Elastic Foundations In Thermal Environments Research Articles

Dynamic response of sandwich functionally graded nanoplate under thermal environments and elastic foundations using dynamic stiffness method

The present paper introduces the development of dynamic stiffness method for analyzing small-scale sandwich functionally graded nanoplates resting on elastic foundation in thermal environments. The mathematical formulation is based on classical plate theory in conjunction with nonlocal elasticity theory. The governing equation is derived using Hamilton’s principle. The dynamic stiffness matrix is obtained through the application of the Levy displacement approach and assembled to form the global stiffness matrix. The final matrix is solved for natural frequency of the plates using the Wittrick–Williams algorithm. The proposed methodology is validated against existing literature, demonstrating a strong agreement. Various parametric studies explore the effects of thermal environments, volume fraction index, sandwich configurations, elastic foundation characteristics, nonlocal parameter and boundary conditions. The results show the versatility of the proposed approach in addressing small scaled complex engineering structures. This research significantly contributes to the understanding and analysis of sandwich functionally graded nanoplates, providing valuable insights for applications in aerospace, structural systems, sensors, actuators, and energy harvesting devices.

EFG meshless-ANN approach for free vibration analysis of functionally graded material plates on elastic foundation in thermal environments

This study focuses on free vibration analysis of functionally graded material (FGM) plates supported by Winkler–Pasternak elastic foundation in thermal environment using element-free Galerkin (EFG) meshless method. Plate kinematics depend on first-order shear deformation theory. Uniform, linear, and nonlinear temperature variations through the thickness direction are considered, along with the temperature-dependent material properties. The numerical outcomes obtained from EFG method are compared with those available in the published literature to validate the proposed method’s accuracy. An artificial neural network (ANN) model that can easily predict the natural frequencies of the plate is constructed from the EFG method outcomes. Further, the effect of foundation parameters, power law index, thickness ratio, temperature variations, and different boundary conditions are investigated; results show that these significantly influence the vibration response of FGM plates supported by the elastic foundation. Increasing the temperature of FGM plates supported by the Winkler–Pasternack foundation causes a decrease in the dimensionless fundamental natural frequency, and the uniform temperature influence is greater than that of linear and nonlinear temperature variation. The proposed EFG-ANN prediction model saves approximately 98.80% computation time when predicting the natural frequency with an accuracy of approximately 98.76% compared to that by EFG meshless method alone.

Analyzing the nonlinear torsional buckling and post-buckling of ES-FG porous cylindrical shells in thermal environment using FSDT in terms of the displacement components

The main aim of this paper is to investigate the nonlinear buckling and post-buckling of eccentrically stiffened sandwich functionally graded porous (FGP) cylindrical shells surrounded by elastic foundations in thermal environments and under torsional load by analytical approach in terms of the displacement components. The shells are reinforced by eccentric rings and stringers attached to the inside and material properties of face sheets and stiffeners are assumed to be continuously graded in the thickness direction. The sandwich cylindrical shell is composed of FG porous core and two FG layer coating. Based on the first order shear deformation theory (FSDT) with von Kármán geometrical nonlinearity and smeared stiffeners technique, the governing equations are derived. Using Galerkin method, the closed form to find critical torsional load and post-buckling load-deflection curves are obtained. The effects of porosity parameters, the thickness of the porous core, temperature, stiffener, foundation, material and dimensional parameters are analyzed.

Nonlinear Vibration of Saturated Porous Functionally Graded Plate in Thermal Environment

In this work we studied investigates the nonlinear vibrations of a rectangular saturated porous functionally graded (FG) plate on elastic foundations in thermal environment. The mechanical properties of the saturated porous material vary smoothly with the thickness in three different distributions of porosity including uniform, symmetrically irregular, and asymmetrically irregular. The basic equations are employed by the Reddy’s higher order shear deformation theory, incorporating the geometrically nonlinear von Kármán strain-displacement relationship, stress-strain relations based on the elastic theory for porous materials by Biot, and an analytical solution obtained through the Galerkin method and Airy’s stress function for the simply supported plate. The influence of the geometrical and material parameters, elastic foundations and temperature increment on the nonlinear vibrations of the saturated porous FG plate were specifically evaluated through numerical investigations. 
 
 

Thermal effects on nonlinear vibration of nonlocal nanobeam embedded in nonlinear elastic medium

Nanotechnology has an impact on our lives in a many ways, from better medical treatments and more efficient energy sources to stronger and lighter materials and advanced electronics and this article presents the implementation of a perturbation method for the vibration analysis of simply supported and clamped–clamped Euler–Bernoulli nanobeams resting on nonlinear elastic foundations in thermal environment using nonlocal elasticity theory. Hamilton's principle is used to construct the differential equation of motion of a nanobeam in conjunction with appropriate boundary conditions. The equations of motion of the Euler–Bernoulli nanobeam are determined using nonlocal elasticity theory. It is shown how thermal loadings affect the vibration of the Euler–Bernoulli nanobeam. The multiple scale method, which is one of the perturbation method, is used to get an approximated solution for the presented system. The effects of temperature, Winkler, Pasternak and nonlinear foundation parameters on the vibration analysis of simply supported and clamped–clamped nanobeams are determined and results are given in tables and graphs.

Natural frequency analysis of sandwich plate with auxetic honeycomb core and CNTRC face sheets using analytical approach and artificial neural network

In this paper, an analytical investigation is presented on the natural frequency analysis of sandwich plate resting on Winkler-Pasternak type elastic foundations in thermal environment. The sandwich plate consists of an auxetic honeycomb core with negative Poisson's ratio, which is assumed to perfectly bond to two carbon nanotube reinforced composite (CNTRC) face sheets to ignore potential interface effects or imperfections in bonding. The material properties of CNTRC are assumed to be temperature dependent. The volume fraction of carbon nanotube (CNT) varies through the thickness dimension according to linear functions with five different distribution patterns of CNT including UD, FG-O, FG-V, FG-Λ and FG-X. The governing equations of motion are derived based on the Reddy's first order shear deformation plate theory and Hamilton's principle, and the expression of the natural frequency is performed via Galerkin method. Artificial neural network (ANN) model is established to accurately predict the natural frequency of the sandwich plate on the basis of 1450 data points collected from analytical results. The effects of various material and geometrical parameters on the natural frequency of the sandwich plate are investigated in details.

Nonlinear static analysis of bi-directional functionally graded sandwich plates in thermal environments by a higher-order finite element model

This study addresses nonlinear static behaviours of bi-directional functionally graded (2D-FGM) sandwich plates lying on an elastic foundation in thermal environments for the first time. The plates comprise two 2D-FGM face sheets and a homogeneous core layer. The material properties of the face sheets change according to the power law in both the longitudinal and thickness directions. Furthermore, the material properties also possess temperature-dependent characteristics in the thermal environment. For the analysis purpose, a higher-order finite element model (FEM) based on Shi’s plate theory that takes into account the geometrically nonlinear von Kármán without regard to material nonlinearity is established. The minimum potential energy principle is used to establish the weak form of governing equations. The four-node rectangular element with the Lagrange and Hermitian interpolation functions is used to discretize the domain of the plate. The nonlinear equilibrium equations are solved by employing Newton–Raphson iterative procedure. The numerical examples comparing the obtained results with the published results in open literature have confirmed the accuracy and convergence of the proposed model. Finally, a few novel parametric studies are conducted to show the effects of the material properties, geometric parameters, temperature, elastic foundation stiffness, and boundary conditions on the nonlinear static behaviours of the 2D-FGM sandwich plates.

Re-examination of nonlinear vibration and nonlinear bending of porous sandwich cylindrical panels reinforced by graphene platelets

Abstract This article re-examines the nonlinear vibration and nonlinear bending responses of porous sandwich cylindrical panels reinforced by graphene platelets resting on elastic foundations in thermal environments. The graphene platelet-reinforced composite (GPLRC) core is assumed to be of multilayers, and each layer may have different porosity coefficient values to achieve a piece-wise functionally graded pattern. By introducing an inhomogeneous model instead of the equivalent isotropic model (EIM), the Young’s moduli along with the shear modulus of the porous GPLRC core are predicted through a generic Halpin–Tsai model in which the porosity is included. The thermomechanical properties of metal face sheets and the porous GPLRC core are assumed to be temperature-dependent. Governing equations of motion for sandwich cylindrical panels with porous GPLRC core are formulated based on Reddy’s third-order shear deformation theory coupled with von Kármán nonlinear strain–displacement relationships. In the modeling, the panel–foundation interaction and the thermal effects are also considered. The analytical solutions for the nonlinear vibration and nonlinear bending problems are obtained by applying a two-step perturbation approach. Numerical studies are performed to compare the results obtained from the present model and the EIM. The results confirm that the EIM is not suitable for linear free vibration analysis of sandwich cylindrical panels with the porous GPLRC core, but the EIM may be valid for the cases of nonlinear vibration and nonlinear bending analyses of the same panel resting on Pasternak elastic foundations.

Snap-buckling and resonance of functionally graded graphene reinforced composites curved beams resting on elastic foundations in thermal environment

This article pays attention to the snap-buckling and resonance behaviors of functionally graded graphene platelets reinforced composites (FG-GPLRCs) curved beams resting on the elastic foundations in a thermal environment. The material properties of the FG-GPLRCs curved beams with immovable clamped-clamped ends are temperature-independent. Considering the influence of von-Kármán nonlinearity, the Euler-Bernoulli beam theory is applied to derive the motion equations. The approximate solutions of nonlinear vibration and snap-through buckling responses of the curved beams under harmonic forces are found with the help of the two-step perturbation method and the modified Lindstedt–Poincaré method. The influences of different parameters including temperature variations, the elastic foundations, the graphene platelets (GPLs) distribution, the weight fraction of GPLs, the number of GPLs layers and the radius of curvature of the curved beams on nonlinear resonance and snap-buckling behaviors are investigated.

Nonlinear Static Stability of Stiffened Nanocomposite Plate s Subjected Various Types of Loads

This work deals with the nonlinear buckling and post-buckling of stiffened nanocomposite plates reinforced functionally graded carbon nanotubes (FG CNTRC) resting on elastic foundation in thermal environment. Obtained results showed that the properties of the nanocomposited plates embedded with single-walled carbon nanotubes are dependent on temperature and altered according to linear functions of the thickness. The governing equations are derived by the third-order shear deformation plate theory taking into account von Kármàn geometrical nonlinearity and solved by both the Airy’s stress function and Galerkin method. In numerical results, the influences of various types of distribution and volume fractions of carbon nanotubes, geometrical parameters, elastic foundations on the nonlinear buckling and post-buckling behaviour of stiffened FG-CNTC plates subjected mechanical, thermal loading and both are demonstrated.
 Keywords: Stiffened FG CNTRC plates; Buckling and Post buckling analysis; Third-order shear deformation theory; Thermal environment; Galerkin method
 This work deals with the nonlinear buckling and post-buckling of stiffened nanocomposite plates reinforced functionally graded carbon nanotubes (FG CNTRC) resting on elastic foundation in thermal environment. Obtained results showed that the properties of the nanocomposited plates embedded with single-walled carbon nanotubes are dependent on temperature and altered according to linear functions of the thickness. The governing equations are derived by the third-order shear deformation plate theory taking into account von Kármàn geometrical nonlinearity and solved by both the Airy’s stress function and Galerkin method. In numerical results, the influences of various types of distribution and volume fractions of carbon nanotubes, geometrical parameters, elastic foundations on the nonlinear buckling and post-buckling behaviour of stiffened FG-CNTC plates subjected mechanical, thermal loading and both are demonstrated.

A semi-analytical solution for dynamic stability analysis of nanocomposite/fibre-reinforced doubly-curved panels resting on the elastic foundation in thermal environment

A semi-analytical solution for dynamic stability analysis of nanocomposite/fibre-reinforced doubly-curved panels resting on the elastic foundation in thermal environment

An analytical approach to geometrically nonlinear free and forced vibration of piezoelectric functional gradient beams resting on elastic foundations in thermal environments

In this article, the geometrically nonlinear free and forced vibrations of a beam made of functional gradient materials are analytically analyzed, in which piezoelectric actuators are bound. Based on the Euler–Bernoulli beam theory and the nonlinear Von-Karman deformation field, the analytical solutions of the nonlinear free vibrations, and forced vibrations of a beam with two clamped ends and resting on an elastic foundation are predicted. Using Hamilton's principle and an approximate multimodal dominant mode method, the nonlinear governing equations are obtained. Due to the lack of forced vibration results of the functionally graded piezoelectric beam subjected to thermal loading and resting on elastic foundations, the results obtained by the current solution were compared with their counterparts. The good agreement between the current solution and equivalent data existing in the open literature proves the efficiency and accuracy of the current resolution analysis method. Finally, the new parametric studies covered in this research include the effects of several parameters such as elastic foundation, thermal loading, and thermal properties of constituent materials on the free and forced nonlinear vibration of the piezoelectric functional gradient beam.

Free vibration and dynamic transient response of functionally graded composite beams reinforced with graphene nanoplatelets (GPLs) resting on elastic foundation in thermal environment

In this article, free vibration and dynamic transient response of a multilayer polymer nanocomposite beam resting on elastic foundation reinforced by graphene platelets (GPLs) non-uniformly distributed through the thickness direction in thermal environment is investigated. Theoretical formulations are derived based on Hamilton’s principle, Timoshenko beam theory relationships. The effective Young’s modulus of the GPL/polymer composite is estimated by Halpin–Tsai micromechanics model to account for the effects of GPL geometry and dimensions. The vibration frequencies of the beam are obtained numerically by generalized differential quadrature method (GDQM). The influences of the distribution pattern, weight fraction, the number of layers, thermal environment, slenderness ratio of the beam, boundary conditions, and types of elastic foundations on the free vibration behavior and transient response are presented. The results show that adding a very small amount of GPLs into polymer matrix as reinforcements together with the elastic foundation, significantly increases the natural frequencies of the beam. Placing more GPLs near the top and bottom surfaces of the beam are the most effective ways to strengthen the beam stiffness and increase the natural frequencies. Besides, with the increasing of foundation’s stiffness, the displacement amplitude of the functionally graded composite beam reinforced by GPLs subjected to impulsive load decreases.

Impact of blast and mechanical loads on the shear deformable stiffened sandwich plate with an auxetic core layer in thermal environment

By using the first order shear deformation theory (FSTD), this paper presents the results of the nonlinear dynamic behavior and natural frequencies of sandwich plate supported by elastic foundations in thermal environment and subjected to mechanical load and blast loading. This work takes advantage of the sandwich plate configuration with three layers: graphene platelet –reinforced composite (GPL) layer – auxetic layer – FGM layer, to analyze the dynamic and vibration problem, in which the auxetic core layer has a negative Poisson's ratios and the FGM layer is reinforced by stiffeners made of full metal or full ceramic depending on a situation of stiffeners at the metal-rich or ceramic-rich side of the plate respectively. Corresponding to the combination of material layers, the mechanical quantities of the problem are processed and calculated to suit the structure and reinforcement conditions. Numerical results are provided to explore the influences of geometrical parameters, elastic foundation parameters, GPL volume fraction, blast and mechanical loads on the nonlinear dynamic behavior and vibration of sandwich plate resting on elastic foundation and in thermal environment. In addition, the study is not only assumed that the material properties depend on environment temperature variation, but also considered the thermal stresses in the stiffeners, as well as considered the effect of imperfections in the original shape of the structure.

Vibration response of a geometrically discontinuous bi-directional functionally graded plate resting on elastic foundations in thermal environment with initial imperfections

The present study includes the free vibration analysis of geometrically imperfect and discontinuous porous functionally graded bi-directional plate (B-FGP) resting on an elastic foundation in a thermal environment. The geometric discontinuity is present in the form of a circular cutout at the center of the plate whereas initial imperfections have been incorporated in terms of geometric as well as porosity inclusions. The kinematic formulation is based on the refined non-polynomial trigonometric higher-order shear deformation theory (HSDT). A new porosity model has been developed to incorporate the influence of the microstructure defect on the effective material properties of the B-FGP. The gradation of properties is done along the thickness (z-direction) as well as the length (x-direction) of the plate using the power-law distribution. A new expression has been given to obtain the solution of the non-linear temperature rise along the thickness of the B-FGP. A continuous Lagrangian four-noded quadrilateral element has been used to perform the finite element formulation with eight degrees of freedom per node. The equations of motion have been derived using a variational approach. The validation and comparative study have been done to authenticate the present formulation. The influence of the cutout radius, elastic foundation parameters, porosity, thermal environment, geometric imperfection, and volume fraction indexes has been discussed in detail.

Influence of magnetic field on the wave propagation response of functionally graded (FG) beam lying on elastic foundation in thermal environment

In the current work, wave propagation in simply supported (S-S) functionally graded (FG) beam is investigated while the beam is exposed to magneto-thermal environments and embedded on two-parameter elastic foundation. The mechanical properties of the structure are supposed to vary through the thickness via the exponential and power law function. The governing equations of the motion are derived by implementing Hamilton’s principle on the basis of refined higher order beam theory which can capture the shear deformation effect. Two novel metal and ceramic with interesting properties named Osmium and Silicon Carbide (SiC) are used as materials of this structure. The thermal loadings are applied to the structure with various temperature changes namely uniform, linear and sinusoidal, through the thickness. Influences of the wide range of parameters such as magnetic field intensity, slenderness ratio, various thermal loadings, exponential- and power-law exponents and elastic foundation coefficient on the wave frequency and phase velocity of the FG beam have been illustrated comparatively and the results are thoroughly discussed to obtain the highlights of each figure.

New Finite Modeling of Free and Forced Vibration Responses of Piezoelectric FG Plates Resting on Elastic Foundations in Thermal Environments

This paper carries out free and forced vibration analysis of piezoelectric FGM plates resting on two-parameter elastic foundations placed in thermal environments. By employing the third-order shear deformation theory and the finite element method, this work establishes free and forced vibration equations of piezoelectric FGM plates, where the materials are assumed to be varied in the thickness directions, and the mechanical properties depend on the temperature. Then, comparative examples are conducted to verify the proposed theory and mathematical model, and the results of this study and other methods meet a very good agreement. Then, effects of geometrical and material properties such as the feedback coefficient, voltage, volume fraction index, temperature as well as the parameters of elastic foundations on free and forced vibration of the plates are investigated, and the conclusions are given out to provide the effective direction for the design and practical use of these structures.

Effect of negative poisson's ratio on the axially compressed postbuckling behavior of FG-GRMMC laminated cylindrical panels on elastic foundations

Auxetic materials are one of the metamaterials that have potential applications in many scientific and engineering fields. In this paper, an investigation is presented on the postbuckling responses of axially loaded graphenereinforced metal matrix composite (GRMMC) laminated cylindrical panels with in-plane negative Poisson's ratio (NPR). The panels are made of GRMMC laminates and rest on an elastic foundation in thermal environments. The graphene volume fraction in GRMMC layer may vary across the panel thickness in order to achieve a piece-wise functionally graded (FG) pattern. The GRMMC layers have in-plane NPR and temperature dependent material properties. The governing differential equations for the GRMMC laminated cylindrical panels are formulated based on the Reddy's third order shear deformation shell theory and are solved by using a singular perturbation technique along with a two-step perturbation approach. Numerical investigation is carried out to study the influence of the in-plane NPR, the FG patterns, the thermal environmental conditions and the foundation stiffness on the postbuckling responses of the GRMMC laminated cylindrical panels under axial compressive load. The results reveal that the in-plane NPR can lead to a substantial change of the postbuckling behaviors of the GRMMC laminated cylindrical panels.

Nonlinear bending analysis of size-dependent FG porous microtubes in thermal environment based on modified couple stress theory

This study deals with the nonlinear bending analysis of elastic tubes made of functionally graded (FG) porous material based on modified couple stress theory. Immovable simply supported and clamped boundary conditions are assumed for the FG porous microtubes resting on nonlinear elastic foundation. Transverse pressure load is applied uniformly on the upper surface of the microtube which is exposed to uniform temperature field. Temperature-dependent material properties of the microtube with uniformly distributed porosity are graded across the radius of the cross-section. The higher-order shear deformation theory of circular beams is presented to approximate the displacement field. The von Kármán type of kinematic assumptions is utilized for nonlinear strain-displacement relations. The uncoupled thermoelasticity theory is used to derive the constitutive equations. With the establishment of the virtual displacement principle, nonlinear differential equations governing the equilibrium position of the microtube are extracted. These equilibrium equations are analytically solved by means of the two-step perturbation technique and Galerkin procedure. Parametric investigations are performed to demonstrate the size-dependent nonlinear bending responses of an FG porous microtube on nonlinear elastic foundation in thermal environment.

Postbuckling Behavior of Functionally Graded Multilayer Graphene Nanocomposite Plate under Mechanical and Thermal Loads on Elastic Foundations

This paper presents an analytical approach to postbuckling behaviors of functionally graded multilayer nanocomposite plates reinforced by a low content of graphene platelets (GPLs) using the first order shear deformation theory, stress function and von Karman-type nonlinear kinematics and include the effect of an initial geometric imperfection. The weight fraction of GPL nano fillers is assumed to be constant in each individual GPL-reinforced composite (GPLRC). The modified Halpin-Tsai micromechanics model that takes into account the GPL geometry effect is adopted to estimate the effective Young’s modulus of GPLRC layers. The plate is assumed to resting on Pasternak foundation model and subjected to mechanical and thermal loads. The results show the influences of the GPL distribution pattern, weight fraction, geometry, elastic foundations, mechanical and temperature loads on the postbuckling behaviors of FG multilayer GPLRC plates.
 Keywords: Postbuckling; Graphene nanocomposite plate; First order shear deformation plate theory.
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