In this article, the free vibration response of sandwich plates with porous electro-magneto-elastic functionally graded (MEE-FG) materials as face sheets and functionally graded carbon nanotube-reinforced composites (FG-CNTRC) as core is investigated. To this end, four-variable shear deformation refined plate theory is exploited. The properties of functionally graded material plate are assumed to vary along the thickness direction of face sheets according to modified power-law expression. Furthermore, properties of FG-CNTRC layer are proposed via a mixture rule. Hamilton’s principle with a four-variable tangential–exponential refined theory is used to obtain the governing equations and boundary conditions of plate. An analytical solution approach is utilized to get the natural frequencies of embedded porous FG plate with FG-CNTRC core subjected to magneto-electrical field. A parametric study is led to fulfill the effects of porosity parameter, external magnetic potential, external electric voltage, types of FG-CNTRC, and different boundary conditions on dimensionless frequencies of porous MEE-FG sandwich plate. It is noteworthy that the numerical consequences can serve as benchmarks for future investigations for this type of structures with porous mediums.
相似文献In this article, an attempt has been made on evaluating the large/nonlinear deflection of functionally graded magneto-electro-elastic porous (FG-MEEP) flat panels taking geometric skewness into consideration. Further, the flat panel is subjected to combined loads which include mechanical, electrical and magnetic loads. The mathematical formulation is derived through higher order shear deformation theory and von-Karman's geometric nonlinearity under the framework of finite element method (FEM). The effective material properties of FG-MEEP material are determined using modified power law. Two forms of material gradation such as ‘B’ rich bottom and ‘F’ rich bottom are modelled and implemented in the analysis. The numerical assessment is carried out to investigate the effect of prominent parameters such as skew angle, porosity distribution, gradient index, porosity volume, functionally graded pattern, electromagnetic loads on the nonlinear deflection of FG-MEEP flat panels. In addition, this study also makes an attempt to evaluate the degree of coupling associated with these parameters.
相似文献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.
相似文献The problem of the nonlinear thermal buckling and post-buckling of magneto-electro-thermo-elastic functionally graded porous nanobeams is analyzed based on Eringen’s nonlocal elasticity theory and by using a refined beam model. The beams with immovable clamped ends are exposed to the external electric voltages, magnetic potentials, a uniform transverse load and uniform temperature change. For the first time, the four types of porosity distribution in the nanobeam are considered and compared in complex electric–magnetic fields. Besides, the new formula of the effective material properties is proposed in this paper to simultaneously estimate the material distribution and porosity distribution in the thickness direction. The generalized variation principle is used to induce the governing equations, then the approximate analytical solution of the METE-FG nanobeams based on physical neutral surface is obtained by using a two-step perturbation technique. Finally, detailed parametric analyses are performed to get an insight into the effects of different physical parameters, including the slenderness ratio, small-scale parameter, volume fraction index, external electric voltages, magnetic potentials, porosity coefficient and different porosity distributions, for providing an effective way to improve post-buckling strength of porous beams.
相似文献This study investigates the effects of fluid–structure and soil–structure interaction on the free vibration response of functionally graded sandwich plates. To this aim, an exemplary problem is analyzed, whereas a metal/ceramic sandwich plate is placed at the bottom of a tank filled in with fluid. Two cases are considered: (i) soft core, i.e., a sandwich plate with metal core and ceramic skins, and (ii) hard core, i.e., a sandwich plate with ceramic core and metal skins. In both cases, the skins are modelled as suitable functionally graded materials (FGMs). The soil is modelled as a Pasternak foundation. The free vibration analysis is carried out according to the extended higher order sandwich plate theory (EHSAPT). The fluid is assumed to be inviscid, incompressible, and irrotational. Hamilton’s principle is exploited to deduce the governing equations and the corresponding boundary conditions. The Rayleigh–Ritz method with two-variable orthogonal polynomials is used to compute the natural frequencies of the sandwich plate. The adopted approach is first validated through comparison with results published in the literature. Then, the effects are studied of several parameters on the dynamic response of the system.
相似文献In this paper, an analytical method is used to study the nonlinear primary resonance of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells with internal stiffeners. The SSFG cylindrical shell is surrounded by linear and nonlinear elastic foundation and the effect of structural damping on the system response is also considered. The material properties of the shell and stiffeners are assumed to be continuously graded in the thickness direction. Three-parameter nonlinear elastic foundation model is consists of two-parameter linear elastic foundation (Winkler and Pasternak) and one hardening/softening cubic nonlinearity parameter. Based on the von Kármán nonlinear equations and the classical plate theory of shells, the strain–displacement relations are derived. The smeared stiffener technique is used to the model of the internal stiffeners. Using the Galerkin method, the partial differential equations of motion are discretized. The nonlinear primary resonance is analyzed by means of the multiple scales method. The effects of various geometrical characteristics, material parameters and elastic foundation coefficients are investigated on the nonlinear primary resonance.
相似文献The main objective of this paper is to develop a numerical model susceptible to solve the numerical locking problems that may appear when applying the conventional solid and shell finite elements of ABAQUS. This model is based on a hexahedral solid shell element. The formulation of this element relays on the combination of the enhanced assumed strain (EAS) and assumed natural strain (ANS) methods with modified First Shear Deformation Theory (FSDT). The developed element is implemented into the ABAQUS user element (UEL) interface. The performance of this element is demonstrated by different benchmark tests from the literature. Our contribution consists on applying a single solid shell element through the thickness direction to predict the low velocity impact behavior on functionally graded material (FGM) circular plates.
相似文献The present work fills a gap on the postbuckling behavior of multilayer functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical and spherical shell panels resting on elastic foundations subjected to central pinching forces and pressure loadings. Based on a higher-order shear deformation theory and the von Kármán’s nonlinear strain–displacement relations, the governing equations of the FG-GPLRC cylindrical and spherical shell panels are established by the principle of virtual work. The non-uniform rational B-spline (NURBS) based isogeometric analysis (IGA), the modified arc-length method and the Newton’s iteration method are employed synthetically to obtain nonlinear load–deflection curves for the panels numerically. Several comparative examples are performed to test reliability and accuracy of IGA and arc-length method in present formulation and programming implementation. Parametric investigations are carried out to illustrate the effects of dispersion type of the graphene platelet (GPL), weight fraction of the GPL, thickness of the panel, radius of the panel and parameters of elastic foundation on the load–deflection curves of the FG-GPLRC shell panels. Some complex load–deflection curves of the FG-GPLRC cylindrical and spherical shell panels resting on elastic foundations may be useful for future references.
相似文献This paper presents a novel topology optimization formulation for shell-infill structures based on a distance regularized parametric level-set method (PLSM). In this method, the outer shell and the infill are represented by two distinct level sets of a single-level set function (LSF). In order to obtain a controllable and uniform shell thickness, a distance regularization (DR) term is introduced to formulate a weighted bi-objective function. The DR term is minimized along with the original objective, regularizing the parametric LSF close to a signed distance function. With the signed distance property, the area between the two-level sets can be contoured as the shell with a uniform thickness. Additionally, the presented formulation retains one important merit of the PLSM that new holes are able to nucleate during the optimization process. With respect to the material of the shell, the infill is filled with a weaker and lighter material with tunable parameters. Particularly, the infill can be pre-designed with isotropic microstructures. Three compliance minimization examples are provided to demonstrate the effectiveness of this formulation.
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