Subroutine SHAPALL

Subroutine INTEG-PNTS of the previous section gives the values of the Gauss point coordinates and the corresponding weights for given n (from 1 to 5). Subroutine SHAPE of section 11.5 calculates the values of shape functions and their derivatives for given and given order of approximation p (from 1 to 3). Now we combine these two subroutines to generate the values of the shape functions and their derivatives at all the Gauss points for given n and given p . This is done through the subroutine SHAPALL. To simplify the calculation of n for given p , we make the choice that E is a constant, A is a linear functions of and f is a quadratic function of . Then is given by equation (12.36) and n is found from inequality (12.29). We choose the minimum value of n .

We use the following notation for the variables.

• Scalar variables:
  i,j : indices for do loop (integer)
  n : number of Gauss points (integer)
  ndofel : number of degrees of freedom per element (integer)
  p : order of approximation (integer)
  pbar : temporary variable (integer)
  psi : natural coordinate
  
• Array variables:
  dshap (ndofel) :           values of the shape function derivates at given (real)
  dshaptot (n,ndofel) :    values of the shape function derivatives at all the Gauss points (real)
  psi (n) :                     Gauss point coordinates (real)
  shap (ndofel) :            shape function values at given (real)
  shaptot (n,ndofel) :     shape function values at all the Gauss points (real)
  w (n) :                       weights corresponding to Gauss point coordinates (real)
  
• INPUT variable : p

• OUTPUT variables : n, psi, w, ndofel, shaptot, dshaptot

Now, the subroutine can be written as follows.

Subroutine SHAPALL (p, n, psi, w, ndofel, shaptot, dshaptot)

pbar = max (2p-1, p+2)

if pbar is odd
     n = (pbar+1)/2
     else
     n = (pbar+2)/2
end if

call INTG-PNTS (n, psi, w)

do i = 1, n
      psi = psi (i)
      call SHAPE ( p, psi, ndofel, shap, dshap)
      do j = 1, ndofel
      shaptot ( i, j ) = shap (ndofel)
      dshaptot ( i, j) = dshap (ndofel)
   end do
end do