In most cases, one can obtain

a more accurate solution by choosing a set of unequally spaced sampling points.

A common method is to select the zeros of orthogonal polynomials. M(x) is

defined in terms of the Legendre polynomials. M1(x) is the first

derivative of M(x). Here xi, xj, i,j=1, …, N are the

coordinates of the sampling points which may be chosen arbitrarily. (3)

(4)

(5) (6) (7)Also use of zeros of the shifted Legendre polynomials good results,

while some authors have chosen the grid points based on trial (Sherborne and

Pandey 19). 2.2

Boundary Conditions Essential boundary

conditions maybe estimated by DQM; similar to the differential equations are.

From the algebraic equations, each boundary condition substitutes the

equivalent equation, that at each point only a single boundary condition is

satisfied. However, in the case of fourth order differential equations or the

higher order, one must satisfy more than one boundary condition at an specific

boundary. Wang suggested a method base on weighting coefficient matrices by

incorporating the boundary conditions in the GDQ discretization, by significant

limitations in boundary conditions for simply supported or clamped with more

than one boundary condition. Malik and Bert also explored the benefits and the

limitations of this method for various types of boundary conditions. Shu and Du

19 suggested different approach in which two opposite edges are coupled to

provide two solutions for two neighbouring points to the edges.For simply support (8) (9)For clamped support (10) (11)2.3

Domain Decomposition For problems having complicated domains

such as those in delaminated plates or beams or plates with cutouts, the

concept of domain decomposition may be used for solving the problems. With this

concept, first the domain is divided into several subdomains. A local mesh can

be generated for each subdomain with more density near the boundaries. Then, GDQ

representation of the governing differential equations for each domain can be

formulated. In this approach, each region may have different number of sampling

points. Finally, the boundary conditions and the compatibility conditions at

the subdomain interfaces should be taken into consideration and satisfied. 1 GDQM Formulation of Delamination Buckling & POST

BUCKLING The essence of the differential quadrature

method is that the partial (ordinary) derivatives of a function with respect to

a variable in governing equation are approximated by a weighted linear sum of

function values at all discrete points in that direction. Its weighting

coefficients do not relate to any special problem and only depend on the grid

space. Thus any partial differential equation can be easily reduced to a set of

algebraic equations. The Von Karman equations are then used to find an analytical

expression for the post buckling behaviour. After the derivation the results

are used to define the ‘effective width’ of a post buckled plate. The geometry

configuration factors, including number and cross-shape or profile of

stiffener, and lay-out or configuration of stiffeners, rib numbers, fibre angle

as well as the stacking sequences of CFRP, have a great influence on the

buckling behaviours of stiffened composite structures. The role of stiffeners

to increase the buckling capacity of plates without increasing the plate

thickness was researched, and it was concluded that by stiffening a flat

rectangular plate, its critical shear stress increases. The amount of this

increase depends on the aspect ratio and both the type and number of stiffeners.