTRC layers and modeled by a refined self-consistent method. The governing equations of the plate are based on a higher order shear deformation plate theory with a von Kármán-type of kinematic nonlinearity and solved by a two-step perturbation technique. The plate-foundation interaction and thermal effects are also included. The material properties of both CNTRC and FRC layers are assumed to be temperature-dependent and are estimated by a micro-mechanical model. A parametric study is conducted to investigate the effects of matrix crack density, foundation stiffness, temperature rise and in-plane boundary conditions on the nonlinear bending and postbuckling behaviors of antisymmetric hybrid laminated plates containing CNTRC layers.

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 vibration of functionally graded fiber reinforced composite laminated beams with piezoelectric fiber reinforced composite actuators in thermal environments

A large amplitude flexural vibration of a hybrid laminated beam resting on an elastic foundation in thermal environments is investigated. The hybrid laminated beam is consists of fiber reinforced composite (FRC) layers and piezoelectric fiber reinforced composite (PFRC) actuators. The fiber reinforcements are assumed to be distributed either uniformly (UD) or functionally graded (FG) of piece-wise type along the thickness of the beam. The motion equations are based on a higher order shear deformation theory and von Kármán strain displacement relationships. The beam-foundation interaction and thermo-piezoelectric effects are also included. The material properties of both FRCs and PFRCs are estimated through a micromechanical model and are assumed to be temperature dependent. A two-step perturbation approach is employed to determine the nonlinear to linear frequency ratios of hybrid laminated beams. Detailed parametric studies are carried out to investigate effects of material property gradient, temperature variation, applied voltage, stacking sequence as well as the foundation stiffness on the linear and nonlinear vibration characteristics of the hybrid laminated beams.

Nonlinear vibration of matrix cracked laminated beams containing carbon nanotube reinforced composite layers in thermal environments

This paper investigates the large amplitude vibration behavior of a matrix cracked laminated beam which contains carbon nanotube reinforced composite (CNTRC) layers resting on an elastic foundation in thermal environments. The motion equations are based on a refined shear-lag model and Euler–Bernoulli beam theory and solved by means of a two-step perturbation approach. The beam-foundation interaction and thermal effects are also included. The material properties of both fiber reinforced composite layers and CNTRC layers are assumed to be temperature-dependent. The effects of the crack density, CNT volume fraction, temperature variation, foundation stiffness, as well as the beam end conditions on the vibration characteristics of hybrid laminated beams with multiple matrix cracks are discussed in detail. Numerical results reveal that the crack density plays an important role in the linear vibration of the hybrid laminated beam, but the effect of crack density is less pronounced on the nonlinear to linear frequency ratios of the same beam.

Nonlinear buckling of higher deformable S-FGM thick circular cylindrical shells with metal–ceramic–metal layers surrounded on elastic foundations in thermal environment

An analytical approach on the nonlinear response of thick functionally graded circular cylindrical shells with temperature independent material property surrounded on elastic foundations subjected to mechanical and thermal loads is presented. Material properties are graded in the thickness direction according to a Sigmoid power law distribution in terms of the volume fractions of constituents (S-FGM). The formulations are based on the third order shear deformation shell theory taking into account von Karman nonlinearity, initial geometrical imperfection and Pasternak type elastic foundation. By applying Galerkin method and using stress function, explicit relations of thermal load–deflection curves of the S-FGM shells are determined. Detailed parametric studies are carried out to investigate effects of volume fraction index, material properties and geometrical shapes, axial compressions and thermal load, foundation stiffness and imperfection on nonlinear buckling behaviors of S-FGM thick circular cylindrical shells. The present analysis is validated by comparing results with other publications.

Nonlinear torsional buckling and postbuckling of eccentrically stiffened FGM cylindrical shells in thermal environment

The main aim of this paper is to investigate the nonlinear buckling and post-buckling of functionally graded stiffened thin circular cylindrical shells surrounded by elastic foundations in thermal environments and under torsional load by analytical approach. Shells are reinforced by closely spaced rings and stringers in which material properties of shell and the stiffeners are assumed to be continuously graded in the thickness direction. The elastic medium is assumed as two-parameter elastic foundation model proposed by Pasternak. Based on the classical shell theory with von Karman geometrical nonlinearity and smeared stiffeners technique, the governing equations are derived. Using Galerkin method with three-term solution of deflection, the closed form to find critical torsional load and post-buckling load–deflection curves are obtained. The effects of temperature, stiffener, foundation, material and dimensional parameters are analyzed.

Nonlinear bending of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments

Nonlinear bending analysis is presented for nanocomposite cylindrical panels subjected to a transverse uniform or sinusoidal load resting on elastic foundations in thermal environments. Carbon nanotubes are used to reinforce the cylindrical panels in two distinguished patterns, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements. The material properties of CNTRCs are assumed to be temperature-dependent and are estimated by a micromechanical model. The governing equations of the panel are derived based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity and are solved by a two-step perturbation technique. The nonlinear bending behaviors of the CNTRC panels with different CNT volume fraction distributions, foundation stiffnesses, temperature rise, and the character of in-plane boundary conditions are studied in details.