• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.1067-1089
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• 2014

In this paper, three dimensional static and dynamic analyses of two dimensional functionally graded annular sector plates have been investigated. The material properties vary through both the radial and axial directions continuously. Graded finite element and Newmark direct integration methods have been used to solve the 3D-elasticity equations in time and space domains. The effects of power law exponents and different boundary conditions on the behavior of FGM annular sector plate have been investigated. Results show that using 2D-FGMs and graded elements have superiority over the homogenous elements and 1D-FGMs. The model has been compared with the result of a 1D-FGM annular sector plate and it shows good agreement.

• Advances in nano research
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• v.12 no.3
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• pp.281-290
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• 2022

In the current research, the thermal buckling characteristics of the bi-directional functionally graded nano-scale tapered beam on the basis of a couple of nonlocal Eringen and classical beam theories are scrutinized. The nonlocal governing equation and associated nonlocal boundary conditions are constructed using the conservation energy principle, and the resulting equations are solved using the generalized differential quadrature method (GDQM). The mechanical characteristics of the produced material are altered along both the beam length and thickness direction, indicating that it is a two-dimensional functionally graded material (2D-FGM). It is thought that the nanostructures are defective because to the presence of porosity voids. Finally, the obtained results are used to design small-scale sensors and make an excellent panorama of developing the production of nanostructures.

• Structural Engineering and Mechanics
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• v.23 no.1
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• pp.63-74
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• 2006

In this paper, the scattering of harmonic elastic anti-plane shear waves by two collinear cracks in functionally graded materials is investigated by means of nonlocal theory. The traditional concepts of the non-local theory are extended to solve the fracture problem of functionally graded materials. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress field near the crack tips. To make the analysis tractable, it is assumed that the shear modulus and the material density vary exponentially with coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips.

• Structural Engineering and Mechanics
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• v.20 no.5
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• pp.559-573
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• 2005

This paper is concerned with the theoretical treatment of transient thermal stresses involving an orthotropic functionally graded thick strip due to nonuniform heat supply in the width direction. The thermal and thermoelastic constants of the strip are assumed to possess orthotropy and vary exponentially in the thickness direction. The transient two-dimensional temperature is analyzed by the methods of Laplace and finite sine transformations. We obtain the exact solution for the simply supported strip under the state of plane strain. Some numerical results for the temperature change, the displacement and the stress distributions are shown in figures. Furthermore, the influence of the orthotropy and nonhomogeneity of the material is investigated.

• Steel and Composite Structures
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• v.24 no.5
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• pp.579-589
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• 2017

The objective of this work is to analyze post-buckling of functionally graded (FG) beams with porosity effect under compression load. Material properties of the beam change in the thickness direction according to power-law distributions with different porosity models. It is known that post-buckling problems are geometrically nonlinear problems. In the nonlinear kinematic model of the beam, total Lagrangian finite element model of two dimensional (2-D) continuum is used in conjunction with the Newton-Raphson method. In the study, the effects of material distribution, porosity parameters, compression loads on the post-buckling behavior of FG beams are investigated and discussed with porosity effects. Also, the effects of the different porosity models on the FG beams are investigated in post-buckling case.

• Steel and Composite Structures
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• v.42 no.5
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• pp.599-615
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• 2022

In the present paper, the numerical dynamic analysis of a functionally graded nano-scale nonuniform tube was investigated according to the high-order beam theory coupled with the nonlocal gradient strain theory. The supposed cross-section is changed along the pipe length, and the material distribution, which combines both metal and ceramics, is smoothly changed in the pipe length direction, which is called axially functionally graded (AFG) pipe. Moreover, the porosity voids are dispersed in the cross-section and the radial pattern that the existence of both material distribution along the tube length and porosity voids make a two-dimensional functionally graded (2D-FG) truncated conical pipe. On the basis of the Hamilton principle, the governing equations and the associated boundary conditions equations are derived, and then a numerical approach is applied to solve the obtained equations.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.473-494
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• 2015

A graded harmonic finite element formulation based on three-dimensional elasticity theory is developed for the structural analysis of 2D functionally graded axisymmetric structures. The mechanical properties of the axisymmetric solid structures composed of two different metals and ceramics are assumed to vary in radial and axial directions according to power law variations as a function of the volume fractions of the constituents. The material properties of the graded element are calculated at the integration points. Effects of material distribution profile on the static deformation, natural frequency and dynamic response analyses of particular axisymmetric solid structures are investigated by changing the power law exponents. It is observed that the displacements, stresses and natural frequencies are severely affected by the variation of axial and radial power law exponents. Good accuracy is obtained with fewer elements in the present study since Fourier series expansion eliminates the need of finite element mesh in circumferential direction and continuous material property distribution within the elements improves accuracy without refining the mesh size in axial and radial directions.

• Structural Engineering and Mechanics
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• v.20 no.4
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• pp.465-476
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• 2005

Free vibration of orthotropic functionally graded beams, whose material properties can vary arbitrarily along the thickness direction, is investigated based on the two-dimensional theory of elasticity. A hybrid state-space/differential quadrature method is employed along with an approximate laminate model, which allows us to obtain the semi-analytical solution easily. With the introduction of continuity conditions at each fictitious interface and boundary conditions at the top and bottom surfaces, the frequency equation for an inhomogeneous beam is derived. A completely exact solution of an FGM beam with material constants varying in exponential way through the thickness is also presented, which serves a benchmark to verify the present method. Numerical results are performed and discussed.

• Advances in aircraft and spacecraft science
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• v.10 no.1
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• pp.19-49
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• 2023

The present study proposes a theoretical and numerical investigation on the dynamic response behaviour of a functional graded (FG) ceramic-metal tapered rotor shaft system, by the differential quadrature finite elements method (DQFEM) to identify the natural frequencies for modelling and analysis of the structure with suitable validations. The purpose of this paper is to explore the influence of heat gradients on the natural frequency of rotation of FG shafts via three-dimensional solid elements, as well as a theoretical examination using the Timoshenko beam mode, which took into account the gyroscopic effect and rotational inertia. The functionally graded material's distribution is described by two distribution laws: the power law and the exponential law. To simulate varied thermal conditions, radial temperature distributions are obtained using the nonlinear temperature distribution (NLTD) and exponential temperature distribution (ETD) approaches. This work deals with the results of the effect on the fundamental frequencies of different material's laws gradation and temperature gradients distributions. Attempts are conducted to identify adequate explanations for the behaviours based on material characteristics. The effect of taper angle and material distribution on the dynamic behaviour of the FG conical rotor system is discussed.

• Smart Structures and Systems
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• v.13 no.1
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• pp.111-135
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• 2014

Based on the Reissner mixed variational theorem (RMVT), finite rectangular layer methods (FRLMs) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, fiber-reinforced composite material (FRCM) and functionally graded material (FGM) sandwich plates subjected to bi-axial compressive loads. In this work, the material properties of the FGM layers are assumed to obey the power-law distributions of the volume fractions of the constituents through the thickness, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the field variables of each individual layer, respectively, and an h-refinement process is adopted to yield the convergent solutions. The accuracy and convergence of the RMVT-based FRLMs with various orders used for expansions of each field variables through the thickness are assessed by comparing their solutions with the exact 3D and accurate two-dimensional ones available in the literature.