Sharif Digital Repository

In this paper, a size-dependent formulation is presented for mechanical analyses of inhomogeneous micro-plates based on the modified couple stress theory. The plate properties can arbitrarily vary through the thickness. The governing differential equations of motion are derived for functionally graded (FG) plates with arbitrary shapes utilizing a variational approach. Moreover, the boundary conditions are provided at smooth parts of the plate periphery and also at the sharp corners of the periphery. Utilizing the derived formulation, the free-vibration behavior as well as the static response of a rectangular FG micro-plate is investigated  

Based on the first-order shear deformation and Donnell's shell theory with von Karman non-linearity, one decoupled stability equation for buckling analysis of functionally graded (FG) and multilayered cylindrical shells with transversely isotropic layers subjected to various cases of combined thermo-mechanical loadings is developed. To this end, the equilibrium equations are uncoupled in terms of the transverse deflection, the force function and a new potential function. Using the adjacent equilibrium method, one decoupled stability equation which is an eighth-order differential equation in terms of transverse deflection is obtained and conveniently solved to present analytical expressions... 

The nonlinear governing equations of three shell theories (Donnell, Love, and Sanders) with first-order approximation and von Kármán’s geometric nonlinearity for laminated sandwich cylindrical shells with isotropic, functionally graded (FG) or isogrid lattice layers are decoupled. This uncoupling makes it possible to present a semi-analytical solution for the nonlinear bending and post-buckling behavior of short and long doubly simply supported, doubly clamped, and cantilever laminated sandwich cylindrical shells subjected to various types of thermo-mechanical loadings. The results for deflection, stress, critical axial traction, and mode shapes in FG shells are verified with those obtained... 

The nonlinear governing equations of three shell theories (Donnell, Love, and Sanders) with first-order approximation and von Kármán’s geometric nonlinearity for laminated sandwich cylindrical shells with isotropic, functionally graded (FG) or isogrid lattice layers are decoupled. This uncoupling makes it possible to present a semi-analytical solution for the nonlinear bending and post-buckling behavior of short and long doubly simply supported, doubly clamped, and cantilever laminated sandwich cylindrical shells subjected to various types of thermo-mechanical loadings. The results for deflection, stress, critical axial traction, and mode shapes in FG shells are verified with those obtained... 

This paper aims to present an explicit relation for thermoelastic damping in nanobeams capturing the small-scale effects on both the continuum mechanics and heat conduction domains. To incorporate small-scale effects, the coupled equations of motion and heat conduction are obtained by employing the nonlocal elasticity theory and the dual-phase-lag heat conduction model. Adopting simple harmonic forms for transverse deflection and temperature increment and solving the governing equations, real and imaginary parts of the frequency are extracted. According to the complex frequency approach, a closed-form size-dependent expression for evaluating thermoelastic damping in nanobeams is derived. To... 

In this paper, a multiplate nonlocal shear model and molecular dynamic simulations are presented to investigate the effects of interlayer shear and nonlocality on the natural frequencies of multilayer graphene sheets (MLGSs). From one aspect in the optimal design of such structures, the interaction between graphene layers, which can significantly vary the static and dynamic behavior due to lack of solidity of layers stack, should be considered. On the other hand, it is requied that the nonlocality phenomenon which has an effective role in the mechanical analysis of nanostructures is taken into account. To this aim, the equation of motion along with corresponding boundary conditions is... 

A novel non-classical continuum model for pull-in analysis of multilayer graphene sheets (MLGSs) is developed to consider the effect of shear interaction between layers based on the nonlocal elasticity theory. The equation governing the motion and corresponding boundary conditions of electrostatically actuated MLGSs are obtained based on the nonlocal shear multiplate theory. The Galerkin method along with the first mode shapes for clamped and cantilever MLGSs together with the method of parameter expansion is used to obtain closed-form expressions of the normalized frequency and time history response. In addition, molecular dynamics (MD) simulations are carried out to validate the pull-in... 

In this paper, a multiplate nonlocal shear model and molecular dynamic simulations are presented to investigate the effects of interlayer shear and nonlocality on the natural frequencies of multilayer graphene sheets (MLGSs). From one aspect in the optimal design of such structures, the interaction between graphene layers, which can significantly vary the static and dynamic behavior due to lack of solidity of layers stack, should be considered. On the other hand, it is requied that the nonlocality phenomenon which has an effective role in the mechanical analysis of nanostructures is taken into account. To this aim, the equation of motion along with corresponding boundary conditions is... 

Design and development of FGMs as the heat treatable materials for high-temperature environments with thermal protection require understanding of exact temperature and thermal stress distribution in the transient state. This information is primary tool in the design and optimization of the devices for failure prevention. Frequently FGMs are used in many applications that presumably produce thermal energy transport via wave propagation. In this study, transient non-Fourier temperature and associated thermal stresses in a functionally graded slab symmetrically heated on both sides are determined. Hyperbolic heat conduction equation in terms of heat flux is used for obtaining temperature... 

Functionally graded materials (FGMs) have been introduced to significantly reduce the temperature and thermal stresses on structures at severe thermal loading. Design and development of FGMs as the heat treatable and energy-absorbing materials for high-temperature and thermal protection systems requires understanding of exact temperature and thermal stress distribution, in order to optimize their resistance to failure. In this study, transient temperature and associated thermal stresses in a functionally graded slab symmetrically heated on both sides are determined by separation of the variables scheme. This method is applied to the heat conduction equation in terms of heat flux for... 

The feasibility and performance of standard and boundary layer perturbation techniques in nonlinear analyses of cylindrical shells are investigated. To this end, the nonlinear axisymmetric behavior of short and long functionally graded (FG) cylindrical shells is considered. The nonlinear governing equations of shell theory with first-order approximation and the von Karman nonlinearity are decoupled. This uncoupling makes it possible to present an analytical solution. A new boundary layer perturbation solution is presented by reducing the governing equations to a normalized form of boundary-layer type. Also, the uncoupled governing equations are solved using standard one-, two-, and...