On the mechanics of FG nanobeams: A review with numerical analysis

Since the classical continuum theories are insufficient to account the small size effects of nanobeams, the nonlocal continuum theories such as Eringen's nonlocal elasticity theory, couple stress theory, strain gradient theory and surface elasticity theory have been proposed by researchers to predict the accurate structural response of isotropic and functionally graded composite nanobeams. This review focuses on research work concerned with analysis of size dependent nanoscale isotropic and functionally graded beams using classical and refined beam theories based on Eringen's nonlocal elasticity theory. The present review article also highlight the possible scope for the future research on nanobeams. In the present study, the authors have developed a new hyperbolic shear deformation theory for the analysis of isotropic and functionally graded nanobeams. The theory satisfy the traction free boundary conditions at the top and the bottom surfaces of the nanobeams. Analytical solutions for the bending, buckling and free vibration analysis of simply-supported nanobeams are obtained using the Navier method. To ensure that the present theory is accurate and valid, the results are compared to previous research

Bending, Vibration and Buckling of Laminated Composite Plates Using a Simple Four Variable Plate Theory

Abstract In the present study, a simple trigonometric shear deformation theory is applied for the bending, buckling and free vibration of cross-ply laminated composite plates. The theory involves four unknown variables which are five in first order shear deformation theory or any other higher order theories. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the shear deformation effect. The transverse displacement includes bending and shear components. The present theory satisfies the zero shear stress conditions at top and bottom surfaces of plates without using shear correction factor. Equations of motion associated with the present theory are obtained using the dynamic version of virtual work principle. A closed form solution is obtained using double trigonometric series suggested by Navier. The displacements, stresses, critical buckling loads and natural frequencies obtained using present theory are compared with previously published results and found to agree well with those

Probabilistic fracture analysis of double edge cracked orthotropic laminated plates using the stochastic extended finite element method

The current computational investigation employs the stochastic extended finite element approach, which the authors have previously developed, to investigate the probabilistic fracture response of double edge cracked orthotropic laminated composite plates under varying stress conditions. The well-known extended finite element method is used to determine the mean and coefficient of variation of stress intensity factors KI and or KII by treating the input parameters as random variables. This is done under the assumption that all of the laminated plate's layers are perfectly bonded to one another and that there is no delamination effect between the layers, the matrix, or the fibres. And it's believed that the plate has through thickness crack. A combination of input random Gaussian variables is used to model the various input factors, such as the lamination angle, the applied loads, and the crack parameters (such the crack length and location). Typical numerical results are shown to investigate the effects of varying degrees of uncertainty in the lamination angle, crack length, crack length to plate width ratio, crack positions, and applied tensile, shear, and combined (tensile and shear) stresses. An excellent agreement arises when the findings generated with the stochastic extended finite element method methodology are assessed against the results found in the published literature through Monte Carlo simulations