Herein, with the aid of the newly proposed theory of nonlocal strain gradient elasticity, the size-dependent nonlinear buckling and postbuckling behavior of microsized shells made of functionally ...graded material (FGM) and subjected to hydrostatic pressure is examined. As a consequence, the both nonlocality and strain gradient micro-size dependency are incorporated to an exponential shear deformation shell theory to construct a more comprehensive size-dependent shell model with a refined distribution of shear deformation. The Mori–Tanaka homogenization scheme is utilized to estimate the effective material properties of FGM nanoshells. After deduction of the non-classical governing differential equations via boundary layer theory of shell buckling, a perturbation-based solving process is employed to extract explicit expressions for nonlocal strain gradient stability paths of hydrostatic pressurized FGM microsized shells. It is observed that the nonlocality size effect causes to decrease the critical hydrostatic pressure and associated end-shortening of microsized shells, while the strain gradient size dependency leads to increase them. In addition, it is found that the influence of the internal strain gradient length scale parameter on the nonlinear instability characteristics of hydrostatic pressurized FGM microsized shells is a bit more than that of the nonlocal one.
To impart desirable material properties, functionally graded (FG) porous silicon has been produced in which the porosity changes gradually across the material volume. The prime objective of this work ...is to predict the influence of the surface free energy on the nonlinear secondary resonance of FG porous silicon nanobeams under external hard excitations. On the basis of the closed-cell Gaussian-random field scheme, the mechanical properties of the FG porous material are achieved corresponding to the uniform and three different FG patterns of porosity dispersion. The Gurtin–Murdoch theory of elasticity is implemented into the classical beam theory to construct a surface elastic beam model. Thereafter, with the aid of the method of multiple time-scales together with the Galerkin technique, the size-dependent nonlinear differential equations of motion are solved corresponding to various immovable boundary conditions and porosity dispersion patterns. The frequency response and amplitude response associated with the both subharmonic and superharmonic hard excitations are obtained including multiple vibration modes and interactions between them. It is found that for the subharmonic excitation, the nanobeam is excited within a specific range of the excitation amplitude, and this range shifts to higher excitation amplitude by incorporating the surface free energy effects. For the superharmonic excitation, by taking surface stress effect into account, the excitation amplitude associated with the peak of the vibration amplitude enhances. Moreover, in the subharmonic case, it is demonstrated that by increasing the porosity coefficient, the value of the excitation frequency at the joint point of the two branches of the frequency-response curve reduces. In the superharmonic case, it is revealed that an increment in the value of porosity coefficient leads to decrease the peak of the oscillation amplitude and the associated excitation frequency.
In this paper, size-dependent dynamic stability of axially loaded functionally graded (FG) composite truncated conical microshells with magnetostrictive facesheets surrounded by nonlinear ...viscoelastic foundations including a two-parameter Winkler–Pasternak medium augmented via a Kelvin–Voigt viscoelastic approach is analyzed considering nonlinear cubic stiffness. To this purpose, von Karman-type kinematic nonlinearity along with modified couple stress theory of elasticity was applied to third-order shear deformation conical shell theory in the presence of magnetic permeability tensor and magnetic fluxes. The numerical technique of generalized differential quadrature (GDQ) was used for the solution of microstructural-dependent dynamic stability responses of FG composite truncated conical microshells. It was seen that moving from prebuckling to postbuckling domain somehow increased the significance of couple stress type of size dependency on frequency. In addition, within both prebuckling and postbuckling regimes, an increase of material gradient index decreased the importance of couple stress type of size dependency on the frequency of an axially loaded FG composite truncated conical microshell. Furthermore, it was revealed that by applying a positive magnetic field to an axially loaded truncated conical microshell with magnetostrictive facesheets, its frequency at a specific axial load value was increased in prebuckling domain and decreased in postbuckling domain. However, this pattern was reversed by applying a negative magnetic field.
With the aid of the non-uniform rational B-spline (NURBS)-based isogeometric technique, for the first time, the size-dependent geometrically nonlinear bending characteristics of microplates made of ...porous functionally graded materials (FGMs) having a central cutout with different shapes are studied. The nonlocal strain gradient continuum elasticity within the framework a hybrid higher-order quasi-3D plate theory is adopted to describe the kinematic relations via only four unknowns. To capture the effective material properties, a porosity-dependent rule of mixture is employed. The nonlocal strain gradient nonlinear load–deflection responses are obtained corresponding to various geometrical and material parameters as well as different boundary conditions. It is revealed that the significance of both the nonlocal and strain gradient reduces. This prediction is the same for all values of the material property gradient index as well as the porosity index. Also, it is demonstrated that a central cutout leads to change the trend of load–deflection response, and this change occurs at a specific value for the applied distributed load which depends on several parameters such as the cutout geometry and boundary conditions. In addition, it is displayed that corresponding to different maximum deflections, the significance of the strain gradient size effect in the absence of nonlocality on the nonlinear flexural stiffness of a porous FGM microplate is more than that of the nonlocal size effect in the absence of the strain gradient size dependency.
In the current study, hydroxyapatite (HA)-MgO scaffolds are fabricated with the aid of the space holder technique using NaCl as the spacer type. After that, the fabricated samples are deposited in ...gelatin (GN) with ibuprofen (IBO) substitution to create GN-IBO thin surface coating. The samples are then synthesized chemically and the associated properties are studied using X-ray diffraction (XRD) and scan electron microscopy (SEM) equipped with the energy dispersive spectroscopy (EDS). The compressive strength, fracture toughness, hardness, porosity, bioactivity, degradation rate, wettability, and roughness of the manufactured HA-MgO bio-nanocomposite scaffolds containing different weight fractions of MgO nanoparticles are predicted. Accordingly, nonlinear mechanical behaviors including nonlinear free vibration and nonlinear vibrations associated with the prebuckling and postbuckling domains of an axially loaded plate-type bone implant made of the HA-MgO bio-nanocomposites coated with the GN-IBO thin layers are investigated analytically via a sandwich plate model. The obtained results reveal that magnesium has no considerable effect on the porosity, however it causes to enhance the compressive strength significantly. The presence of magnesium ions also leads to reduce the crystallinity of HA about 30-100 nm due to entering MgO nanoparticles into the network. The results related to the sample with 10 wt% MgO nanoparticles indicate that the microscopic structure of the fabricated bio-nanocomposite scaffold is three-dimensional with porous architecture. Also, it is shown that the solubility of the HA composed with MgO nanoparticles decreases with higher bioactivity.
As one of the innovative materials, functionally graded (FG) composite materials have the capability to vary microstructure and design attributes from one side to other representing the desired ...material properties. The prime aim of this work is to analyze the surface stress effect on the nonlinear free vibration response of FG cylindrical nanoshells incorporating various modal interactions. To this end, the Gurtin–Murdoch theory of elasticity together with the von Karman geometrical nonlinearity is implemented to the classical shell theory to construct an efficient size-dependent shell model. In order to take the modal interactions between the main oscillation mode and various symmetric vibration modes, the lateral deflection of the FG nanoshell is expressed as combination of the simple main vibration mode and convergent symmetric modes. Thereafter, the solution of problem is considered as the summation of the homogenous and particular parts to put the Galerkin technique to use. Finally, the multiple time-scales method is employed to achieve analytical expression for the surface elastic-based frequency response of FG nanoshells. It is displayed that in the presence of modal interaction, by increasing the shell deflection, the value of the frequency ratio decreases while in the absence of modal interaction, it enhances.
Functionally graded multilayer shallow arch structures have gained significant attention due to their unique mechanical properties and potential applications. This review aims to provide a ...comprehensive overview of the static and dynamic behaviors of small-scaled functionally graded multilayer shallow arch structures, covering design and analysis aspects. The review begins by introducing functionally graded materials (FGMs) and their advantages in tailoring material properties. It then focuses on fabrication procedures for these structures. The design considerations are explored in detail, discussing various approaches for material composition grading and layer configuration. The influence of key parameters on structural behavior is examined, including material properties, layer thickness, and arch geometry. Mechanical analysis techniques for studying the static and dynamic behaviors of these structures are discussed. The review highlights the potential applications of FGMs in small-scaled shallow arch structures, such as bridges, tunnels, spaceships, and medical implants. This information is valuable for researchers interested in real-life applications. The review concludes by summarizing key findings and suggesting future research directions. It emphasizes investigating additional factors like temperature effects, geometric nonlinearities, and environmental conditions. The integration of advanced computational techniques with experimental validation is recommended for more accurate predictions and reliable design guidelines. Challenges in designing cost-effective and practical structures for real-world applications are acknowledged. Future research may focus on addressing these challenges and developing new techniques for large-scale engineering projects. The review provides insights into the fundamental scientific considerations and limitations of these structures. Overall, this state-of-the-art review serves as a valuable resource for researchers, engineers, and practitioners interested in designing and analyzing small-scaled functionally graded multilayer shallow arch structures. It offers insights into their computational static and dynamic behaviors and their potential applications in diverse fields.
The current investigation deals with proposing a numerical analysis for the geometrically nonlinear large-amplitude vibrations of arbitrary-shaped microplates having variable thickness with various ...patterns in the presence of couple stress type of microstructural size dependency. To accomplish this purpose, the isogeometric analysis (IGA) is employed to achieve exact geometrical description as well as higher-order efficient smoothness with no meshing difficulty. On the other hand, the modified couple stress continuum mechanics is applied to a refined quasi-3D plate model having the capability to take the thickness stretching into consideration with only four variables. The microplates are assumed made of functionally graded (FG) composites, the material properties of which are changed continuously through the variable thickness. The variation of microplate thickness obeys three different schemes including linear, concave, and convex ones. It is highlighted that by changing the pattern of the thickness variation from convex type to linear one, and then from linear type to concave one, the both classical and couple stress continuum-based nonlinear frequency of the microplates having different shapes increases due to a higher value of the average plat thickness. On the other hand, by considering this change in the thickness variation pattern, it is seen that the significance of the couple stress size effect increases. For this reason, the significance of the stiffening scheme associated with the gradient of rotation gets lower through increment of the material gradient index of a FG composite microplate.
•Development a nonlocal strain gradient BDFGM exponential shear deformable beam model.•Incorporation of deviation of the associated physical neutral plane from the mid-plane counterpart.•Presentation ...of the size-dependent nonlinear bending of BDFGM micro/nano-beams.•Presentation the size-dependent postbuckling behavior of BDFGM micro/nano-beams.•Prediction the influence of the axial and lateral material property gradient indexes.
In this work, different homogenization schemes are employed to analyze both size-dependent postbuckling and nonlinear bending behavior of micro/nano-beams, made of a bi-directional functionally graded material (BDFGM), under external axial compression and distributed load. To such different homogenization models, including Reuss, Voigt, Mori-Tanaka, and Hashin–Shtrikman bounds schemes, together with nonlocal strain gradient elasticity theory are adopted within the framework of refined exponential shear deformation beam theory, to develop a comprehensive size-dependent BDFGM beam model. Deviation of associated physical neutral plane, from mid-plane counterpart, is also considered. Nonlocal strain gradient load-deflection responses of BDFGM micro/nano-beam are obtained by numerical solution methodology for both nonlinear bending and postbuckling behaviors corresponding to different values of the lateral and longitudinal material property indices and various small scale parameters. We observed that by decreasing the values of material property gradient indices, associated with BDFGM, difference between the estimations of various homogenization schemes is raised. We also indicated that increasing maximum deflection, decreasing the significance of nonlocal size effect on the bending strength of BDFGM micro/nano-beams, whereas strain gradient size effect becomes more important. In addition, we found that at lower material property gradient indices, bending strength reduction in BDFGM micro/nano-beams, causes by the axial gradient property is higher than lateral gradient property. At higher values of these indices, however, the trend is opposite.
•Development a surface elastic-based conical shell model.•Nonlinear oscillation analysis of composite nanoshells with in-plane heterogeneity.•Introducing the functionally graded composite type of ...surface continuum shell theory.•Study the geometrical nonlinearity on the surface elastic frequency-response.
In the current investigation, a new formulation for nonlinear vibration behaviors of functionally graded (FG) composite conical nanoshells are constructed using Gurtin-Murdoch elasticity theory based on higher-order shear deformation shell theory (HSDFST) framework. Both Voigt and Reuss homogenization procedures are considered for the estimation of the mechanical characteristics of FG materials. Using generalized differential quadrature method (GDQM) together with Galerkin technique, the surface elastic-based nonlinear frequency-responses of FG composite conical nanoshell are obtained. It has been illustrated that the decrease of material property gradient index or transformation of boundary condition from full simply supported to full clamped, surface stress effect on the nonlinear frequency of a FG composite conical nanoshell reduces. Also, decreasing semi-vertex angle increases the frequency ratio of ωNL/ωL which reveals higher geometrical nonlinearity. However, it is seen that surface elasticity effect on the nonlinear vibration behavior of FG composite conical nanoshells is not significant.
