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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. [ABSTRACT FROM AUTHOR]

This article presents a size dependent mathematical model and an analytical solution methodology to accurately simulate and analyze the size dependent buckling behavior of piezoelectrically layered sandwich nanobeams with perforated core embedded in an elastic medium with flexoelectricity. The electric enthalpy energy function is expressed in terms of the electric and the flexoelectric effects. Regular squared cutouts perforation pattern is adopted for the perforated core. Closed forms for the equivalent geometrical parameters of perforated core are developed. The shear deformation effect is incroporated using the Timoshenko beam theory (TBT). To capture the nonlocality and the microstructure length scale effects, the nonlocal strain gradient elasticity theory is modified and adopted to include the electromechanical nonclassical effects. The Hamiltonian principle is utilized to derive the equilibrium equations. An analytical solution methodology is developed to derive closed forms for critical buckling loads. The developed solution procedure is implemented into a MATLAB software code. The accuracy of the developed procedure is verified by comparing obtained results with corresponding cases reported in the literature. Influences of different design variables on the electromechanical buckling behavior are explored through intensive parametric studies. Results obtained showed the significant effects of the flexoelectricity and the piezoelectric parameters on the size dependent buckling behavior of piezoelectric sandwich nanobeams with perforated core. Size dependent electromechanical as well as mechanical buckling behaviors could be controlled by adjusting these parameters. The developed procedure and the obtained numerical results are helpful in many technological and industrial applications as MEMS and NEMS. [ABSTRACT FROM AUTHOR]

The present study is focused on the development of an analytical solution for the buckling analysis of carbon nanotube reinforced functionally graded (FG-CNTRC) laminated plates resting on Pasternak elastic foundation and subjected to different nonuniform edge loads. The analytical solution is formulated using a two-step procedure: First, an accurate in-plane stress solution is developed by superimposing three suitable Airy's stress functions; second, the stress solution is utilized to compute the critical buckling loads using the Galerkin's procedure. Results from parametric studies show that the buckling behavior of FG-CNTRC plates greatly depends on the type of nonuniform loads, plate configurations, and support parameters. [ABSTRACT FROM AUTHOR]

In this study, we have introduced, for the first time, a novel integral quasi-3D higher-order shear deformation theory (HSDT) employing a third-order shape function. This approach is employed to analyze the free vibration characteristics of a cracked porous functionally graded material (FGM) beam supported on a three-parameter elastic foundation (Winkler/Pasternak/Kerr). This new Quasi HSDT introduces a stretching effect that surpasses the capabilities of FSDT and other HDST. The employed shape function satisfies the conditions of shear stress nullity at both the higher and lower facets without the need for correction factors. The study incorporates a mathematical model representing Winkler/Pasternak/Kerr foundation types into the Hamiltonian to derive the equations of motion. The FGM beam studied in this paper is assumed to be composed of materials with a distribution that varies according to a power law along its height. Our results are compared with previous studies and we reinforce our findings with a parametric study assessing the impact of crack attributes on the natural frequencies of the FG plate. This study presents an advanced integral quasi-3D HSDT, applied for the first time, to analyze the behavior of FG beams resting on a three-parameter foundation. [ABSTRACT FROM AUTHOR]

In this research, the thermally induced vibration of the plates on the elastic foundation has been investigated. The plate is made of functionally graded materials (FGMs) that is graded along the thickness. All mechanical and thermal properties dependent on temperature are taken into account. To apply the temperature dependence of thermomechanical properties, the well-known Touloukian equation is used. The two-parameter elastic foundation, Winkler–Pasternak, is considered to be linear, isotropic, and homogeneous. The general formulation and equations governing the phenomenon of thermally induced vibration have been written under the assumptions of linear uncouple thermoelasticity. The one-dimensional transient heat conduction equation has been discretized with the help of the finite element method in the direction of thickness, and it has been solved over time by applying the Crank–Nicolson method. Also, the thermally induced force and moment resultants in each time step have been calculated based on the temperature profile. To obtain the equations of motion, Hamilton's principle based on the first-order shear deformation theory has been used, and the obtained equations and boundary conditions have been discretized by applying the generalized differential quadrature (GDQ) method and solved by using Newmark time marching scheme. [ABSTRACT FROM AUTHOR]

The key aim of this research is to develop an analytical model for the forced vibration of graphene-reinforced composite (GRC) cylindrical shell with viscous damping and thermal environment effects under several boundary conditions. The prescribed mechanical and thermal characteristics of the GRC layer are evaluated utilizing a micromechanical extended Halpin–Tsai technique. Further, the governing equations are determined to be grounded on the shear deformation theory (SDT) with the von Kármán-form in terms of the geometric nonlinearity. The basic nonlinear partial differential governing equation is transformed into a nonlinear ordinary differential equation with the Galerkin-based method. The resulting ordinary governing differential equations are systematically solved based on the multiple scales scheme in order to obtain the nonlinear forced vibration frequency response of the laminated GRC cylindrical shell in the presence of damping impact and subjected to multiple boundary conditions. The validation of the obtained expressions is achieved by comparing them with the available literature data where the comparison revealed a clear consistency between them. Moreover, a parametric investigation is provided to illustrate the impacts of the distribution of graphene layers, elastic foundation coefficients, damping ratios, temperature effects and dimensionless radial excitation amplitude on the forced nonlinear amplitude-frequency ratio responses for a functionally-graded graphene-reinforced composite (FG-GRC)-layered cylindrical shells. The analytical outcomes indicate that the different distribution types of graphene, elastic foundation coefficients, damping ratios, temperature, and radial excitation parameters have a noteworthy impact on the frequency–amplitude behaviors of an FG-GRC-layered cylindrical shell. In addition, the new insights gained from this research might contribute to a deeper understanding of the nonlinear forced vibration responses in subsequent analysis and design techniques for giving appropriate benchmark findings. [ABSTRACT FROM AUTHOR]

In this research, natural frequency response of functionally-graded multilayer graphene-reinforced composite plate with circular cutout reinforced by orthogonal stiffeners is investigated for the first time. The structure is surrounded by Winkler-type elastic support. The plate is composed of polymethyl methacrylate (PMMA) as matrix material and reinforced by graphene platelets (GPLs). The material of the orthogonal stiffeners is the same as that for the matrix. Rule of mixtures and Halpin–Tsai approach are applied to estimate the effective material properties of the composite plate. Third-order shear deformation plate theory and finite element procedure is employed to obtain the element matrices of the structure. Natural frequencies and mode shapes of the stiffened plate are reported for different variables such as nanofillers dispersion patterns, width and height of the stiffeners, aspect ratio of plate, plate thickness ratio, weight fraction of nanofillers, number of stiffeners, boundary conditions, elastic foundation stiffness parameter and size of circular cutout. The obtained results denote that with the addition of a set of stiffeners, fundamental frequency enhanced up to 32.3% with just about 10% increase of mass. [ABSTRACT FROM AUTHOR]

This paper presents a novel shear deformation theory for analyzing porous microbeams' bending, buckling, and free vibration resting on a foundation. The proposed shear function incorporating three kinetic variables satisfies zero-traction boundary conditions on the top and bottom surfaces of the beams and does not require a shear correction factor. The modified couple stress theory accounts for the size-dependent effects, and the governing equations are derived from Lagrange's equation using the proposed shear function. Legendre–Ritz functions are developed to analyze the porous microbeams' buckling, free vibration, and bending behaviors. The effects of material length scale parameter, porosity, span-to-height ratio, boundary condition, and foundation parameter on the mechanical responses of beams are investigated. Numerical results demonstrate the accuracy and efficiency of the proposed theory and can serve as benchmarks for future analysis of porous microbeams on elastic foundations. [ABSTRACT FROM AUTHOR]

This article uses the semi-analytical approach to study the combined nonlinear vibration and nonlinear response of a damped porous microplate under nonuniform periodic parametric excitation to understand the complete nonlinear dynamic behavior of the plate. The plate is supported by a Winkler-Pasternak elastic foundation and modeled using modified strain gradient and third-order shear deformation theories to simulate the small-scale effects and shear deformation, respectively. Using Hamilton's principle, the governing partial differential equations of motion are derived and solved using Galerkin's method to convert them into ordinary differential equations (ODEs). These ODEs are solved using a combined incremental harmonic balance (IHB) and arc-length continuation approaches to get the nonlinear vibration (frequency–amplitude curves). The same ODEs are solved using the Newmark-β technique to obtain the nonlinear response (time–amplitude curves). The effect of elastic foundation parameters and aspect ratio on mode shape is presented. The effect of parameters such as the porosity coefficient, type of porosity, Winkler-Pasternak elastic foundation parameters, different size-dependent theories, plate thickness, size of plate, damping coefficient, different loading profiles, and loading concentrations on the nonlinear vibration and nonlinear response is examined. Also, the dependence of initial displacements on the frequency–amplitude curves with respect to the excitation frequency is demonstrated with the help of time-amplitude curves. [ABSTRACT FROM AUTHOR]

In this paper, an analytical solution for exploring the buckling characteristics of functionally graded (FG) plate is presented based on a quasi-3D shear deformation theory. It is considered that the plate is subjected to different types of in-plane compressive load. The FG plate is placed on three-parameter foundation WinklerPasternak-Kerr. The overall material properties of FG plate are assumed to be varied across the thickness and are estimated through the Voigt micromechanical model. The governing equations are obtained on the base of the quasi-3D deformation theory that contain undetermined integral forms and involves only four unknowns to derive. Equations of motion are derived from the principal of virtual work and the analytical solution is used to determine the critical buckling loads. By the discussion of numerical examples and the comparison with those of the reports in the literature, the convergence and the reliability of the present approach are validated. Finally, the parametric investigations of the in-plane buckling are carried out, including the influence of boundary conditions, elastic foundation, plate geometric parameters and power law index. The results reveal that the critical buckling loads are strongly influenced by several parameters such as boundary conditions, elastic foundation parameters and geometric shape of the plate. [ABSTRACT FROM AUTHOR]

The nonlinear vibration response of rectangular plates made of functionally graded porous materials (FGPs) induced by hygrothermal loading is investigated in this article using a numerical approach. The effect of elastic foundation on the vibrations is taken into account according to the Winkler–Pasternak model. Hygroscopic stresses produced due to nonlinear rise in moisture concentration are also considered. The temperature-dependent material properties of plate are computed based on the modified Voigt's rule of mixture and Touloukian experiments for even and uneven distribution patterns of porosity. Within the framework of the first-order shear deformation plate theory and von-Kármán nonlinearity, Hamilton's principle is utilized in order to derive the equations of motions. To achieve the temporal evolution of maximum lateral deflection of hygrothermally-induced plates, the generalized differential quadrature (GDQ) and Newmark integration methods are employed. Selected numerical results are presented to study the influences of temperature distribution, porosity volume fraction, moisture concentration, geometrical parameters, elastic foundation parameters and FG index on the geometrically nonlinear vibrations of FG porous plates with various boundary conditions. [ABSTRACT FROM AUTHOR]

Purpose: This paper proposes a novel shear deformation theory to study the static bending and buckling of nanoplates subjected to flexomagnetic influence. This is done using the revolutionary shear strain theory and establishing finite element formulations based on the finite element technique. Methods: This study uses a finite element method to solve the nanoplate bending and buckling problem while taking into consideration the flexoelectromagnetic effect. Results: The investigation's novel aspects are summarized: since the flexomagnetic effect makes the plate stiffer, the maximum deflection is lowered when this effect is included. This effect also has varying influences on the plate under various boundary conditions, particularly the maximum position of the deflection, stress, Hz, and Bz responses. The thinner the plate thickness, the more pronounced the flexomagnetic effect. The flexomagnetic effect causes the thickness distribution of the stress components, Hz, and Bz to diverge from that of conventional structures (where this effect is disregarded), particularly for plates with CFFF boundary conditions. The longer the length of the compression zone increases, the lower the critical buckling load of the plate. The greater the stiffness of the elastic foundation, the better the plate can withstand compressive loads. Conclusion: The findings of this work provide a significant scientific foundation for the computation and development of nanoplates with magnetic properties. To design a structure that meets the necessary criteria, it is crucial to carefully choose geometric characteristics, boundary conditions, and stiffness parameters of the elastic foundation. According to this study, potential areas for additional research include investigating the impact of the flexomagnetic effect on nanoplates including fractures, optimizing nanostructures that exhibit flexomagnetic effects, and calculating the influence of flexomagnetic effects and temperature on nanostructures. [ABSTRACT FROM AUTHOR]

Large deflection nonlinear bending of functionally graded (FG) porous cylindrical panels reinforced with graphene platelets (GPLs) on a Pasternak-type elastic foundation is examined by developing a reliable and effective 2D meshfree-based nonlinear numerical method. The large displacement field is express by the first-order shear deformation theory (FSDT) and the von Kármán nonlinearity, and approximated by 2D natural element method (NEM) in conjunction with the stabilized MITC3+ shell concept and the shell surface–rectangular grid geometry transformation. The nonlinear simultaneous equations are solved by a load incremental Newton–Raphson scheme. The developed nonlinear numerical method is justified from by comparing with the reference solutions, and the load–deflection and bending moment of FG-GPLRC porous cylindrical panels on elastic foundation are scrutinizingly examined. Four different symmetric GPL distribution patters (except for FG-Λ) and three different symmetric porosity distributions are considered and their combined effects on the nonlinear bending behavior are investigated, as well as the effects of foundation stiffness and GPL amount. Also, the results are compared with those of FG CNT-reinforced porous cylindrical panels. [ABSTRACT FROM AUTHOR]

Free vibrations of porous functionally graded material (FGM) plates with complex shapes are analyzed by using the R-functions method. The thickness of the plate is variable in the direction of one of the axes. Two types of porosity distributions through the thickness are considered: uniform (even) and non-uniform (uneven). The elastic foundation is defined by two parameters (Winkler and Pasternak). To obtain the mathematical model of the problem, the first-order shear deformation theory of the plate (FSDT) is used. The effective material properties in the thickness direction are modeled by means of a power law. Variational Ritz's method joined with the R-functions theory is used for obtaining a semi-analytical solution of the problem. The approach is applied to a number of case studies and validated by means of comparative analyses carried out on rectangular plates with a traditional finite element approach. The proof of the efficiency of the approach and its capability to handle actual engineering problems is fulfilled for FGM plates having complex shapes and various boundary conditions. The effect of different parameters, such as porosity distribution, volume fraction index, elastic foundation, FGM types, and boundary conditions, on the vibrations is studied. [ABSTRACT FROM AUTHOR]

Excessive vibration has always been a serious problem for conical shell structures, while the application of the graphene-based free-constrained layer (GFCL) based on carbon fiber-reinforced composite (CFRC) structure is a novel way to improve structural performance. An analytical model for vibration and dynamic characteristics of the GFCL-CFRC conical shell resting on the Winkler–Pasternak elastic foundation with arbitrary boundary conditions is constructed, and four types of GFCL porosity distribution and GFCL dispersion pattern are considered in this model. The multi-segment technique and virtual spring technique are utilized to simulate arbitrary boundary conditions. Then, the first-order shear deformation theory (FSDT) and Hamilton's principle are employed to obtain the motion equation of the GFCL-CFRC conical shell, and the motion equation of the GFCL-CFRC conical shell is solved by the Ritz method. In conclusion, the dispersion mode of GFCL, thickness ratio of GFCL, and fiber angle have influence on the dynamic performance. With a reasonable design, the dynamic performance of the GFCL-CFRC conical shell can be further improved. [ABSTRACT FROM AUTHOR]

The nanoplates have been used extensively in electronic devices, during the working process they can be affected by external forces. To enhance the working performance of mechanical systems, flexoelectric effects are usually added, therefore, it is necessary to study the mechanical behavior of these material structures under the effect of these effects. This is the first research to examine the vibration response and static buckling of variable flexoelectric nanoplates using the FEM and novel shear deformation theory type hyperbolic sine functions, where the thickness is adjusted by linear and nonlinear rules. This is a simple theory, which does not need any shear correction factors, while the mechanical responses of the structures are still described exactly. The numerical results of this work are compared with those of the analytical approach and other methods. Then, the influences of geometrical and material parameters on the free vibration and static bucking of the structure are explored. The data shows that the flexoelectric effect has a strong effect on the free vibration and static bucking behavior as well as the vibration mode shapes of the nanoplates. The working performance is increased when taking into account the effect of flexoelectricity. This work also shows that for each changing rule of plate thickness, the flexoelectric effect also significantly changes the mechanical response of the plate. This is an important suggestion in the design and use of plate structures in engineering practice. [ABSTRACT FROM AUTHOR]

Today, due to the many applications of sandwich beams in industry, studying the forced vibrations of these structures is important. In these structures, amplifiers are used to improve mechanical properties. In this paper, metal-based graphene (copper) is used to improve the mechanical properties. This research uses a functionally graded (FG) graphene-reinforced copper-based composite (GRCC) sandwich beam and FG soft porous core, subjected to two moving loads and located on an elastic foundation. The equations are derived using Soldatos' higher-order shear deformation theory in axial and transverse directions. The exact problem under the magnetic field is solved using the Laplace method, which has not been done. The advantages of this method are the simplicity of solving and reducing to zero the error percentage that exists in numerical solutions. The results are compared with previous works. Finally, the effect of various parameters such as magnetic, porosity coefficient, elastic constant, thickness ratio, and velocity of moving load on the dynamic response of the sandwich beam is investigated. It should be noted that the results can be used to construct this type of structure. [ABSTRACT FROM AUTHOR]

The present paper deals with the modal analysis of sigmoid functionally graded (S-FGM) rectangular plate resting on elastic foundation by using the dynamic stiffness method (DSM). The DSM is formulated based on the exact solutions of the governing differential equations, and thereby it results in the very accurate computation of the natural frequencies. To obtain the DSM results for thicker plates, the study incorporates first-order shear deformation theory (FSDT) which includes the important effects of transverse shear deformation and rotatory inertia. The governing equations and the associated natural boundary conditions are derived using Hamilton's principle, and the solution is sought in the Levy form where two opposite edges of the plate are simply supported. The present study also contributes by highlighting mistakes in the classical plate theory (CPT)-based DSM formulation published in a recent work and presents a correct CPT-based mathematical formulation. For both these cases, the frequency-dependent dynamic stiffness matrix of the S-FGM plate gives rise to the transcendental eigenvalue problem, which is solved by using the Wittrick and Williams algorithm. Comparison with the available literature establishes the accuracy of the method. In addition, a parametric study is presented for various geometric and stiffness parameters of the elastically supported S-FGM plates using both CPT- and FSDT-based formulations, and accurate frequency results are reported. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this article is to investigate the porosity-dependent impact study of a plate with Winkler–Pasternak elastic foundations reinforced with agglomerated carbon nanotubes (CNTs). Design/methodology/approach: Based on the first-order shear deformation plate theory, the strain energy related to elastic foundations is added to system strain energy. Using separation of variables and Lagrangian generalized equations, the nonlinear and time-dependent motion equations are extracted. Findings: Verification examples are fulfilled to prove the precision and effectiveness of the presented model. The impact outputs illustrate the effects of various distribution of CNTs porosity functions along the plate thickness direction, Winkler–Pasternak elastic foundations and different boundary conditions on the Hertz contact law, the plate center displacement, impactor displacement and impactor velocity. Originality/value: This paper investigates the effect of Winkler–Pasternak elastic foundations on the functionally graded porous plate reinforced with agglomerated CNTs under impact loading. [ABSTRACT FROM AUTHOR]

Cylindrical panels are one of the most essential structural members of engineering structures, with mechanical, civil, aeronautical, and marine engineering applications. They are subjected to a wide range of vibrational loads. This article presents a novel higher-order porosity distribution and a free vibration analysis for porous orthotropic cylindrical panels resting on elastic foundations under higher-order shear deformation theory. It is assumed that cylindrical panels are composed of porous materials with uniformly and non-uniformly distributed pores. The porous panels' material properties are distributed in the thickness direction using specific functions. The equations of motion are derived using Hamilton's principle based on trigonometrical shear deformation theory and solved by performing the Galerkin solution procedure with simply supported edge conditions. The accuracy of the obtained natural frequency equation is confirmed by comparing the results to those of previously published in literature. Under comprehensive parametric studies, the influence of porosity coefficient, porosity distribution patterns, radius-to-curve length ratio, orthotropy, and stiffness of elastic foundation parameters on the free vibration response of porous orthotropic cylindrical panels are discussed in detail. [ABSTRACT FROM AUTHOR]

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 C 0 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. [ABSTRACT FROM AUTHOR]

In this work, static bending responses and natural frequency characteristics of functionally graded porous plates on elastic foundations are investigated. To serve this purpose, we present a hyperbolic quasi-3D shear deformation theory that takes into account both shear strain and normal deformation but requires only four variables to approximate the displacement field regardless of the shear correction factor. The virtual work principle is utilized to derive the equations of motion. The analytical solution in closed form is obtained by using Navier's technique. Numerical comparisons are conducted to validate the accuracy and efficiency of the present approach. Using this numerical model, the influences of gradient index, porosity fraction, geometric parameters, and foundation stiffness parameters on the deflection and fundamental frequency of FGP sandwich plates are comprehensively studied. [ABSTRACT FROM AUTHOR]

• Developed a novel quasi-3D shear deformation theory for FGM plate analysis. • Analyzed mechanical buckling and free vibration of thick FGM plates on elastic foundations. • Finite strip method used for computationally efficient plate discretization. • Validated results against existing theories, demonstrating superior accuracy. • Model addresses varying boundary conditions and elastic foundation types. This paper explores the elastic buckling and free vibration behavior of thick functionally graded material (FGM) plates placed on elastic foundations, using two-dimensional (2D) and quasi-three-dimensional (quasi-3D) shear deformation theories. The material properties of the FGM plates are assumed to vary continuously through the thickness based on a power-law distribution. By minimizing the total potential energy and solving the associated eigenvalue problem, the classical finite strip method is applied to determine the critical buckling loads and natural frequencies of the FGM plates. A key novelty of this work lies in the development of a quasi-3D shear deformation theory, which incorporates thickness stretching effects, providing a more accurate distribution of transverse shear strains across the plate thickness. Additionally, the FSM is utilized to efficiently discretize the in-plane geometry, offering a computationally cost-effective solution for analyzing free vibration and mechanical buckling characteristics. The elastic foundation is modeled using Winkler and two-parameter Pasternak models. The complexity of the governing equations is reduced by decomposing the transverse displacement into bending, shear, and thickness stretching components. Numerical results for FGM plates with various boundary conditions are validated by comparing them with analytical solutions from existing literature. Additionally, the effects of parameters such as plate thickness-to-length ratio, length-to-width ratio, boundary conditions, and the power-law index are analyzed and discussed. [Display omitted] [ABSTRACT FROM AUTHOR]

• Buckling and post-buckling of microplates under localized heating is assessed. • Analytical expressions for pre-buckling stresses are developed using Airy's stress function. • The plate is modelled using Reddy's TSDT and von Kármán geometric nonlinearity. • The small-scale effects are included using the modified strain gradient theory. • Governing equation of motion are derived using the Galerkin's method. The semi-analytical framework is developed for in-plane thermal stresses within the microplates under localized heating. Localized heating is modelled using Fourier Series expansions over the complete domain of the plate. These stresses within the plate are estimated after solving the in-plane thermoelasticity problem using Airy's stress approach. Utilizing these stresses, present work also studies the buckling and post-buckling behaviour of a porous metal foam microplate resting on Winkler and Pasternak elastic foundations. The plate is modelled using Reddy's third-order shear deformation theory (TSDT) and von Kármán geometric nonlinearity, and the size-dependent effects are included using the modified strain gradient theory (MSGT). Galerkin's weighted residual method converts the partial differential equations (PDEs) into algebraic equations. The post-buckling equilibrium path is obtained using the modified Newton-Raphson method. The mode shapes of the microplate for the various configurations of the plate with different boundary conditions due to localized thermal loading are plotted. Also, these mode shapes are compared with the mode shapes of the microplate due to in-plane mechanical loading. The parametric effect of porosity, elastic foundation parameters, thickness of plate, size of plate, boundary conditions and loading concentrations on the buckling and post-buckling behaviour of the plate is studied. [ABSTRACT FROM AUTHOR]

This paper aims to carry out comprehensively the static bending, free vibration, and buckling analyses of two-layer FGM plates with shear connectors resting on elastic foundations, where two-layer FGM plates resting on Winker's-Pasternak elastic foundations taking into account relative sliding movements are analyzed by using the combination of Navier's solution and finite element method based on nth -order shear deformation plate theory. The plate is made up of two layers of FG materials joined by metal shear connectors. Lagrange and Hermitian shape functions are used to establish stiffness matrices, mass matrices, geometric stiffness matrices, and element force vectors. The suggested method and mechanical model are accurate when compared to the computed data from this research and reputable literature. The computed data accurately describes the mechanical response of the structure. Then a series of parameter investigations are conducted to capture the effects of the structure's geometrical and material features on the mechanical behavior of two-layer FG plates. The numerical results of this study may be utilized as a basis for future research, applications, and design of similar structures in mechanical and civil engineering practice. This is also a critical foundation for studying the dynamic behavior of structures with shear connectors. [ABSTRACT FROM AUTHOR]

This article presents the finite element method (FEM) used four-unknown shear deformation theory for the static bending and hygro-thermo-mechanical vibration analysis of sandwich functionally graded porous (SFGP) doubly curved nanoshells resting on the elastic foundation (EF). The configurations of SFGP nanoshells include a homogenous core made of full ceramic while the top and bottom layers vary through the thickness with the law of uneven porosity distribution. The governing equations are obtained by using Hamilton's principle and the nonlocal elasticity theory of Eringen (nonlocal theory). For the first time, a four-node quadrilateral element with ten degrees of freedom (DOFs) for each node using Lagrangian and Hermitian interpolation functions to approximate the membrane and bending displacement fields are proposed to analyze the SFGP nanoshells. The numerical results are compared with other exact solutions to evaluate the performance of the proposed method. Furthermore, influences of geometrical parameters and material properties such as the power-law index n , the porosity coefficient ξ , the nonlocal coefficient μ , and EF-stiffness (K w , K s ) on the static bending, free vibration of SFGP nanoshells are comprehensive studied. [ABSTRACT FROM AUTHOR]

Two-variable sinusoidal shear and normal deformation theory is used in this paper for elastic analysis of doubly curved nanoshells resting on elastic foundation. Thickness stretching effect is accounted based on higher-order shear and normal deformation theory. The transverse displacement is decomposed into bending and stretching components based on two-variable sinusoidal shear deformation theory. Unlike classical structural theories for plates and shells, the present theory considers an extra variable as transverse displacement along the thickness direction. 3D constitutive relations are presented based on generalized Hooke's law. The principle of virtual work is used for derivation of governing equations and proper boundary conditions. An extensive parametric analysis is performed to present variation of in-plane and transverse displacements along the thickness direction in terms of the nonlocal parameter, opening angles and foundation characteristics. Comparison of results with and without thickness stretching effect show that the present theory improves results about 4% with respect to the structural theories without stretching effect. [ABSTRACT FROM AUTHOR]

A finite element modeling combined with the strain gradient theory (SGT) and the refined higher-order shear deformation beam theory is developed to study the dynamic instability of magnetically embedded functionally graded porous (FGP) nanobeams. Nanobeams with elastic foundation (EF) subjected to an axially oscillating load are analyzed. Nanobeams are made of functionally graded material (FGM) with an uneven porosity distribution. A three-node beam element with 8 degrees of freedom (DOFs) for two outer nodes and 2 DOFs for the middle node, which has the C1 and C2 continuous Hermite shape functions, is used to simulate nanobeams. Besides, Bolotin's method is employed to determine the instability region of FGP nanobeams. The accuracy of the proposed method is tested by comparing it with other published works. In addition, the influences of various parameters such as magnetic potential, small-scale parameter, porosity coefficient, stiffness foundation, boundary conditions (BCs) on the dynamic instability of nanobeams are studied in detail. [ABSTRACT FROM AUTHOR]

In this paper, an examination on the backbone curves of nanocomposite beams reinforced with graphene platelet (GPL) on elastic foundation exposed to a temperature increment is accomplished. By means of the Hamilton principle and in the framework of a third-order shear deformation beam theory, i.e. Reddy's beam theory (RBT), along with the von Karman nonlinear strains, the nonlinear motion equations are disclosed. The Halpin–Tsai micromechanical model is exploited in order to release the effective modulus of elasticity of the nanocomposite beam while the thermal expansion coefficient, Poisson's ratio and the mass density are estimated resorting to the rule of mixtures. Elastic foundation, and uniform temperature (UD) rising impacts are incorporated during the mechanical modeling of the nanocomposite beam. The Ritz scheme together with an iterative procedure reveals the nonlinear natural frequency associated to an assumed deflection in order to sketch the corresponding backbone curve. The outcomes are validated in comparison with the available results. Some case studies are established for the sake of clarifying the impressions of the distribution pattern of the GPL, the beam length to its thickness ratio, the weight fraction of the GPL, the elastic foundation, the boundary condition type, and the temperature changes on the first backbone curve of the nanocomposite beam. It is elucidated that the increment of the weight fraction of the GPL with X/O distribution pattern decreases/increases the hardening behavior of clamped–clamped (C-C) and simply-supported beam, while the softening behavior of a clamped-free (C-F) nanocomposite beam is independent of the division pattern, and the weight fraction of the GPL. Moreover, the temperature increment unlike the elastic foundation develops the hardening behavior of the backbone curves of simply supported and C-C nanocomposite beams. Although the backbone curve associated to a C-F nanocomposite beam is invariant with respect to the temperature, the elastic foundation develops the softening trend of C-F nanocomposite beams. [ABSTRACT FROM AUTHOR]

This study presents a hyperbolic shear deformation theory for free vibration of functionally graded plates on elastic foundations. The field of displacements is chosen based on the assumptions that axial and transverse displacements consist of components due to bending and shear. The components of the axial shear displacements give rise to the parabolic variation in the shear strain through the thickness, such that the shear stresses vanish on the plate boundaries. Therefore, the shear correction factor is not necessary. The material properties of the functionally graded plate are assumed to vary through the thickness according to the power law of the volume fraction of the constituents. The elastic foundation is modeled as a Pasternak foundation. The equations of motion are derived using Hamilton's principle. The analytical solutions were established from Navier's approach, and the results obtained are found to be in good agreement with the solutions of three-dimensional elasticity and with the solutions of the various plate theories. The effects of the power law index, the thickness ratio, and the foundation parameters on the natural frequency of the plates were also evaluated. [ABSTRACT FROM AUTHOR]

In this article, vibration characteristics of three different types of Single-Walled Carbon Nanotubes (SWCNTs) such as armchair, chiral, and zigzag carbon nanotubes have been investigated considering the effects of surface energy and surface residual stresses. The nanotubes are embedded in the elastic substrate of the Winkler type and are also exposed to low and high-temperature environments. A new refined beam theory namely, one-variable shear deformation beam theory has been combined with Hamilton's principle to develop the governing equations of the proposed model. The size-dependent behavior of the SWCNTs is addressed by Eringen's nonlocal elasticity theory whereas the model is investigated analytically by employing Navier's technique. Also, a parametric study has been conducted to analyze the effects of various scaling parameters such as small scale parameter, temperature change, thermal environments, Winkler modulus, and length of the beam. The results are also validated with previously published articles in special cases witnessing robust agreement. [ABSTRACT FROM AUTHOR]

In this paper, a five-variable displacement field is developed within the framework of the higher-order shear deformation theory (HSDT) for the examination of the free vibrations and the buckling loads of simply supported laminated plate resting on an elastic foundation. The theory is applicable to frame-up with thick and thin plates. Hamilton's principle is employed to obtain the governing differential equations (GDEs), which are discretized via multiquadric radial basis function (MQRBF). The present study highlights the influence of the elastic foundation and different types of transverse loading, as well as the effects of the span to thickness, aspect ratio, orthotropy ratio, and number of layers, on the results. The paper targets inclining reliable benchmarks for the most recent advancements of the topic to be utilized as references in future validation tests. [ABSTRACT FROM AUTHOR]

The main objective of this research work is focused on the vibration analysis of auxetic sandwich cylindrical shell structures resting on an elastic foundation. In the analysis, the sandwich shell structure is composed of three layers in which the middle layer consists of auxetic material with a negative Poisson's ratio, and the two skin layers are isotropic homogeneous materials. The motion equation is extracted according to the first-order shear deformation theory (FSDT) and the Hamilton principle. The governing equations of coupled partial differential equations are solved by the generalized differential quadrature (GDQ) method, and the natural frequencies are determined. By comparing the experimental results with the numerical results calculated by commercial finite element software, the validity of the proposed theoretical model is verified. Finally, the influences of geometrical parameters and elastic foundation on the vibration behavior of sandwich shell structures have been investigated. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration of the functionally graded porous (FGP) non-uniform annular-nanoplates lying on Winkler foundation (WF) is studied by using the smoothed finite element method based on the first-order shear deformation theory (FSDT). The combination of the mixed interpolation of the tensorial components for the three-node triangular element (MITC3 element) and the edge-based smoothed finite element method (ES-FEM) creates the ES-MITC3 element. This element is employed to avoid the shear locking problem as well as to improve the accuracy of the original MITC3 element. The small-scale effect is considered based on the nonlocal theory. Applying Hamilton's principle, the governing equation of the FGP non-uniform thickness annular-nanoplate is derived. Material properties of the nanoplate are characterized by two parameters: power-law index (k) and maximum porosity distributions (Ω) in the forms of cosine functions. The results of the present work are compared with other published work to verify accuracy and reliability. Moreover, the effects of geometry parameters and material properties on the free vibration of FGP non-uniform annular-nanoplates are comprehensively investigated. [ABSTRACT FROM AUTHOR]

This paper uses the finite element method to simulate the mechanical, electric, and polarization behaviors of piezoelectric nanoplates resting on elastic foundations subjected to static loads, in which the flexoelectric effect is taken into consideration. The finite element formulations are established by employing a new type of shear deformation theory, which does not need any shear correction factors, but still accurately describes the stress field of the plate. The numerical results show clearly that the flexoelectric effect has a strong influence on the mechanical responses of the nanoplates. In particular, the normal stress distribution in the thickness direction is no longer linear when the flexoelectric coefficient is large enough, and this phenomenon differs completely from that of conventional plates. In addition, the distribution of the electric field and the polarization also depend on boundary conditions, which were not investigated in the published works. [ABSTRACT FROM AUTHOR]

• The nonlinear forced vibration of hybrid nanocomposite toroidal shell segments is studied. • The toroidal shell consists of polymeric resin, carbon nanotubes (CNTs) and graphene platelets (GPLs). • The multi-scales method is used to estimate the frequency-amplitude relationship. while the Runge Kutta method was used to obtain the dynamic response of the shell. • The nonlinear primary resonance and dynamic response of hybrid nanocomposites toroidal shell are analyzed. • The effects of different geometrical and foundation parameters on the forced vibration behavior are examined. This study proposes a unique three-phase functionally graded (FG) hybrid nanocomposite material reinforcing the toroidal shell segments to investigate the nonlinear forced vibration using Reddy's higher-order shear deformation theory, von Karman geometrical nonlinearity and Stein-McElman's assumption along with the Hamilton principle. The examined toroidal shell's material consists of polymeric resin, carbon nanotubes (CNTs), and graphene platelets (GPLs) as nanocomposites. The material properties have been derived based on a modified Halpin-Tsai micromechanical model. Four distribution patterns have been studied: uniform (UD), FG-X, FG-O, and FG-V. The continuous distribution of GPLs and CNTs leads to inhomogeneous position-dependent properties throughout the shell thickness. The obtained differential equations of motion have been reduced to ordinary equations using Galerkin's technique. A multi-scales method (MSM) is used to estimate a closed-form solution representing the frequency-amplitude relation, and the state space representation is used along with numerical fourth-order Runge Kutta method (RK4) to obtain the nonlinear dynamic response of the toroidal shell. The accuracy of the current results obtained has been verified by comparing them with the relevant literature and numerical results using (RK4). In addition, the influence of both GPLs and CNTs weight fractions, nanofillers' distribution types, longitudinal and circumferential wave numbers, elastic foundation parameters, static axial compression load, transverse excitation load, damping ratio, geometrical characteristics of the toroidal shell on the dimensionless natural frequency, nonlinear primary resonance (frequency-amplitude curve), and nonlinear dynamic response are carefully studied. The results found that combining (GPLs & CNTs) into the shell's matrix improves performance, especially in concave shells compared to convex ones. The FG-X pattern reduces peak resonance amplitude and improves natural frequency. A reduction of 12.3 % is observed for convex shells, and 21.5 % for concave shells compared to FG-O. [ABSTRACT FROM AUTHOR]

Folded structures hold significant importance in aerospace technology due to their distinct design, effectively reconciling strength with a lightweight framework. Within aerospace applications, these structures fulfill diverse roles, serving as pivotal elements in aircraft wings, fuselage sections, and essential components of spacecraft and satellites. This study delves into the free vibration behavior of folded sandwich plates composed of a porous core and functionally graded carbon nanotube-reinforced composite (FG-CNTRC) coatings, resting on a two-parameter elastic foundation. Leveraging first-order shear deformation plate theory (FSDT), elasto-dynamic equations are established for each individual plate segment. Utilizing the two-dimensional generalized differential quadrature method (2D-GDQM), these equations are discretized. Subsequently, by applying boundary conditions to all six edges, including traditional clamped, simply supported, and free configurations, and incorporating continuity conditions for displacements, forces, and moments at the joint borders, natural frequencies and modal shapes are extracted for the folded plate structure. The validity of the proposed formulation and results is demonstrated by comparing them with numerical examples for both composite flat and folded plates. This comparison provides strong support for the accuracy and reliability of the present study. The study comprehensively examines the influence of various parameters on natural frequencies, including modal shape visualizations under different boundary configurations, plate thickness, crank angle, porosity parameter, core thickness, foundation stiffness, and CNTs distribution type. [ABSTRACT FROM AUTHOR]

The dynamic behavior of functionally graded (FG) sandwich beams resting on the Pasternak elastic foundation under an arbitrary number of harmonic moving loads is presented by using Timoshenko beam theory, including the significant effects of shear deformation and rotary inertia. The equation of motion governing the dynamic response of the beams is derived from Lagrange's equations. The Ritz and Newmark methods are implemented to solve the equation of motion for obtaining free and forced vibration results of the beams with different boundary conditions. The influences of several parametric studies such as layer thickness ratio, boundary condition, spring constants, length to height ratio, velocity, excitation frequency, phase angle, etc., on the dynamic response of the beams are examined and discussed in detail. According to the present investigation, it is revealed that with an increase of the velocity of the moving loads, the dynamic deflection initially increases with fluctuations and then drops considerably after reaching the peak value at the critical velocity. Moreover, the distance between the loads is also one of the important parameters that affect the beams' deflection results under a number of moving loads. [ABSTRACT FROM AUTHOR]

A new simple "four-variable shear deformation" plate model is proposed in this work to demonstrate the hygro-thermal environment effects on dynamic and buckling of functionally graded material "sandwich plates" supported by "Winkler–Pasternak" elastic foundations. Equations of motion are obtained from Hamilton's principle containing the hygro-thermal influences. This model uses only "four variables" and considers trigonometric variation of "transverse shear stress." In addition, these stresses become zero at the upper and lower surfaces of the "sandwich plate." The novelty of this formulation is the addition of the integral term in the field of displacement, which leads to a reduction of the number of unknowns and basic equations. Various kinds of functionally graded material "sandwich plates" are examined in this study. To verify the validity of the model, the calculated results are compared with the existing results. Comparison investigations reveal that the computed results of the proposed formulation are in excellent agreement with those of other "higher shear deformation theories." Parametric investigation is established to demonstrate the effects of temperature rise, moisture condition, elastic foundation coefficients, and power law index on the vibration and buckling of functionally graded material "sandwich plates." [ABSTRACT FROM AUTHOR]

This article presents an investigation on the postbuckling behavior of doubly curved graphene-reinforced composite (GRC) laminated panels supported by an elastic foundation and subjected to lateral pressure and in thermal environments. The piece-wise GRC layers are arranged in a functionally graded (FG) pattern along the thickness direction of the panels. The overall mechanical properties of the FG-GRCs are assumed to be temperature dependent and are estimated through the extended Halpin-Tsai micromechanical model. 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 first deduced to a boundary layer type that includes nonlinear prebuckling deformations and initial geometric imperfections of the panel. The postbuckling equilibrium path for the perfect and geometrically imperfect GRC laminated doubly curved panels are obtained by applying a singular perturbation technique along with a two-step perturbation approach. The impacts of material property gradient, temperature variation, panel curvature ratio, as well as foundation stiffness on the postbuckling behavior of FG-GRC laminated doubly curved panels are investigated. [ABSTRACT FROM AUTHOR]

The work presents a finite element modeling of beam resting on a two-parameter layered soil. The behavior of the soil continuum and the beam are assumed to be linear and homogeneous isotropic. Using the strain energy expressions, the shear strain of the beam element and the soil foundation are taken together in the analysis. In this approach, the stiffness matrix of each component is elaborated and integrated in the finite element analysis. First, various examples are elaborated to show the effectiveness of the proposed approach and the ability of the numerical program developed for this concern. Second, the analysis is widened to study the influence of the soil properties on the interface continuum and on the beam responses. Third, a parametric study is carried out to highlight the effect of the position of springs at the interface continuum, the properties of soil, the deepest of the soil foundation and the ballast layer on the response of the interface and the beam itself. Moreover, shear deformations are presented to show the crucial influence on the beam, on the structure and on the interface behaviors. Obtained results show pertinent results corresponding to the interface continuum and the beam responses. [ABSTRACT FROM AUTHOR]

Abstract The aim of this work is to establish a two dimensional (2D) and quasi three dimensional (quasi-3D) shear deformation theories, which can model the free vibration of FG plates resting on elastic foundations using a new shear strain shape function. The proposed theories have a novel displacement field which includes undetermined integral terms and contains fewer unknowns with taking into account the effects of both transverse shear and thickness stretching. The mechanical properties of the plates are assumed to vary through the thickness according to a power law distribution in terms of the volume fractions of the constituents. The elastic foundation parameters are introduced in the present formulation by following the Pasternak (two-parameters) mathematical model. Hamilton's principle is employed to determine the equations of motion. The closed form solutions are derived by using Navier's method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. The efficiency of the proposed theory is ascertained by comparing the results of numerical examples with the different 2D, 3D and quasi-3D solutions found in literature. [ABSTRACT FROM AUTHOR]

This paper investigates the nonlinear response of doubly curved functionally graded material sandwich panels resting on elastic foundations, exposed to thermal environments and subjected to uniform external pressure. The material properties of both face sheets and core layer are assumed to be temperature dependent, and effective material properties of functionally graded material layers are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Formulations are based on first-order shear deformation shell theory taking geometrical nonlinearity, initial geometrical imperfection, Pasternak type elastic foundations, and tangential edge constraints into consideration. Approximate solutions are assumed to satisfy simply supported boundary conditions and Galerkin procedure is applied to derive expressions of buckling loads and nonlinear load–deflection relation. The effects of material, geometry and foundation parameters, face sheet thickness ratio, initial geometrical imperfection, thermal environments and degree of tangential restraint of edges on the snap-through instability, and nonlinear response of spherical and cylindrical functionally graded material sandwich panels are analyzed and discussed in detail. [ABSTRACT FROM AUTHOR]

• The equivalent model of the MRE-filled corrugated structure is obtained by employing the representative volume element (RVE). • The governing motion equations of the sandwich plate are derived via the first-order shear deformation theory (FSDT). • Based on the modified Fourier series and the Rayleigh-Ritz method, the energy functions of the sandwich plate are solved. The main barrier to the application of corrugated structures in vibration suppression is their low loss factor. The use of magnetorheological elastomer (MRE) as a novel type of smart material has the potential to improve the energy dissipation capacity of the corrugated structure. In this study, the dynamic behavior of the corrugated composite sandwich plate filled with MRE resting on elastic foundations is investigated. The equivalent model of the MRE-filled corrugated structure is obtained by employing the representative volume element (RVE). Then, the governing motion equations of the sandwich plate are derived via the first-order shear deformation theory (FSDT). Based on the modified Fourier series and the Rayleigh-Ritz method, the energy functions of the sandwich plate are solved. In this work, the analysis of geometric parameters, loading type, and magnetic field on the dynamic behavior of the corrugated sandwich is conducted. Numerical results show that increasing the magnetic field intensity, stiffness of boundary, and elastic foundation improves the dynamic performance of the structure. This reveals that the response behavior of the structure is significantly affected by the magnetic field intensity, as well as the stiffnesses of the boundary and elastic foundation. [ABSTRACT FROM AUTHOR]

The buckling analysis of thick composite annular sector plates reinforced with functionally graded carbon-nanotubes (CNTs) is presented under in-plane and shear loadings based on the higher-order shear deformation theory. It is considered that the plate is resting on the Pasternak-type elastic foundation. The overall material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are estimated through the micromechanical model. The governing equations are derived on the basis of the higher-order shear deformation plate theory, and the quadratic form of the energy functional of the system is presented. An efficient numerical method is presented in the context of variational formulation to obtain the discretized version of stability equations. The validation of the present study is demonstrated through comparisons with the results available in the literature and then comprehensive numerical results are given to investigate the impacts of model parameters on the stability of CNT-reinforced composite annular sector plates. [ABSTRACT FROM AUTHOR]

This paper proposes a four-variable shear deformation refined plate theory for free vibration analysis of embedded smart plates made of porous magneto-electro-elastic functionally graded (MEE-FG) materials. Magneto-electro-elastic properties of FG plate are supposed to vary through the thickness direction and are estimated through the modified power-law rule in which the porosities with even and uneven type are approximated. The governing differential equations and boundary conditions of embedded porous FG plate under magneto-electrical field are derived through Hamilton's principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factors. An analytical solution procedure is used to achieve the natural frequencies of embedded porous FG plate supposed to magneto-electrical field with various boundary condition. Influences of several important parameters such as material graduation exponent, porosity volume fraction, magnetic potential, electric voltage, various boundary conditions, elastic foundation parameters and plate side-to-thickness ratio on natural frequencies of embedded porous MEE-FG plate are investigated and discussed in detail. It is concluded that these parameters play significant roles on the dynamic behavior of porous MEE-FG plates resting on elastic foundation. Presented numerical results can serve as benchmarks for future analyses of MEE-FG plates with porosity phases. [ABSTRACT FROM AUTHOR]

This paper deals with the effect of matrix cracks on the free and forced vibration characteristics of a shear deformable laminated beam which contains carbon nanotube reinforced composite (CNTRC) layers. Two matrix-cracked models, namely self-consistent model (SCM) and elasticity theory model (ETM), are selected to describe the degraded stiffness of the beam. The beam rests on a two-parameter elastic foundation in thermal environments. Based on a higher order shear deformation theory and von Kármán nonlinear strain-displacement relationships, the motion equations are established and solved by means of a two-step perturbation approach. The material properties of both fiber reinforced composite (FRC) layers and CNTRC layers are assumed to be temperature-dependent. The effects of the crack density, CNT volume fraction, temperature variation, as well as the foundation stiffness on the dynamic responses of hybrid laminated beams with multiple matrix cracks are discussed in detail. [ABSTRACT FROM AUTHOR]

Buckling behavior of nonlocal Functionally Graded Piezoelectric (FGP) beams on elastic substrate via a higher order beam model is examined. The present beam model takes into consideration the shear deformation effects needless of any shear correction factor. Employing power-law function, the gradation of material properties of the beam is described. Incorporation of small scale parameter is carried out using nonlocal elasticity theory. Implementing an analytical approach which satisfies simply-supported boundary conditions, the governing equations derived from Hamilton's principle are solved. The obtained results are compared with those provided in the literature. It is indicated that the buckling behavior of piezoelectric Nanobeams is significantly influenced by elastic foundation parameters, external voltage, scale parameter, power-law index and slenderness ratio. [ABSTRACT FROM AUTHOR]

For the first time, a novel theoretical model is presented for analyzing the effects of the arbitrary-distributed Kerr foundation on the free vibration and transient responses of the functionally graded material (FGM) plate in a thermal environment. According to the power law distribution, the mechanical characteristics of FGM plates are assumed to vary with plate thickness. The three-parameter Kerr model is founded on the independence of the upper and lower elastic layers with respect to the shear layer. The shape and location of the elastic foundation can be determined arbitrarily using mathematical functions. In the area of the FGM plate, the distribution of the elastic foundation is assumed to be either centralized or decentralized. The Reddy's third-order shear deformation theory is utilized to express the governing equations. Then, the dynamical characteristics of the FGM plate are obtained by using the Galerkin's method. To validate the accuracy of the current computational model, the achieved results are compared to those derived from published literature. In addition, graphical representations of the effects of stiffness, distributions, and geometrical parameters of elastic foundation, geometrical parameters of plate, material properties, and thermal environment on the vibrational characteristics of the plates are provided. [Display omitted] • Reddy's third-order shear deformation theory for thermally vibrational analyses of FGM plates. • The shape and location of the elastic foundation can be determined arbitrarily using mathematical functions. • Many temperature environments are considered: uniform temperature increases and temperature variations across the thickness. • Effects of the Kerr foundation, geometrical parameters, material properties, and thermal models are investigated in depth. [ABSTRACT FROM AUTHOR]

In the present paper, the shear post-buckling behavior of the FGM rectangular plates is analyzed, for the first time. Furthermore, effects of the elastic foundation on the post-buckling deformation/distortion patterns and strengths are investigated. The exact energy-based 3D theory of elasticity is implemented through incorporation of the general form of Green’s strain tensor. A fully consistent 3D Hermitian element with up to the second-order mixed derivatives continuity is utilized to satisfy continuity of the stress and distortion components at the mutual nodes of the adjacent elements. The post-buckling equilibrium paths are traced using an arc-length solution scheme in conjunction with the modified Newton–Raphson method. A comprehensive sensitivity analysis is accomplished to evaluate effects of the heterogeneity index, elastic foundation stiffness, aspect ratio, and the considered two types of practical boundary conditions on the post-buckling deformation patterns, mode jumping, and equilibrium paths. Results obtained based on post-buckling observations of properly adopted reference points reveal that mode jumping and larger distortions may occur due to increasing the post-buckling loads, the elastic foundation leads to larger number of the local deformation regions, and the buckling strengths reduce remarkably when two opposite edges are clamped. [ABSTRACT FROM AUTHOR]