Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory

Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets

Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory

A variational free-discontinuity formulation of brittle fracture was given by Francfortand Marigo [1], where the total energy is minimized with respect to the crackgeometry and the displacement field simultaneously. The entire evolution of cracksincluding their initiation and branching is determined by this minimization principlerequiring no further criterion. However, a direct numerical discretization of themodel faces considerable difficulties as the displacement field is discontinuous inthe presence of cracks.

A Continuum Phase Field Model for Fracture

Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach

Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory

An efficient numerical method within the framework of variational formulation is employed to study the buckling and vibration of axially-compressed functionally graded carbon nanotube-reinforced composite (FG-CNTRC) conical shells. The effective material properties of functionally graded composite conical shell are estimated based on the extended rule of mixture. To derive the governing equations, the matrix form of Hamilton's principle is first presented on the basis of the first order shear deformation theory. Then, employing the generalized differential quadrature (GDQ) method in axial direction and periodic differential operators in circumferential direction, the numerical differential and integral operators are introduced to perform the discretization process. The comparison study is carried out to verify the accuracy and efficiency of the proposed method. Numerical results indicate that the volume fraction and types of distribution of CNTs have considerable effects on the buckling and vibration characteristics of FG-CNTRC conical shells subjected to axial loadings.

Numerical study on the buckling and vibration of functionally graded carbon nanotube-reinforced composite conical shells under axial loading

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

In this paper, the free vibration characteristics of embedded functionally graded carbon nanotube-reinforced composite (FG-CNTRC) spherical shells are studied based on a numerical approach. The elastic foundation is considered to be Pasternak-type. Moreover, the extended rule of mixture is used so as to obtain the material properties of FG-CNTRC. The shell is also modeled according to the first-order shear deformation shell theory. The energy functional of the structure is obtained first. Using differential operators, the discretized form of the energy functional is derived. By means of the variational differential quadrature (VDQ) method, the reduced forms of mass and stiffness matrices are then obtained. Selected numerical results are given to investigate the effects of different parameters such as elastic foundation coefficients, boundary conditions, CNT volume fraction, thickness-to-radius ratio and type of distribution of CNT on the vibrations of FG-CNTRC spherical shells.

Vibrational analysis of functionally graded carbon nanotube-reinforced composite spherical shells resting on elastic foundation using the variational differential quadrature method

In this study buckling analysis of a functionally graded conical shell integrated with piezoelectric layers that is subjected to combined action of thermal and electrical loads is presented. The material properties of functionally graded conical shells are assumed to vary continuously through the thickness direction based on a power law form. The governing equations, including the equilibrium and stability equations, are obtained based on the classical shell theory and the Sanders nonlinear kinematics relations. The case of uniform temperature distribution through the shell domain is considered. The prebuckling forces are obtained considering the membrane solutions of linear equilibrium equations. Minimum potential energy criterion is employed to establish the stability equations. The single-mode Galerkin method is used to obtain the critical buckling temperature difference. The results are compared with the known data in the open literature. Finally, some numerical results are presented to study the effects of applied actuator voltage, shell geometry, and power law index of FGM on thermal buckling behavior of the conical shell.

Jalal Torabi

Papers

Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory

Numerical study on the buckling and vibration of functionally graded carbon nanotube-reinforced composite conical shells under axial loading

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

Vibrational analysis of functionally graded carbon nanotube-reinforced composite spherical shells resting on elastic foundation using the variational differential quadrature method

Linear thermal buckling analysis of truncated hybrid FGM conical shells