• Advances in nano research
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• v.7 no.5
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• pp.293-310
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• 2019

In this paper, thermal-buckling behavior of the functionally graded (FG) nanocomposite plates reinforced with graphene oxide powder (GOP) is studied under three types of thermal loading once the plate is supposed to be rested on a two-parameter elastic foundation. The effective material properties of the nanocomposite plate are considered to be graded continuously through the thickness according to the Halpin-Tsai micromechanical scheme. Four types of GOPs' distribution namely uniform (U), X, V and O, are considered in a comparative way in order to find out the most efficient model of GOPs' distribution for the purpose of improving the stability limit of the structure. The governing equations of the plate have been derived based on a refined higher-order shear deformation plate theory incorporated with Hamilton's principle and solved analytically via Navier's solution for a simply supported GOP reinforced (GOPR) nanocomposite plate. Some new results are obtained by applying different thermal loadings to the plate according to the GOPs' negative coefficient of thermal expansion and considering both Winkler-type and Pasternak-type foundation models. Besides, detailed parametric studies have been carried out to reveal the influences of the different types of thermal loading, weight fraction of GOP, aspect and length-to-thickness ratios, distribution type, elastic foundation constants and so on, on the critical buckling load of nanocomposite plates. Moreover, the effects of thermal loadings with various types of temperature rise are investigated comparatively according to the graphical results. It is explicitly shown that the buckling behavior of an FG nanocomposite plate is significantly influenced by these effects.

• Structural Engineering and Mechanics
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• v.85 no.3
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• pp.289-304
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• 2023

The main objective of this paper is to study the effect of porosity on the buckling behavior of thick functionally graded sandwich plate resting on various boundary conditions under different in-plane loads. The formulation is made for a newly developed sandwich plate using a functional gradient material based on a modified power law function of symmetric and asymmetric configuration. Four different porosity distribution are considered and varied in accordance with material propriety variation in the thickness direction of the face sheets of sandwich plate, metal foam also is considered in this study on the second model of sandwich which containing metal foam core and FGM face sheets. New quasi-3D high shear deformation theory is used here for this investigate; the present kinematic model introduces only six variables with stretching effect by adopting a new indeterminate integral variable in the displacement field. The stability equations are obtained by Hamilton's principle then solved by generalized solution. The effect of Pasternak and Winkler elastic foundations also including here. the present model validated with those found in the open literature, then the impact of different parameters: porosities index, foam cells distribution, boundary conditions, elastic foundation, power law index, ratio aspect, side-to-thickness ratio and different in-plane axial loads on the variation of the buckling behavior are demonstrated.

• Structural Engineering and Mechanics
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• v.68 no.5
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• pp.603-619
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• 2018

In this research, an effective computational technique is carried out for nonlinear and post-buckling analyses of cracked imperfect composite plates. The laminated plates are assumed to be moderately thick so that the analysis can be carried out based on the first-order shear deformation theory. Geometric non-linearity is introduced in the way of von-Karman assumptions for the strain-displacement equations. The Ritz technique is applied using Legendre polynomials for the primary variable approximations. The crack is modeled by partitioning the entire domain of the plates into several sub-plates and therefore the plate decomposition technique is implemented in this research. The penalty technique is used for imposing the interface continuity between the sub-plates. Different out-of-plane essential boundary conditions such as clamp, simply support or free conditions will be assumed in this research by defining the relevant displacement functions. For in-plane boundary conditions, lateral expansions of the unloaded edges are completely free while the loaded edges are assumed to move straight but restricted to move laterally. With the formulation presented here, the plates can be subjected to biaxial compressive loads, therefore a sensitivity analysis is performed with respect to the applied load direction, along the parallel or perpendicular to the crack axis. The integrals of potential energy are numerically computed using Gauss-Lobatto quadrature formulas to get adequate accuracy. Then, the obtained non-linear system of equations is solved by the Newton-Raphson method. Finally, the results are presented to show the influence of crack length, various locations of crack, load direction, boundary conditions and different values of initial imperfection on nonlinear and post-buckling behavior of laminates.

• Steel and Composite Structures
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• v.35 no.1
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• pp.61-76
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• 2020

In this paper, the dynamic behaviour of an inclined functionally graded material (FGM) beam with different boundary conditions under a moving mass is investigated based on the first-order shear deformation theory (FSDT). The material properties vary continuously along the beam thickness based on the power-law distribution. The system of motion equations is derived by using Hamilton's principle. The finite element method (FEM) is adopted to develop a general solution procedure. The moving mass is considered on the top surface of the beam instead of supposing it on the mid-plane. In order to consider the Coriolis, centrifugal accelerations and the friction force, the contact force method is used. Moreover, the effects of boundary conditions, the moving mass velocity and various material distributions are studied. For verification of the present results, a comparative fundamental frequency analysis of an FGM beam is conducted and the dynamic transverse displacements of the homogeneous and FGM beams traversed by a moving mass are compared with those in the existing literature. There is a good accord in all compared cases. In this study for the first time in dynamic analysis of the inclined FGM beams, the Coriolis and centrifugal accelerations of the moving mass are taken into account, and it is observed that these accelerations can be ignored for the low-speeds of the moving mass. The new provided results for dynamics of the inclined FGM beams traversed by a moving mass can be significant for the scientific and engineering community in the area of FGM structures.

• Advances in nano research
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• v.12 no.1
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• pp.73-79
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• 2022

Due to the extensive use of concrete structures in various applications, the improvement of their strength and quality has become of great importance. A new way of achieving this purpose is to add different types of nanoparticles to concrete admixtures. In this work, a mathematical model has been employed to analyze the vibration of concrete beams reinforced by graphene oxide (GO) nanoparticles. To verify the accuracy of the presented model, an experimental study has been conducted to compare the compressive strengths of these beams. Since GO nanoparticles are not readily dissolved in water, before producing the concrete samples, the GO nanoparticles are dispersed in the mixture by using a shaker, magnetic striker, ultrasonic devices, and finally, by means of a mechanical mixer. The sinusoidal shear deformation beam theory (SSDBT) is employed to model the concrete beams. The Mori-Tanaka model is used to determine the effective properties of the structure, including the agglomeration influences. The motion equations are calculated by applying the energy method and Hamilton's principle. The vibration frequencies of the concrete beam samples are obtained by an analytical method. Three samples containing 0.02% GO nanoparticles are made and their compressive strengths are measured and compared. There is a good agreement between our results and those of the mathematical model and other papers, with a maximum difference of 1.29% between them. The aim of this work is to investigate the effects of nanoparticle volume fraction and agglomeration and the influences of beam length and thickness on the vibration frequency of concrete structures. The results show that by adding the GO nanoparticles, the vibration frequency of the beams is increased.

• Geomechanics and Engineering
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• v.31 no.1
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• pp.99-112
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• 2022

The present study examines the natural frequencies (NFs) of perfect/imperfect functionally graded sandwich beams (P/IP-FGSBs), which are composed of a porous core constructed of functionally graded materials (FGMs) and a homogenous isotropic metal and ceramic face sheets resting on elastic foundations. To accomplish this, the material properties of the FGSBs are assumed to vary continuously along the thickness direction as a function of the volume fraction of constituents expressed by the modified rule of the mixture, which includes porosity volume fraction represented using four distinct types of porosity distribution models. Additionally, to characterize the reaction of the two-parameter elastic foundation to the Perfect/Imperfect (P/IP) FGSBs, the medium is assumed to be linear, homogeneous, and isotropic, and it is described using the Winkler-Pasternak model. Furthermore, the kinematic relationship of the P/IP-FGSBs resting on the Winkler-Pasternak elastic foundations (WPEFs) is described using trigonometric shear deformation theory (TrSDT), and the equations of motion are constructed using Hamilton's principle. A closed-form solution is developed for the free vibration analysis of P/IP-FGSBs resting on the WPEFs under four distinct boundary conditions (BCs). To validate the new formulation, extensive comparisons with existing data are made. A detailed investigation is carried out for the effects of the foundation coefficients, mode numbers (MNs), porosity volume fraction, power-law index, span to depth ratio, porosity distribution patterns (PDPs), skin core skin thickness ratios (SCSTR), and BCs on the values of the NFs of the P/IP-FGSBs.

• Structural Engineering and Mechanics
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• v.88 no.2
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• pp.159-168
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• 2023

Cost-effective high precision hybrid elements are presented in a hierarchical form for dynamic analysis of plates. The costs associated with controlling the vibrations of ferromagnetic plates can be minimized by adequate determination of the amount of electric current and magnetic field. In the present study, the effect of magnetic field and electric current on nonlinear vibrations of ferromagnetic plates is investigated. The general form of Lorentz forces and Maxwell's equations have been considered for the first time to present new relationships for electromagnetic interaction forces with ferromagnetic plates. In order to derive the governing nonlinear differential equations, the theory of third-order shear deformations of three-dimensional plates has been applied along with the von Kármán large deformation strain-displacement relations. Afterward, the nonlinear equations are discretized using the Galerkin method, and the effect of various parameters is investigated. According to the results, electric current and magnetic field have different effects on the equivalent stiffness of ferromagnetic plates. As the electric current increases and the magnetic field decreases, the equivalent stiffness of the plate decreases. This is a phenomenon reported here for the first time. Furthermore, the magnetic field has a more significant effect on the steady-state deflection of the plate compared to the electric current. Increasing the magnetic field and electric current by 10-times results in a reduction of about 350% and an increase of 3.8% in the maximum steady-state deflection, respectively. Furthermore, the nonlinear frequency decreases as time passes, and these changes become more intense as the magnetic field increases.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.11
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• pp.5979-5986
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• 2013

This study carried out a geometrical nonlinear dynamic analysis of laminated composite shell structures. Based on the first-order shear deformation shell theory and nonlinear formulation of Sanders, the Newmark method and Newton-Raphson iteration are used for dynamic solution considering nonlinear effects. The effects of radius, fiber angles, and layup sequences on the nonlinear dynamic response for various parameters are studied using a nonlinear dynamic finite element program developed for this study. The several numerical results were in good agreement with those reported by other investigators for square composite plates, and the new results reported in this paper show the significant interactions between the radius, fiber angles and layup sequence in the laminate. Key observation points are discussed and a brief design guideline of laminated composite shells is given.

• Smart Structures and Systems
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• v.9 no.6
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• pp.505-534
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• 2012

The present work deals with second order statistics of post buckling response of piezoelectric laminated composite cylindrical shell panel subjected to hygro-thermo-electro-mechanical loading with random system properties. System parameters such as the material properties, thermal expansion coefficients and lamina plate thickness are assumed to be independent of the temperature and electric field and modeled as random variables. The piezoelectric material is used in the forms of layers surface bonded on the layers of laminated composite shell panel. The mathematical formulation is based on higher order shear deformation shell theory (HSDT) with von-Karman nonlinear kinematics. A efficient $C^0$ nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is developed for the implementation of the proposed problems in random environment and is employed to evaluate the second order statistics (mean and variance) of the post buckling load of piezoelectric laminated cylindrical shell panel. Typical numerical results are presented to examine the effect of various environmental conditions, amplitude ratios, electrical voltages, panel side to thickness ratios, aspect ratios, boundary conditions, curvature to side ratios, lamination schemes and types of loadings with random system properties. It is observed that the piezoelectric effect has a significant influence on the stochastic post buckling response of composite shell panel under various loading conditions and some new results are presented to demonstrate the applications of present work. The results obtained using the present solution approach is validated with those results available in the literature and also with independent Monte Carlo Simulation (MCS).

• Composites Research
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• v.12 no.4
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• pp.42-54
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• 1999

FMLC(Fiber-Metal Laminate Composites) is a new structural material combining thin metal laminate with adhesive fiber prepreg, it nearly include all the advantage of metallic materials, for example: good plasticity, impact resistance, processibility, light weight and excellent fatigue properties. This research studied the optimum design of the FMLC subject to various loading conditions using genetic algorithm. The finite element method based on the shear deformation theory was used for the analysis of FMLC. Tasi-Hill failure criterion and Miser yield criterion were taken as fitness functions of the fiber prepreg and the metal laminate, respectively. The design variables were fiber orientation angles. In genetic algorithm, the tournament selection and the uniform crossover method were used. The elitist model was also used to be effective evolution strategy and the creeping random search method was adopted in order to approach a solution with high accuracy. Optimization results were given for various loading conditions and compared with CFRP(Carbon Fiber Reinforced Plastic). The results show that the FMLC is more excellent than the CFRP in point and uniform loading conditions and it is more stable to unexpected loading because the deviation of failure index is smaller than that of CFRP.