Sharif Digital Repository

The individual and combined effect of shear deformation and rotary inertia on the columns was discussed. It was shown that the shear deformation effect always tends to reduce the buckling load. It was observed that rotary inertia for supported columns has no effect on the buckling load. The critical buckling load of perfect columns subjected to static axial loading was calculated using the Euler-Bernoulli theory  

In this paper, different physical differential equations related to heat transfer and shear deformation of beams are solved by new but powerful analytical methods: Liao's Homotopy method (H.M), Homotopy method with Pade approximation and the He's Homotopy-Perturbation Method (HPM). Nonlinear convective-radiative cooling equation, nonlinear heat equation with cubic nonlinearity and the shear deformation of sandwich beams are used as examples to illustrate the solution procedures. Comparison of the applied methods with exact solutions reveals that both methods are greatly effective  

The response of an infinite Timoshenko beam subjected to a harmonic moving load based on the thirdorder shear deformation theory (TSDT) is studied. The beam is made of laminated composite, and located on a Pasternak viscoelastic foundation. By using the principle of total minimum potential energy, the governing partial differential equations of motion are obtained. The solution is directed to compute the deflection and bending moment distribution along the length of the beam. Also, the effects of two types of composite materials, stiffness and shear layer viscosity coefficients of foundation, velocity and frequency of the moving load over the beam response are studied. In order to... 

The objective of this paper is to apply He's homotopy perturbation method (HPM) to analyze nonlinear free vibration of simply supported Timoshenko beams considering the effects of rotary inertia and shear deformation. First, the equation governing the nonlinear free vibration of a Timoshinko beam is nondimensionalized. Galerkin's projection method is utilized to reduce the governing nonlinear partial differential equation to a nonlinear ordinary differential equation. HPM is then used to find analytic expressions for nonlinear natural frequencies of the pre-stretched beam. A parametric study has also been applied in order to investigate the effects of design parameters such as applied axial... 

In this article an analytical solution is presented for power output from a piezoelectric shallow shell energy harvester using higher order shear deformation theory (HSDT). The energy harvester is made of an elastic substrate layer coupled with one or two surface bonded piezoelectric layers. Mechanical equations of motion with Gauss's equation are derived on the basis of HSDT and solved simultaneously for simply-supported mechanical boundary conditions. The electromechanical frequency response functions that relate the power output and circuit load resistance are identified from the exact solutions. Using Rayleigh damping the influence of structural damping is taken into account. Also... 

In this study, the energy concept along with the first- and third-order shear deformation theories (FSDT and TSDT) are used to predict the large deflection and through the thickness stress of FGM plates. These responses are studied and discussed as a function of plate thickness and the order "n" of a power law function which is considered for the through the thickness variation of the properties of the FGM plate. The results show that the energy method powered by the FSDT and FSDT is capable of predicting the effects of plate thickness on the deformation and the through the thickness stress. Here, also the effects of power "n" on the plate response is clearly depicted. Notably, the... 

In this study, nonlinear bending of functionally graded (FG) circular sector plates with simply supported radial edges subjected to transverse mechanical loading has been investigated. Based on the first-order shear deformation plate theory with von Karman strain-displacement relations, the nonlinear equilibrium equations of sector plates are obtained. Introducing a stress function and a potential function, the governing equations which are five non-linear coupled equations with total order of ten are reformulated into three uncoupled ones including one linear edge-zone equation and two nonlinear interior equations with total order of ten. The uncoupling makes it possible to present... 

In this paper, the large amplitude free vibration of a cantilever Timoshenko beam is considered. To this end, first Hamilton's principle is used in deriving the partial differential equation of the beam response under the mentioned conditions. Then, implementing the Galerkin's method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the natural frequency of the thick-cantilevered beam  

Dynamic and stability analysis of non-uniform Timoshenko beam under axial loads is carried out. In the first case of study, the axial force is assumed to be perpendicular to the shear force, while for the second case the axial force is tangent to the axis of the beam column. For each case, a pair of differential equations coupled in terms of the flexural displacement and the angle of rotation due to bending was obtained. The parameters of the frequency equation were determined for various boundary conditions. Several illustrative examples of uniform and non-uniform beams with different boundary conditions such as clamped supported, elastically supported, and free end mass have been... 

In this article, the edge-zone equation of Mindlin-Reissner plate theory, for composite plates laminated of transversely isotropic layers is studied. Analytical solutions are obtained for both circular sector and completely circular plates with various boundary conditions. The boundary-layer function and its effect on the stresses are numerically studied. Effects of plate thickness and boundary conditions are investigated. The results for circular and completely circular plates are exactly the same as those of rectangular plates in our previous work. Therefore, this boundary layer phenomenon seems to be geometry independent. © Springer-Verlag 2000  

The dissimilar wedge with finite radius under antiplane shear deformation is analyzed. The finite Mellin transform is used to solve the governing differential equation. By simply letting the wedge radius approaches infinity, the solution is obtained  

In the present study, by starting from the reduced form of elasticity displacement field for a long flat laminate, an analytical method is developed in order to accurately calculate the interlaminar stresses near the free edges of generally laminated composite plates under extension. The constant parameter appearing in the reduced displacement field, which describes the global rotational deformation of a laminate, is appropriately obtained by employing an improved first-order shear deformation theory. The accuracy and effectiveness of the proposed first-order theory are verified by means of comparison with the results of Reddy's layerwise theory as a three-dimensional benchmark. Reddy's... 

Based on elasticity theory the reduced form of displacement field is developed for long antisymmertic angle-ply composite laminates subjected to extensional and/or torsional loads. Analytical solutions to the edge-effect problem of such laminates under a uniform axial strain are developed using the first-order shear deformation theory of plates and Reddy's layerwise theory. For a special set of boundary conditions an elasticity solution is presented to verify the validity and accuracy of the layerwise theory. Various numerical results are then developed within the layerwise theory for the interlaminar stresses through the thickness and across the interfaces of antisymmetric angle-ply... 

This is the first research on the frequency analysis of a graphene nanoplatelet composite circular microplate in the framework of a numerical-based generalized differential quadrature method. Stresses and strains are obtained using the higher order shear deformation theory. The microstructure is surrounded by a viscoelastic foundation. Rule of the mixture is used to obtain varying mass density and Poisson’s ratio, whereas the module of elasticity is computed by a modified Halpin–Tsai model. Governing equations and boundary conditions of the graphene nanoplatelet composite circular microplate are obtained by implementing Hamilton’s principle. The results show that outer to inner radius ratio... 

In this article, thermal buckling and frequency analysis of a size-dependent laminated composite cylindrical nanoshell in thermal environment using nonlocal strain–stress gradient theory are presented. The thermodynamic equations of the laminated cylindrical nanoshell are based on first-order shear deformation theory, and generalized differential quadrature element method is implemented to solve these equations and obtain natural frequency and critical temperature of the presented model. The results show that by considering C–F boundary conditions and every even layers’ number, in lower value of length scale parameter, by increasing the length scale parameter, the frequency of the structure... 

Natural frequency and damping behavior of three-layer cylindrical shells with a viscoelastic core layer and functionally graded face layers are studied in this article. Using functionally graded face layers can reduce the stress discontinuity in the face–core interface that causes a catastrophic failure in sandwich structures. The viscoelastic layer is expressed using a fractional-order model, and the functionally graded layers are defined by a power law function. Assuming the classical shell theory for functionally graded layers and the first-order shear deformation theory for the viscoelastic core, equations of motion are derived using Lagrange’s equation and then solved via Rayleigh–Ritz... 

In this paper, free vibration analysis of cross-ply layered composite beams (LCB) with finite length and rectangular cross-section rested on an elastic foundation is investigated by finite element method. Based on the Timoshenko beam theory which includes the shear deformation and rotary inertia, the stiffness and mass matrices of a LCB are obtained using the energy method. Then, the natural frequencies are calculated by employing eigenvalue technique. The obtained results are verified against existing data in the literatures for a LCB with no foundation and uniform cross-section. Good agreements are observed between these cases. In the same way, the natural frequencies of a specific case,... 

An analytical thermoelasticity solution for hollow finite-length cylinders made of functionally graded materials exposed to thermal loads, internal pressure and axial loadings is presented. For this purpose, the governing differential equations of equilibrium are obtained using the principle of minimum total potential energy. A first-order shear deformation shell theory, which accounts for the transverse shear strains and rotations, is considered for expressing displacement field. The governing differential equations are reduced to a set of linear algebraic equations using Fourier expansion series of the displacement field components in the axial coordinate. Subsequently, solution of the... 

In this paper, two corotational modeling for elastic-plastic, mixed hardening materials at finite deformations are introduced. In these models, the additive decomposition of the strain rate tensor as well as the multiplicative decomposition of the deformation gradient tensor is used. For this purpose, corotational constitutive equations are derived for elastic-plastic hardening materials with the non-linear Armstrong-Frederick kinematic hardening and isotropic hardening models. As an application of the proposed constitutive modeling, the governing equations are solved numerically for the simple shear problem with different corotational rates and the stress components are plotted versus the...