A review of theories for the modeling and analysis of functionally graded plates and shells

Recent development in modeling and analysis of functionally graded materials and structures

The main objective of this paper is to present the buckling and vibration analysis of thermally pre-stressed functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates resting on the elastic foundation via the variational differential quadrature (VDQ) method. The material properties of nanocomposite plate are considered to continuously vary across the thickness and are estimated according to the modified rule of mixture. The governing equations are derived on the basis of first order shear deformation theory. Applying two-dimensional generalized differential quadrature (GDQ) method, the energy functional of the structure is discretized. Then, based on Hamilton's principle and the VDQ method, the reduced forms of mass and stiffness matrices are obtained. After verifying the accuracy of the present method, comprehensive numerical results are presented to examine the effects of important parameters on the stability and vibrational behavior of the nanotube-reinforced composite annular sector plates. The results indicate that functionally graded distributions of CNTs in the thickness direction and the increase of elastic foundation coefficients can improve the stability of the structure.

Buckling and vibration analysis of embedded functionally graded carbon nanotube-reinforced composite annular sector plates under thermal loading

A refined plate theory for functionally graded plates resting on elastic foundation

Thermally induced bifurcation buckling of rectangular composite plates reinforced with single walled carbon nanotubes is investigated in this research. Distribution of CNTs across the thickness of the plate is considered to be uniform or functionally graded. Thermomechanical properties of the constituents are considered to be temperature dependent. Equivalent properties of the composite media are obtained by means of a modified rule of mixtures approach. First order shear deformation plate theory is used to formulate the governing equations. An energy based Ritz method is used to obtain the algebraic presentation of the stability equations. Due to their fast convergence feature, Chebyshev polynomials are adopted as the basis of the shape functions. Various combinations of clamped, simply supported, sliding supported and free boundary conditions with normal to edge immovable or movable features are considered. An iterative process is applied to obtain the critical buckling temperature of composite plates with temperature dependent material properties. Numerical result are given to explore the influences of various parameters such as characteristics of CNTs, geometrical characteristics of the plate and boundary conditions. It is shown that, in most of the cases, FG-X pattern of the CNTs is the most influential case since it results in higher critical buckling temperatures.

Thermal buckling of temperature dependent FG-CNT reinforced composite plates

Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation

Buckling of rectangular plates made of functionally graded material (FGM) under various types of thermal loading is considered. It is assumed that the plate is in contact with an elastic foundation during deformation. The derivation of equations is based on the classical plate theory. It is assumed that the mechanical and thermal non-homogeneous properties of FGM plate vary smoothly by distribution of power law across the plate thickness. Using the non-linear strain-displacement rela- tions, the equilibrium and stability equations of plates made of FGMs are derived. The boundary conditions for the plate are assumed to be clamped for all edges. The elastic foundation is modelled by two parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. Three distinct analytical solutions are presented to study the thermal buckling problem of thin FGM plates. These methods may be useful to study the eigenvalue problems for other loading types of FGM plates. Closed-form solutions are presented and effects of various parameters, such as geometric characteristics and Pasternak elastic coefficients, are presented comprehensively.

Thermal buckling of clamped thin rectangular FGM plates resting on Pasternak elastic foundation (Three approximate analytical solutions)

M IRZAVAND and Eslami [1] have presented the thermal buckling analysis of simply supported functionally graded material (FGM) cylindrical shells that are integratedwith the surfacebonded piezoelectric actuators. Shen [2] reported the thermal postbuckling behavior of FGM cylindrical shells based on the thirdorder theory of shell via a singular perturbation method. Shen et al. [3,4] also made a study on the postbuckling response of an FGM cylindrical shell embedded in a Pasternak elastic medium and under mechanical load in thermal environments. The buckling analysis of FGM truncated conical shells subjected to combined axial extension loads and hydrostatics pressure and resting on the Pasternak-type elastic foundationwere studied analytically by Sofiyev [5]. Recently, the present authors reported the explicit expressions for mechanical buckling loads of thick FGM cylindrical shells in contact with a Pasternak-type elastic medium [6]. In the present Note, buckling of cylindrical shells made of FGM in contact with the Pasternak elastic foundation subjected to uniform temperature rise is investigated. The material properties of an FGM shell are assumed to be temperature-dependent and vary continuously as a power form through the thickness of a shell. The boundary conditions are assumed to be a fixed simply supported type. The equilibrium and stability equations are obtained, and stability equations are reduced to one equation. The investigation ends in a closed-form solution for the FGM cylindrical shells under uniform thermal load, and numerical results are presented.

Thermal Buckling of Functionally Graded Material Cylindrical Shells on Elastic Foundation

Instability of sandwich plates with functionally graded material (FGM) face sheets, which are in contact with elastic foundation and subjected to thermal or mechanical loading, is considered. The derivation of equations is based on the first-order shear deformation plate theory. It is assumed that the thermo-mechanical non-homogeneous properties of FGM layers vary smoothly by distribution of power law across the plate thickness. Using the non-linear strain–displacement relations, the equilibrium and stability equations of sandwich plates are derived. The boundary conditions for the plate are assumed to be simply supported in all edges. The elastic foundation is modelled by the two parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. Closed-form solutions are presented to calculate the critical buckling load or temperature, which are useful for engineers in design. The effects of the foundation parameters, sandwich plate dimensions, and power law index of the FGM laye...

Thermal and mechanical buckling of sandwich plates with FGM face sheets resting on the Pasternak elastic foundation

Computational modeling of open-channel flows at low Froude (F) numbers is often carried out using the rigid-lid assumption to prescribe the water surface location. However, the presence of ...

Elaheh Bagherizadeh

Papers

Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation

Thermal buckling of clamped thin rectangular FGM plates resting on Pasternak elastic foundation (Three approximate analytical solutions)

Thermal Buckling of Functionally Graded Material Cylindrical Shells on Elastic Foundation

Thermal and mechanical buckling of sandwich plates with FGM face sheets resting on the Pasternak elastic foundation

Comparative Hydrodynamic Study of Rigid-Lid and Level-Set Methods for LES of Open-Channel Flow