
58 Meshless methods and their numerical properties
by differentiation of the basis functions in the B(x, y) vector. It is further
evident that the present shape functions N
n
(x, y) satisfy the consistency
conditions dened as Equation (3.10) or (3.11) for all the independent basis
functions b
i
(x, y) (i = 1, 2, …, β). In particular, when b
1
(x, y) = 1.0, b
2
(x,y)
= x and b
3
(x,y) = y are taken in the discretised consistency conditions of
Equation (3.11), one can have
=−−∆
Bu vC xyKx uy vS Nxyi1.0(,)*( ,) (,
,)
)
nn
n
N
k
n
k
nn n
n
N
T T
(3.17)
=−−∆
xuvxyKxuyvxS Nxyx iBC(,)*(,)( ,) (,)(2)
nn
n
N
k
n
k
nn nnn
n
N
T T
(3 . 18 )
=−−∆
BCyuvxyKxuyv