A Review Paper on Comparison of Numerical Techniques for Finding Approximate Solutions to Boundary Value Problems on Post-Buckling in Functionally Graded Materials

The use of finite element models as research tools in biomechanics and orthopedics grew exponentially over the last two decades. However, the attention to mesh quality, model validation and appropriate energy balance methods and the reporting of these metrics has not kept pace with the general use of finite element modeling. Therefore, the purpose of this review was to develop the nonlinear filter and thermal buckling of an FGM panel under the combined effect of elevated temperature conditions and aerodynamic loading is investigated using a finite element model based on the thin plate theory and von Karman strain-displacement relations to account for moderately large deflection. It is found that the temperature increase has an adverse effect on the FGM panel flutter characteristics through decreasing the critical dynamic pressure. Decreasing the volume fraction enhances flutter characteristics, but this is limited by the structural integrity aspect. Structural finite element analysis has been employed to determine the FGM panel's adaptive response while under the influence of a uniaxial compressive load in excess of its critical buckling value. By increasing the applications of using composite materials inside aviation stages, it is visualized that the versatile FGM plate setup will broaden the operational execution over traditional materials and structures, especially when the structure is presented to a raised temperature. The vicinity of air motion facilitating stream brings about delaying the locking temperature and in stifling under loads, while the temperature build gives route for higher thermal-cycle abundance

Geometrically nonlinear thermo-mechanical analysis of graphene-reinforced moving polymer nanoplates

The main target of this study is to investigate nonlinear transient responses of moving polymer nano-size plates fortified by means of Graphene Platelets (GPLs) and resting on a Winkler-Pasternak foundation under a transverse pressure force and a temperature variation. Two graphene spreading forms dispersed through the plate thickness are studied, and the Halpin-Tsai micro-mechanics model is used to obtain the effective Young's modulus. Furthermore, the rule of mixture is employed to calculate the effective mass density and Poisson's ratio. In accordance with the first order shear deformation and von Kármán theory for nonlinear systems, the kinematic equations are derived, and then nonlocal strain gradient scheme is used to reflect the effects of nonlocal and strain gradient parameters on small-size objects. Afterwards, a combined approach, kinetic dynamic relaxation method accompanied by Newmark technique, is hired for solving the time-varying equation sets, and Fortran program is developed to generate the numerical results. The accuracy of the current model is verified by comparative studies with available results in the literature. Finally, a parametric study is carried out to explore the effects of GPL's weight fractions and dispersion patterns, edge conditions, softening and hardening factors, the temperature change, the velocity of moving nanoplate and elastic foundation stiffness on the dynamic response of the structure. The result illustrates that the effects of nonlocality and strain gradient parameters are more remarkable in the higher magnitudes of the nanoplate speed

Dispersion of Elastic Waves in Functionally Graded CNTs-Reinforced Composite Beams

This work deals with the wave propagation analysis in functionally graded carbon nanotubes (CNTs)-reinforced composite beams lying on an elastic medium. Despite the large amount of experimental and theoretical studies in the literature on the mechanical behavior of composite structures strengthened with CNTs, limited attention has been paid to the effect of an axial graduation of the reinforcing phase on the mechanical response of CNTs-reinforced composite beams. In this paper, CNT fibers are graded across the beam length, according to a power-law function, which expresses a general variation from a linear to parabolic pattern. An Euler-Bernoulli beam theory is considered herein to model the CNTs-reinforced composite structure resting on a Winkler–Pasternak foundation, whose governing equations are derived from the Hamiltonian principle. The theoretical solution of the problem checks for the sensitivity of the mechanical response to different parameters, i.e., the wave number, power index, Winkler and Pasternak coefficients, that could serve for further computational/experimental studies on the same problem, even from a design standpoint

Theoretical and numerical solution for the bending and frequency response of graphene reinforced nanocomposite rectangular plates

none4siIn this work, we study the vibration and bending response of functionally graded gra-phene platelets reinforced composite (FG-GPLRC) rectangular plates embedded on different sub-strates and thermal conditions. The governing equations of the problem along with boundary conditions are determined by employing the minimum total potential energy and Hamilton’s principle, within a higher-order shear deformation theoretical setting. The problem is solved both theoretically and numerically by means of a Navier-type exact solution and a generalized differential quadrature (GDQ) method, respectively, whose results are successfully validated against the finite element pre-dictions performed in the commercial COMSOL code, and similar outcomes available in the litera-ture. A large parametric study is developed to check for the sensitivity of the response to different foundation properties, graphene platelets (GPL) distribution patterns, volume fractions of the rein-forcing phase, as well as the surrounding environment and boundary conditions, with very inter-esting insights from a scientific and design standpoint.openSafarpour M.; Forooghi A.; Dimitri R.; Tornabene F.Safarpour, M.; Forooghi, A.; Dimitri, R.; Tornabene, F

THERMAL BUCKLING AND BENDING ANALYSES OF CARBON FOAM BEAMS SANDWICHED BY COMPOSITE FACES UNDER AXIAL COMPRESSION

The bending and critical buckling loads of a sandwich beam structure subjected to thermal load and axial compression were simulated and temperature distribution across sandwich layers was investigated by finite element analysis and validated analytically. The sandwich structure was consisted of two face sheets and a core, carbon fiber and carbon foam were used as face sheet and core respectively for more efficient stiffness results. The analysis was repeated with different materials to reduce thermal strain and heat flux of sandwich beams. Applying both ends fixed as temperature boundary conditions, temperature induced stresses were observed, steady-state thermal analysis was performed, and conduction through sandwich layers along with their deformation nature were investigated based on the material properties of the combination of face sheets and core. The best material combination was found for the reduction of heat flux and thermal strain, and addition of aerogel material significantly reduced thermal stresses without adding weight to the sandwich structure

Recent Advances in Theoretical and Computational Modeling of Composite Materials and Structures

The advancement in manufacturing technology and scientific research has improved the development of enhanced composite materials with tailored properties depending on their design requirements in many engineering fields, as well as in thermal and energy management. Some representative examples of advanced materials in many smart applications and complex structures rely on laminated composites, functionally graded materials (FGMs), and carbon-based constituents, primarily carbon nanotubes (CNTs), and graphene sheets or nanoplatelets, because of their remarkable mechanical properties, electrical conductivity and high permeability. For such materials, experimental tests usually require a large economical effort because of the complex nature of each constituent, together with many environmental, geometrical and or mechanical uncertainties of non-conventional specimens. At the same time, the theoretical and/or computational approaches represent a valid alternative for designing complex manufacts with more flexibility. In such a context, the development of advanced theoretical and computational models for composite materials and structures is a subject of active research, as explored here for a large variety of structural members, involving the static, dynamic, buckling, and damage/fracturing problems at different scales

Forced vibration characteristics of embedded graphene oxide powder reinforced metal foam nanocomposite plate in thermal environment

Abstract Dynamic behavior of a new class of nanocomposites consisted of metal foam as matrix and graphene oxide powders as reinforcement is presented in this study in the framework of forced vibration. Graphene oxide powders are dispersed through the thickness of a plate made from metal foam material according to four various functionally graded patterns on the basis of the Halpin-Tsai micromechanical homogenization method. Also, three kinds of porosity distributions including two symmetric and one uniform patterns are considered for the metal foam matrix. As external effects, the plate is rested on the Winkler-Pasternak substrate and under uniform thermal and transverse dynamic loadings. By an incorporation of the refined higher order plate theory and Hamilton's principle, the governing equations of the dynamically loaded graphene oxide powder reinforced metal foam nanocomposite plate are derived and then solved with Galerkin exact solution method to achieve the resonance frequencies and dynamic deflections of the structure. Moreover, the influence of different boundary conditions is taken into account. The results indicate that the forced vibrational response of the graphene oxide powder strengthened metal foam nanocomposite plate is dramatically dependent on various parameters such as graphene oxide powders' weight fraction, different boundary conditions, various porosity distributions, foundation parameters and temperature change of uniform thermal loading

Thermomechanical Buckling Analysis of the E&P-FGM Beams Integrated by Nanocomposite Supports Immersed in a Hygrothermal Environment

none4siDue to the widespread use of sandwich structures in many industries and the importance of understanding their mechanical behavior, this paper studies the thermomechanical buckling behavior of sandwich beams with a functionally graded material (FGM) middle layer and two composite external layers. Both composite skins are made of Poly(methyl methacrylate) (PMMA) reinforced by carbon-nano-tubes (CNTs). The properties of the FGM core are predicted through an exponential-law and power-law theory (E&P), whereas an Eshelby-Mori-Tanaka (EMT) formulation is applied to capture the mechanical properties of the external layers. Moreover, different high-order displacement fields are combined with a virtual displacement approach to derive the governing equations of the problem, here solved analytically based on a Navier-type approximation. A parametric study is performed to check for the impact of different core materials and CNT concentrations inside the PMMA on the overall response of beams resting on a Pasternak substrate and subjected to a hygrothermal loading. This means that the sensitivity analysis accounts for different displacement fields, hygrothermal environments, and FGM theories, as a novel aspect of the present work. Our results could be replicated in a computational sense, and could be useful for design purposes in aerospace industries to increase the tolerance of target productions, such as aircraft bodies.Khorasani, Mohammad; Lampani, Luca; Dimitri, Rossana; Tornabene, FrancescoKhorasani, Mohammad; Lampani, Luca; Dimitri, Rossana; Tornabene, Francesc

Thermomechanical buckling analysis of the e&p-fgm beams integrated by nanocomposite supports immersed in a hygrothermal environment

Due to the widespread use of sandwich structures in many industries and the importance of understanding their mechanical behavior, this paper studies the thermomechanical buckling behavior of sandwich beams with a functionally graded material (FGM) middle layer and two composite external layers. Both composite skins are made of Poly(methyl methacrylate) (PMMA) reinforced by carbon-nano-tubes (CNTs). The properties of the FGM core are predicted through an exponential-law and power-law theory (E&P), whereas an Eshelby–Mori–Tanaka (EMT) formulation is applied to capture the mechanical properties of the external layers. Moreover, different high-order displacement fields are combined with a virtual displacement approach to derive the governing equations of the problem, here solved analytically based on a Navier-type approximation. A parametric study is performed to check for the impact of different core materials and CNT concentrations inside the PMMA on the overall response of beams resting on a Pasternak substrate and subjected to a hygrothermal loading. This means that the sensitivity analysis accounts for different displacement fields, hygrothermal environments, and FGM theories, as a novel aspect of the present work. Our results could be replicated in a computational sense, and could be useful for design purposes in aerospace industries to increase the tolerance of target productions, such as aircraft bodies