Abstract: Dynamic analysis of composite doubly curved panels with variable thickness subjected to different pulse types using Generalized Differential Quadrature method (GDQ) is presented in this study. Panels with variable thickness are used in the construction of aerospace and marine industry. Giving variable thickness to panels can allow the designer to get optimum structural efficiency. For this reason, estimating the response of variable thickness panels is very important to design more reliable structures under dynamic loads. Dynamic equations for composite panels with variable thickness are obtained using virtual work principle. Partial derivatives in the equation of motion are expressed with GDQ and Newmark average acceleration scheme is used for temporal discretization. Several examples are used to highlight the effectiveness of the proposed method. Results are compared with finite element method. Effects of taper ratios, boundary conditions and loading type on the response of composite panel are investigated.
Abstract: In this paper geometrically nonlinear static behavior of laminated composite hollow super-elliptic beams is investigated using generalized differential quadrature method. Super-elliptic beam can have both oval and elliptic cross-sections by adjusting parameters in super-ellipse formulation (also known as Lamé curves). Equilibrium equations of super-elliptic beam are obtained using the virtual work principle. Geometric nonlinearity is taken into account using von-Kármán nonlinear strain-displacement relations. Spatial derivatives in strains are expressed with the generalized differential quadrature method. Transverse shear effect is considered through the first-order shear deformation theory. Static equilibrium equations are solved using Newton-Raphson method. Several composite super-elliptic beam problems are solved with the proposed method. Effects of layer orientations of composite material, boundary conditions, ovality and ellipticity on bending behavior are investigated.
Abstract: The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into classical plate theory (CLPT). A Generalized Differential Quadrature Method (GDQM) approach is utilized and numerical solutions for the critical buckling loads are obtained. Then, molecular dynamics (MD) simulations are performed for a series of zigzag SLGSs with different side-lengths and with various boundary conditions, the results of which are matched with those obtained by the nonlocal plate model to numerical the appropriate values of nonlocal parameter relevant to each type of boundary conditions.
Abstract: In the present study we have investigated axial
buckling characteristics of nanocomposite beams reinforced by
single-walled carbon nanotubes (SWCNTs). Various types of beam
theories including Euler-Bernoulli beam theory, Timoshenko beam
theory and Reddy beam theory were used to analyze the buckling
behavior of carbon nanotube-reinforced composite beams.
Generalized differential quadrature (GDQ) method was utilized to
discretize the governing differential equations along with four
commonly used boundary conditions. The material properties of the
nanocomposite beams were obtained using molecular dynamic (MD)
simulation corresponding to both short-(10,10) SWCNT and long-
(10,10) SWCNT composites which were embedded by amorphous
polyethylene matrix. Then the results obtained directly from MD
simulations were matched with those calculated by the mixture rule
to extract appropriate values of carbon nanotube efficiency
parameters accounting for the scale-dependent material properties.
The selected numerical results were presented to indicate the
influences of nanotube volume fractions and end supports on the
critical axial buckling loads of nanocomposite beams relevant to
long- and short-nanotube composites.
Abstract: The effect of non-homogeneity on the free transverse vibration of thin rectangular plates of bilinearly varying thickness has been analyzed using generalized differential quadrature (GDQ) method. The non-homogeneity of the plate material is assumed to arise due to linear variations in Young’s modulus and density of the plate material with the in-plane coordinates x and y. Numerical results have been computed for fully clamped and fully simply supported boundary conditions. The solution procedure by means of GDQ method has been implemented in a MATLAB code. The effect of various plate parameters has been investigated for the first three modes of vibration. A comparison of results with those available in literature has been presented.
Abstract: In this article, the phenomenon of nonlinear
consolidation in saturated and homogeneous clay layer is studied.
Considering time-varied drainage model, the excess pore water
pressure in the layer depth is calculated. The Generalized Differential
Quadrature (GDQ) method is used for the modeling and numerical
analysis. For the purpose of analysis, first the domain of independent
variables (i.e., time and clay layer depth) is discretized by the
Chebyshev-Gauss-Lobatto series and then the nonlinear system of
equations obtained from the GDQ method is solved by means of the
Newton-Raphson approach. The obtained results indicate that the
Generalized Differential Quadrature method, in addition to being
simple to apply, enjoys a very high accuracy in the calculation of
excess pore water pressure.