• Structural Engineering and Mechanics
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• v.75 no.1
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• pp.1-18
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• 2020

Present research is aimed to investigate the free vibration behavior of functionally graded (FG) nanocomposite conical panel reinforced by graphene platelets (GPLs) on the elastic foundation. Winkler-Pasternak elastic foundation surrounds the mentioned shell. For each ply, graphaene platelets are randomly oriented and uniformly dispersed in an isotropic matrix. It is assumed that the Volume fraction of GPLs reainforcement could be different from layer to layer according to a functionally graded pattern. The effective elastic modulus of the conical panel is estimated according to the modified Halpin-Tsai rule in this manuscript. Cone is modeled based on the first order shear deformation theory (FSDT). Hamilton's principle and generalized differential quadrature (GDQ) approach are also used to derive and discrete the equations of motion. Some evaluations are provided to compare the natural frequencies between current study and some experimental and theoretical investigations. After validation of the accuracy of the present formulation and method, natural frequencies and the corresponding mode shapes of FG-GPLRC conical panel are developed for different parameters such as boundary conditions, GPLs volume fraction, types of functionally graded and elastic foundation coefficients.

• Steel and Composite Structures
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• v.20 no.1
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• pp.205-225
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• 2016

In this study the finite element method is utilized to predict the deflection and vibration characteristics of rectangular plates made of saturated porous functionally graded materials (PFGM) within the framework of the third order shear deformation plate theory. Material properties of PFGM plate are supposed to vary continuously along the thickness direction according to the power-law form and the porous plate is assumed of the form where pores are saturated with fluid. Various edge conditions of the plate are analyzed. The governing equations of motion are derived through energy method, using calculus of variations while the finite element model is derived based on the constitutive equation of the porous material. According to the numerical results, it is revealed that the proposed modeling and finite element approach can provide accurate deflection and frequency results of the PFGM plates as compared to the previously published results in literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as porosity volume fraction, material distribution profile, mode number and boundary conditions on the natural frequencies and deflection of the PFGM plates in detail. It is explicitly shown that the deflection and vibration behaviour of porous FGM plates are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FGM plates with porosity phases.

• Structural Engineering and Mechanics
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• v.51 no.5
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• pp.727-741
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• 2014

The functionally graded beam (FGB) is investigated in this study on both dynamic and static loading in case of resting on a soil medium rather than on the usual Winkler-Pasternak elastic foundation. The powerful ABAQUS software was used to model the problem applying finite element method. In the present study, two different soil models are taken into account. In the first model, the soil is assumed to be an elastic plane stress medium. In the second soil model, the Drucker-Prager yield criterion, which is one of the most well-known elastic-perfectly plastic constitutive models, is used for modelling the soil medium. The results are shown to evaluate the effects of the different soil models, stiffness values of the elastic soil medium on the normal and shear stress and free vibration properties. A comparison was made to those from the existing literature. Numerical results show that considering real soil as a continuum space affects the results of the bending and the modal properties significantly.

• Steel and Composite Structures
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• v.35 no.2
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• pp.295-306
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• 2020

This paper deals with free vibration analysis of non-uniform column resting on elastic foundations and subjected to follower force at its free end. The internal pores and graphene platelets (GPLs) are distributed in the matrix according to different patterns. The model is proposed with material parameters varying in the thickness of column to achieve graded distributions in both porosity and nanofillers. The elastic modulus of the nanocomposite is obtained by using Halpin-Tsai micromechanics model. The differential quadrature method as an efficient and accurate numerical approach is used to discretize the governing equations and to implement the boundary conditions. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution. Results show that for better understanding of mechanical behavior of nanocomposite column, it is crucial to consider porosities inside the material structure.

• Steel and Composite Structures
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• v.30 no.6
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• pp.567-576
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• 2019

Time-dependent creep analysis of a rotating functionally graded cantilever beam with trapezoidal longitudinal cross section subjected to thermal and inertia loading is investigated using first-order shear deformation theory (FSDT). The model described in this paper is a simple simulation of a turbine blade working under creep condition. The material is a metal based composite reinforced by a ceramic where the creep properties of which has been described by the Sherby's constitutive model. All mechanical and thermal properties except Poisson's ratio are assumed to be variable longitudinally based on the volume fraction of constituent. The principle of virtual work as well as first order shear deformation theory is used to derive governing equations. Longitudinal distribution of displacements and stresses are investigated for various volume fractions of reinforcement. Method of successive elastic solution is employed to obtain history of stresses and creep deformations. It is found that stresses and displacements approach their steady state values after 40000 hours. The results presented in this paper can be used for selection of appropriate longitudinal distribution of reinforcement to achieve the desired stresses and displacements.

• Structural Engineering and Mechanics
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• v.71 no.5
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• pp.525-544
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• 2019

In the present study, buckling and free vibration analyses of annular thin sector plate made of functionally graded materials (FGMs) resting on visco-elastic Pasternak foundation, subjected to external radial, circumferential and shear in-plane loads is investigated. Material properties are assumed to vary along the thickness according to an power law with Poisson's ratio held constant. First, based on the classical plate theory (CPT), the governing equation of motion is derived using Hamilton's principle and then is solved using the generalized differential quadrature method (GDQM). Numerical results are compared to those available in the literature to validate the convergence and accuracy of the present approach. Finally, the effects of power-law exponent, ratio of radii, thickness of the plate, sector angle, and coefficients of foundation on the fundamental and higher natural frequencies of transverse vibration and critical buckling loads are considered for various boundary conditions. Also, vibration and buckling mode shapes of functionally graded (FG) sector plate have been shown in this research. One of the important obtained results from this work show that ratio of the frequency of FG annular sector plate to the corresponding values of homogeneous plate are independent from boundary conditions and frequency number.

• Steel and Composite Structures
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• v.43 no.1
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• pp.31-54
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• 2022

This paper is concerned with the buckling behavior of functionally graded graphene reinforced porous nanocomposite beams based on the finite element method (FEM) using two variables trigonometric shear deformation theory. Both Young's modulus and material density of the FGP beam element are simultaneously considered as grading through the thickness of the beam. The finite element approach is developed using a nonlocal strain gradient theory. The governing equations derived here are solved introducing a 3-nodes beam element, and then the critical buckling load is calculated with different porosity distributions and GPL dispersion patterns. After a convergence and validation study to verify the accuracy of the present model, a comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern of GPL reinforcements on the Buckling behavior of the nanocomposite beam. The effects of various structural parameters such as the dispersion patterns for the graphene and porosity, thickness ratio, boundary conditions, and nonlocal and strain gradient parameters are brought out. The results indicate that porosity distribution and GPL pattern have significant effects on the response of the nanocomposite beams, and the results allows to identify the most effective way to achieve improved buckling behavior of the porous nanocomposite beam.

• Steel and Composite Structures
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• v.43 no.1
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• pp.1-17
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• 2022

The free and forced nonlinear dynamic behaviors of Porous Functionally Graded Material (PFGM) plates are examined by means of a High-Order Implicit Algorithm (HOIA). The formulation is developed using the Third-order Shear Deformation Theory (TSDT). Unlike previous works, the formulation is written without resorting to any homogenization technique neither rule of mixture nor considering FGM as a laminated composite, and the distribution of the porosity is assumed to be gradually variable through the thickness of the PFGM plates. Using the Hamilton principle, we establish the governing equations of motion. The Finite Element Method (FEM) is used to compute approximations of the resulting equations; FEM is adopted using a four-node quadrilateral finite element with seven Degrees Of Freedom (DOF) per node. Nonlinear equations are solved by a HOIA. The accuracy and the performance of the proposed approach are verified by presenting comparisons with literature results for vibration natural frequencies and dynamic response of PFGM plates under external loading. The influences of porosity volume fraction, porosity distribution, slenderness ratio and other parameters on the vibrations of PFGM plate are explored. The results demonstrate the significant impact of different physical and geometrical parameters on the vibration behavior of the PFGM plate.

• Steel and Composite Structures
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• v.45 no.5
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• pp.621-640
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• 2022

In the present article, the vibration response of a geometrically imperfect bi-directional functionally graded plate (2D-FGP) with geometric discontinuities and micro-structural defects (porosities) has been investigated. A porosity model has been developed to incorporate the effective material properties of the bi-directional FGP which varies in two directions i.e. along the axial and transverse direction. The geometric discontinuity is also introduced in the plate in the form of a circular cut-out at the center of the plate. The structural kinematic formulation is based on the non-polynomial trigonometric higher-order shear deformation theory (HSDT). Finite element formulation is done using C° continuous Lagrangian quadrilateral four-noded element with seven degrees of freedom per node. The equations of motion have been derived using a variational approach. Convergence and validation studies have been documented to confirm the accuracy and efficiency of the present formulation. A detailed investigation study has been done to evaluate the influence of the circular cut-out, geometric imperfection, porosity inclusions, partial supports, volume fraction indexes (along with the thickness and length), and geometrical configurations on the vibration response of 2D-FGP. It is concluded that after a particular cut-out dimension, the vibration response of the 2D FGP exhibits non-monotonic behavior.

• Steel and Composite Structures
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• v.46 no.1
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• pp.33-51
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• 2023

This research presents a multi-material topology optimization for functionally graded material (FGM) and nonFGM with elastic buckling criteria. The elastic buckling based multi-material topology optimization of functionally graded steels (FGSs) uses a Jacobi scheme and a Method of Moving Asymptotes (MMA) as an expansion to revise the design variables shown first. Moreover, mathematical expressions for modified interpolation materials in the buckling framework are also described in detail. A Solid Isotropic Material with Penalization (SIMP) as well as a modified penalizing material model is utilized. Based on this investigation on the buckling constraint with homogenization material properties, this method for determining optimal shape is presented under buckling constraint parameters with non-homogenization material properties. For optimal problems, minimizing structural compliance like as an objective function is related to a given material volume and a buckling load factor. In this study, conflicts between structural stiffness and stability which cause an unfavorable effect on the performance of existing optimization procedures are reduced. A few structural design features illustrate the effectiveness and adjustability of an approach and provide some ideas for further expansions.