Discretisation and Interpolation - The Boundary Element Method with Programming - page 44

4(6)

¦

(3.27)

f e

x N [ N K x

mn () kn () n

n 1

where

N

() ()

[ are linear or quadratic Serendipity shape functions as presented for the

mn

N f are the same infinite shape
functions as for the one-dimensional element, with K substituted for [ and the values
for m(n) and k(n) are given in Table 3.3

one-dimensional finite boundary elements,

() ()

kn

Table 3.3

Values for m and k in Equation (3.27)

n m k

1 1 1

2 2 1

3 2 2

4 1 2

5 3 1

6 3 2

3.6 SUBROUTINES FOR SHAPE FUNCTIONS

Here we start building our library of Subroutines for future use. We create routines for
the calculation of Serendipity, infinite and Lagrange shape functions. Only the listing for
the first one is shown here.
As explained in Chapter 3, some variables will be defined as global, that is, as
accessible to all the subroutines in a MODULE and all programs which use them via the
USE statement. The dimensions for the array Ni, which contains the shape functions,
depend on the type of element and will be set by the main program.

SUBROUTINE Serendip_func(Ni,xsi,eta,ldim,nodes,inci)
!---------------------------------
! Computes Serendipity shape functions Ni(xsi,eta)
! for one and two-dimensional (linear/parabolic) finite
! boundary elements
!---------------------------------
REAL,INTENT(OUT) :: Ni(:) ! Array with shape function
REAL,INTENT(IN) :: xsi,eta! intrinsic coordinates
INTEGER,INTENT(IN):: ldim ! element dimension
INTEGER,INTENT(IN):: nodes ! number of nodes
INTEGER,INTENT(IN):: inci(:)! element incidences
REAL:: mxs,pxs,met,pet ! temporary variables
SELECT CASE (ldim)
CASE (1)! one-dimensional element