Analysis of layered panels with mixed edge boundary conditions using state space differential quadrature method

2021 ◽  
pp. 114355
Author(s):  
Balavishnu Udayakumar ◽  
KV Nagendra Gopal
Keyword(s):  
Boundary Conditions ◽  
State Space ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method

Three-Dimensional Static and Free Vibrational Analysis of Graphene Reinforced Composite Circular/Annular Plate Using Differential Quadrature Method

2019 ◽  
Vol 11 (08) ◽  
pp. 1950073 ◽  
Author(s):  
H. Bisheh ◽  
A. Alibeigloo ◽  
M. Safarpour ◽  
A. R. Rahimi
Keyword(s):  
Boundary Conditions ◽  
State Space ◽  
Annular Plate ◽  
Differential Quadrature Method ◽  
Weight Fraction ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Thickness Direction ◽  
Annular Plates ◽  
Reinforced Composite

Free vibrational and bending behavior of functionally graded graphene platelet reinforced composite (FG-GPLRC) circular and annular plate with various boundary conditions is studied using the differential quadrature method (DQM). The weight fraction differs gradually across the thickness direction. Effective elasticity modulus of the nanocomposite has been estimated by the modified Halpin–Tsai model. Using equations of motion in the framework of the elasticity theory and constitutive relation, the state-space first-order differential equation along the thickness direction is derived. A semi-analytical solution is carried out based on the application of DQM along the radial direction and the state-space technique across the thickness of the plate. The present approach is validated by comparing the numerical results with those reported in the literature. Effect of graphene platelets (GPLs) weight fraction, different GPL distribution patterns, thickness-to-radius and outer-to-inner radius ratios and edge boundary conditions on the static and vibrational behavior of GPLs reinforced composite circular/annular plates are examined. The results implied that GPLs can improve the composite strength against different loading and GPLs could have an extraordinary reinforcing influence on the static and vibrational behavior of the circular/annular plates.

A modified state space differential quadrature method for free vibration analysis of soft-core sandwich panels

2017 ◽  
Vol 21 (6) ◽  
pp. 1843-1879 ◽  
Author(s):  
Balavishnu Udayakumar ◽  
KV Nagendra Gopal
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
State Space ◽  
Vibration Analysis ◽  
Differential Quadrature Method ◽  
Sandwich Panels ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Soft Core ◽  
Quadrature Method

Modifications and improvements to conventional state space differential quadrature method are proposed for free vibration analysis of thick, soft-core sandwich panels with arbitrary edge boundary conditions, using an exact two-dimensional elasticity model. The modifications are based on a systematic procedure to implement all possible combinations of edge boundary conditions including simply supported, clamped, free and guided edges. Natural frequencies and mode shapes are obtained and compared with exact elasticity solutions from state space method and approximate solution from finite element simulations; demonstrating the high numerical accuracy and rapid convergence of the modified method. Further, the proposed framework is compared to the conventional implementation of the state space differential quadrature method for thick cantilever sandwich panels and is shown to give results with better accuracy and faster convergence.

Elasticity Solution of Free Vibration and Bending Behavior of Functionally Graded Carbon Nanotube-Reinforced Composite Beam with Thin Piezoelectric Layers Using Differential Quadrature Method

2015 ◽  
Vol 07 (01) ◽  
pp. 1550002 ◽  
Author(s):  
A. Alibeigloo ◽  
K. M. Liew
Keyword(s):  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Mechanical Behavior ◽  
State Space ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Reinforced Composite ◽  
Piezoelectric Layers

Based on the theory of elasticity, bending and free vibrational analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam embedded in piezoelectric layers are carried out, using the state-space differential quadrature method (DQM). Applying the DQM to the governing differential equations and boundary conditions along the longitudinal directions, new state equations about state variables at discrete points are derived. By using the state-space technique across the thickness direction, semi- analytical closed form solutions are derived. The method is validated by comparing numerical results for beams without piezoelectric layers. Both the direct and the inverse piezoelectric effects are investigated and the influence of piezoelectric layers on the mechanical behavior of beam is studied. Furthermore, the effects of CNT volume fraction, kind of CNT distribution, length to thickness ratio and edge boundary conditions on the mechanical behavior of the beams are examined.

Structural Analysis by the Differential Quadrature Method Using Modified Weighting Matrices

1998 ◽  
Author(s):  
Siu-Tong Choi ◽  
Yu-Tuan Chou
Keyword(s):  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Sampling Point ◽  
Order Partial Differential Equation ◽  
Quadrature Method ◽  
The Finite Element Method ◽  
Computationally Efficient ◽  
Base Points ◽  
Sampling Points

Abstract The differential quadrature method has lately been more and more often used for analysis of engineering problems as an alternative for the finite element method or finite difference method. In this paper, static, dynamic and buckling analyses of structural components are performed by the differential quadrature method. To improve the accuracy of this method, an approach is proposed for selecting the sampling points which include base points and conditional points. The base points are taken as the roots of the Legendre polynomials. Accuracy of the problems analyzed will be increased by using the base points. The conditional points are determined according to boundary conditions and specified conditions of external load. A modified algorithm is proposed for applying two or more boundary conditions in a sampling point at boundary of domain, such that the higher-order partial differential equation can be solved without adding new sampling points. By applying this approach to variety problems, such as deflections of beam under nonuniformly distributed loading, vibration and buckling analyses of beam and plate, it is found that numerical results of the present approach are more accurate than those obtained by the equally-spaced differential quadrature method and is computationally efficient.

scholarly journals A Mixed Layerwise-Differential Quadrature Method for 3-D Vibration and Buckling Analyses of Orthogonally Stiffened Composite Conical Shell

2019 ◽  
Vol 24 (2) ◽  
pp. 217-227
Author(s):  
Mostafa Talebitooti
Keyword(s):  
Boundary Conditions ◽  
Conical Shell ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Algebraic Equations ◽  
Discrete Elements ◽  
Arbitrary Boundary ◽  
Stiffened Shells

A layerwise-differential quadrature method (LW-DQM) is developed for the vibration analysis of a stiffened laminated conical shell. The circumferential stiffeners (rings) and meridional stiffeners (stringers) are treated as discrete elements. The motion equations are derived by applying the Hamilton’s principle. In order to accurately account for the thickness effects and the displacement field of stiffeners, the layerwise theory is used to discretize the equations of motion and the related boundary conditions through the thickness. Then, the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equations applying the DQM in the meridional direction. The advantage of the proposed model is its applicability to thin and thick unstiffened and stiffened shells with arbitrary boundary conditions. In addition, the axial load and external pressure is applied to the shell as a ratio of the global buckling load and pressure. This study demonstrates the accuracy, stability, and the fast rate of convergence of the present method, for the buckling and vibration analyses of stiffened conical shells. The presented results are compared with those of other shell theories and a special case where the angle of conical shell approaches zero, i.e. a cylindrical shell, and excellent agreements are achieved.

Analysis of free vibration of an isotropic plate with surface or internal long crack using generalized differential quadrature method

2019 ◽  
Vol 55 (1-2) ◽  
pp. 42-52
Author(s):  
Milad Ranjbaran ◽  
Rahman Seifi
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Isotropic Plate ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Generalized Differential

This article proposes a new method for the analysis of free vibration of a cracked isotropic plate with various boundary conditions based on Kirchhoff’s theory. The isotropic plate is assumed to have a part-through surface or internal crack. The crack is considered parallel to one of the plate edges. Existence of the crack modified the governing differential equations which were formulated based on the line-spring model. Generalized differential quadrature method discretizes the obtained governing differential equations and converts them into an algebraic system of equations. Then, an eigenvalue analysis was used to determine the natural frequencies of the cracked plates. Some numerical results are given to demonstrate the accuracy and convergence of the obtained results. To demonstrate the efficiency of the method, the results were compared with finite element solutions and available literature. Also, effects of the crack depth, its location along the thickness, the length of the crack and different boundary conditions on the natural frequencies were investigated.

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