Elastic Foundations In Thermal Environments Research Articles

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.

Postbuckling of axially compressed nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments

This paper presents a postbuckling analysis of carbon nanotube-reinforced composite (CNTRC) cylindrical panels resting on elastic foundations and subjected to axial compression in thermal environments. The cylindrical panels are reinforced by aligned single-walled carbon nanotubes (SWCNTs) which are assumed to be functionally graded (FG) through the thickness direction with different types of distributions. The material properties of FG-CNTRC panels are estimated through an extended rule of mixture micromechanical model. The governing equations are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity. The panel–foundation interaction and thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. A singular perturbation technique along with a two-step perturbation approach is employed to determine the buckling loads and postbuckling equilibrium paths. Numerical results reveal that the CNT volume fraction, temperature rise, foundation stiffness, and the panel geometric parameters have a significant effect on the buckling load and postbuckling behavior of CNTRC cylindrical panels. The results for uniformly distributed (UD) CNTRC cylindrical panels are compared with those of FG-CNTRC cylindrical panels. The results also confirm that for an CNTRC cylindrical panel with immovable unloaded straight edges, the postbuckling path of the panel is no longer the bifurcation type.

Nonlinear bending of FGM cylindrical panels resting on elastic foundations in thermal environments

Abstract A nonlinear bending analysis is presented for a simply supported, functionally graded cylindrical panel resting on an elastic foundation in thermal environments. The panel is exposed to elevated temperature and is subjected to a transverse uniform or sinusoidal load. Material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent, and graded in the thickness direction based on Mori-Tanaka micromechanics model. The formulations are based on a higher order shear deformation shell theory with a von Karman-type of kinematic nonlinearity and include shell panel–foundation interaction and the thermal effects. A two-step perturbation technique is employed to determine the load-deflection and load-bending moment curves. The numerical illustrations concern nonlinear bending response of FGM cylindrical panels with two constituent materials resting on Pasternak elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The effects of the volume fraction index, temperature variation, foundation stiffness as well as the character of in-plane boundary conditions are also examined.

Nonlinear analysis of shear deformable FGM beams resting on elastic foundations in thermal environments

Abstract This paper deals with the large amplitude vibration, nonlinear bending and thermal postbuckling of functionally graded material (FGM) beams resting on an elastic foundation in thermal environments. Two kinds of micromechanics models, namely, Voigt model and Mori-Tanaka model, are considered. The motion equations are based on a higher order shear deformation beam theory that includes beam–foundation interaction. The thermal effects are also included and the material properties of FGMs are assumed to be temperature-dependent. The numerical illustrations concern the nonlinear vibration, nonlinear bending and thermal postbuckling of FGM beams resting on Pasternak elastic foundations under different thermal environmental conditions. It is found that the FGM beam with intermediate material properties does not necessarily have intermediate nonlinear frequencies. The thermal postbuckling path of simply supported FGM beams is no longer of the bifurcation type for both uniform and non-uniform temperature fields.

Nonlinear buckling of imperfect eccentrically stiffened metal–ceramic–metal S-FGM thin circular cylindrical shells with temperature-dependent properties in thermal environments

Abstract In this paper, an analytical approach is presented to investigate the nonlinear static buckling for imperfect eccentrically stiffened functionally graded thin circular cylindrical shells with temperature-dependent properties surrounded on elastic foundation in thermal environment. Both shells and stiffeners are deformed simultaneously due to temperature. 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) with metal–ceramic–metal layers. The Lekhnitsky smeared stiffeners technique with Pasternak type elastic foundation, stress function and the Bubnov–Galerkin method are applied. Numerical results are given for evaluating effects of temperature, material and geometrical properties, elastic foundations and eccentrically outside stiffeners on the buckling and post-buckling of the S-FGM shells. The obtained results are validated by comparing with those in the literature.

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

This paper investigates the large amplitude vibration behavior of nanocomposite cylindrical panels resting on elastic foundations in thermal environments. Two kinds of carbon nanotube-reinforced composite (CNTRC) panels, namely, uniformly distributed and functionally graded reinforcements, are considered. The material properties of FG-CNTRC panels are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The motion equations are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity. The panel-foundation interaction and thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. The equations of motion are solved by a two-step perturbation technique to determine the nonlinear frequencies of the CNTRC panels. Numerical results demonstrate that the natural frequencies of the CNTRC panels are reduced but the nonlinear to linear frequency ratios of the CNTRC panels are increased as the temperature rises. In contrast, natural frequencies are increased but the nonlinear to linear frequency ratios are decreased by increasing the foundation stiffness. The results reveal that the natural frequencies are increased by increasing the CNT volume fraction, whereas the CNTRC panels with intermediate CNT volume fraction do not necessarily have intermediate nonlinear to linear frequency ratios.

Nonlinear vibration of shear deformable FGM cylindrical panels resting on elastic foundations in thermal environments

This paper investigates the large amplitude vibration behavior of a shear deformable FGM cylindrical panel resting on elastic foundations in thermal environments. Two kinds of micromechanics models, namely, Voigt model and Mori–Tanaka model, are considered. The motion equations are based on a higher order shear deformation shell theory that includes shell panel-foundation interaction. The thermal effects are also included and the material properties of FGMs are assumed to be temperature-dependent. The equations of motion are solved by a two step perturbation technique to determine the nonlinear frequencies of the FGM cylindrical panel. Detailed parametric studies are carried out to investigate effects of volume fraction index, temperature variation, panel curvature ratio, foundation stiffness and in-plane boundary conditions on nonlinear vibration behaviors of FGM cylindrical panels. The results confirm that in most cases Voigt model and Mori–Tanaka model have the same accuracy for predicting the vibration characteristics of FGM cylindrical panels.

Nonlinear postbuckling of an eccentrically stiffened thin FGM plate resting on elastic foundations in thermal environments

This paper first time presents an analytical investigation on the nonlinear postbuckling of imperfect eccentrically stiffened thin FGM plates under temperature and resting on elastic foundation using a simple power-law distribution (P-FGM). Both of the FGM plate and stiffeners are deformed under thermal loads. The formulations are based on the classical plate theory taking into account geometrical nonlinearity, initial geometrical imperfection, temperature-dependent properties and the Lekhnitsky smeared stiffeners technique with Pasternak type elastic foundation. By applying Galerkin method and using stress function, effects of material and geometrical properties, temperature, elastic foundation and eccentrically stiffeners on the buckling and postbuckling loading capacity of the eccentrically stiffened FGM plate in thermal environments are analyzed and discussed. Some results were compared with the one of the other authors.

Nonlinear postbuckling of imperfect eccentrically stiffened P-FGM double curved thin shallow shells on elastic foundations in thermal environments

This paper first time presents an analytical investigation on the nonlinear postbuckling for imperfect eccentrically stiffened FGM double curved thin shallow shells on elastic foundation using a simple power-law distribution (P-FGM) in thermal environments. The formulations are based on the classical shell theory taking into account geometrical nonlinearity, initial geometrical imperfection, temperature-dependent properties and the Lekhnitsky smeared stiffeners technique with Pasternak type elastic foundation. By applying Galerkin method and using stress function, explicit relations of thermal load–deflection curves for simply supported curved eccentrically stiffened FGM shells are determined. Effects of material and geometrical properties, temperature, elastic foundation and eccentrically stiffeners on the buckling and postbuckling loading capacity of the imperfect eccentrically stiffened P-FGM double curved shallow shells in thermal environments are analyzed and discussed.

Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments

This paper studies the behaviors of large amplitude vibration, nonlinear bending and thermal postbuckling of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) resting on an elastic foundation in thermal environments. Two types of carbon nanotube-reinforced composite (CNTRC) beams, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The material properties of FG-CNTRCs are assumed to be graded in the beam thickness direction, and are estimated through a micromechanical model. The motion equations of a CNTRC beam on an elastic foundation are derived based on a higher order shear deformation beam theory. The thermal effects are also included in the motion equations and the material properties of CNTRCs are assumed to be temperature-dependent. Numerical studies are carried out for the nonlinear vibration, nonlinear bending and thermal postbuckling of CNTRC beams resting on Pasternak elastic foundations under different thermal environmental conditions. It is found that a CNTRC beam with intermediate CNT volume fraction does not necessarily have intermediate nonlinear frequencies, buckling temperatures and thermal postbuckling strengths. Thermal postbuckling path of unsymmetric FG-CNTRC beams is no longer the bifurcation type.

Nonlinear dynamic response of sandwich plates with FGM face sheets resting on elastic foundations in thermal environments

This paper presents an investigation on the nonlinear dynamic response of sandwich plates with FGM face sheets resting on elastic foundations in thermal environments. The material properties of FGM layer are assumed to be graded in the thickness direction according to the Mori–Tanaka scheme. The governing equations of the plate that includes plate–foundation interaction are solved by a two-step perturbation technique. The thermal effects are also included and the material properties of both FGM face sheets and homogeneous core layer are assumed to be temperature-dependent. Two cases of the in-plane boundary conditions are considered. Initial stresses caused by thermal loads or in-plane edge loads are introduced. The numerical illustrations concern the nonlinear dynamic response of sandwich plates resting on Pasternak elastic foundations under different sets of thermal environmental conditions, from which results for single-layer FGM plates are also obtained for comparison purposes. The numerical results show that foundation stiffness and initial stress have a significant effect on the dynamic response of both single-layer and sandwich FGM plates. They also show that the core-to-face sheet thickness ratio has a significant effect on the dynamic response of sandwich FGM plates. The results reveal that the volume fraction distribution of FGM layer has a significant effect on the dynamic response of single-layer FGM plates, whereas this effect is less pronounced for the sandwich plate with FGM face sheets.

Nonlinear stability analysis of double-curved shallow fgm panels on elastic foundations in thermal environments

An analytical investigation into the nonlinear response of thick functionally graded double-curved shallow panels resting on elastic foundations and subjected to thermal and thermomechanical loads is presented. Young’s modulus and Poisson’s ratio are both graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of constituents. All formulations are based on the classical shell theory with account of geometrical nonlinearity and initial geometrical imperfection in the cases of Pasternak-type elastic foundations. By applying the Galerkin method, explicit relations for the thermal load–deflection curves of simply supported curved panels are found. The effects of material and geometrical properties and foundation stiffness on the buckling and postbuckling load-carrying capacity of the panels in thermal environments are analyzed and discussed.

Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments

This paper presents an investigation on the nonlinear dynamic response of carbon nanotube-reinforced composite (CNTRC) plates resting on elastic foundations in thermal environments. Two configurations, i.e., single-layer CNTRC plate and three-layer plate that is composed of a homogeneous core layer and two CNTRC surface sheets, are considered. The single-walled carbon nanotube (SWCNT) reinforcement is either uniformly distributed (UD) or functionally graded (FG) in the thickness direction. The material properties of FG-CNTRC plates are assumed to be graded in the thickness direction, and are estimated through a micromechanical 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 also included and the material properties of CNTRCs are assumed to be temperature-dependent. The equations of motion that includes plate-foundation interaction are solved by a two-step perturbation technique. Two cases of the in-plane boundary conditions are considered. Initial stresses caused by thermal loads or in-plane edge loads are introduced. The effects of material property gradient, the volume fraction distribution, the foundation stiffness, the temperature change, the initial stress, and the core-to-face sheet thickness ratio on the dynamic response of CNTRC plates are discussed in detail through a parametric study.

Assessment of Voigt and Mori–Tanaka models for vibration analysis of functionally graded plates

The small- and large-amplitude vibrations are presented for a functionally graded rectangular plate resting on a two-parameter (Pasternak-type) elastic foundation in thermal environments. Two kinds of micromechanics models, namely, Voigt (V) model and Mori–Tanaka (M–T) model, are considered. The motion equations are based on a higher order shear deformation plate theory that includes plate-foundation interaction. The thermal effects are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent. Two cases of the in-plane boundary conditions are considered. Initial stresses caused by thermal loads or in-plane edge loads are introduced. The accuracy of Voigt and Mori–Tanaka models for the vibration analysis of FGM plates is investigated. The comparison studies reveal that the difference between these two models is much less compared to the difference caused by different solution methodologies and plate theories. The results show that the difference of the fundamental frequencies between M–T and V solutions is very small, and the difference of the nonlinear to linear frequency ratios between M–T and V solutions may be negligible.