program p53       
!-----------------------------------------------------------------------------
!      program 5.3 plane strain of an elastic solid using uniform
!      8-node quadrilateral elements numbered in the x direction
!-----------------------------------------------------------------------------
 use new_library   ;  use geometry_lib   ;   implicit none
 integer::nels,nxe,neq,nband,nn,nr,nip,nodof=2,nod=8,nst=3,ndof,loaded_nodes,&
          i,k,iel,ndim=2
 real::aa,bb,e,v,det ;  character(len=15) :: element = 'quadrilateral'        
!--------------------------- dynamic arrays-----------------------------------
 real    ,allocatable :: kb(:,:),loads(:),points(:,:),dee(:,:),coord(:,:),    &
                         jac(:,:), der(:,:),deriv(:,:),weights(:),            & 
                         bee(:,:),km(:,:),eld(:),sigma(:),g_coord(:,:)
 integer, allocatable :: nf(:,:), g(:) , num(:)  , g_num(:,:) , g_g(:,:)       
!--------------------------input and initialisation----------------------------
  open (10,file='p53.dat',status=    'old',action='read')
  open (11,file='p53.res',status='replace',action='write')                      
  read (10,*) nels,nxe,nn,nip,aa,bb,e,v      ;    ndof=nod*nodof 
  allocate ( nf(nodof,nn), points(nip,ndim),g(ndof), g_coord(ndim,nn),        &
            dee(nst,nst),coord(nod,ndim),jac(ndim,ndim),weights(nip),         &
            der(ndim,nod), deriv(ndim,nod), bee(nst,ndof), km(ndof,ndof),     &
            eld(ndof),sigma(nst),num(nod),g_num(nod,nels),g_g(ndof,nels))       
  nf=1; read(10,*) nr ;if(nr>0)read(10,*)(k,nf(:,k),i=1,nr)
  call formnf(nf);neq=maxval(nf)        ;  nband = 0              
  call deemat (dee,e,v); call sample(element,points,weights)
!----------------loop the elements to find bandwidth and neq-------------------
  elements_1: do iel = 1 , nels
              call geometry_8qx(iel,nxe,aa,bb,coord,num); g_num(:,iel) = num
              call num_to_g(num,nf,g); g_coord(:,num)=transpose(coord)
              g_g(:,iel)=g  ;  if(nband<bandwidth(g))nband=bandwidth(g)
  end do elements_1
    write(11,'(a)') "Global coordinates "
    do k=1,nn;write(11,'(a,i5,a,2e12.4)')"Node",k,"       ",g_coord(:,k);end do
    write(11,'(a)') "Global node numbers "
    do k = 1 , nels; write(11,'(a,i5,a,8i5)')                                  &
                              "Element ",k,"        ",g_num(:,k); end do  
    write(11,'(2(a,i5))')                                                      &
             "There are ",neq ,"  equations and the half-bandwidth is", nband
             allocate(kb(neq,nband+1),loads(0:neq)); kb=.0        
!--------------- element stiffness integration and assembly--------------------
 elements_2: do iel = 1 , nels
             num = g_num(: , iel);  g = g_g( : , iel)
             coord = transpose(g_coord(:,num)) ; km=0.0   
          gauss_pts_1: do i = 1 , nip
               call shape_der (der,points,i) ; jac = matmul(der,coord) 
               det = determinant(jac); call invert(jac)
               deriv = matmul(jac,der) ; call beemat (bee,deriv) 
             km = km + matmul(matmul(transpose(bee),dee),bee) *det* weights(i)
          end do gauss_pts_1   
   call formkb (kb,km,g)
 end do elements_2                                                             
 loads=.0; read(10,*)loaded_nodes,(k,loads(nf(:,k)),i=1,loaded_nodes) 
!----------------------------equation solution--------------------------------
    call cholin(kb) ;call chobac(kb,loads) 
    write(11,'(a)') "The nodal displacements are :"
    write(11,'(a)') "Node         Displacement"
    do k=1,nn; write(11,'(i5,a,2e12.4)') k,"   ",loads(nf(:,k)); end do
!------------------------recover stresses at centroids ------------------------
   i = 1 ; points = .0
        write(11,'(a)') "The centroidal stresses are :"
 elements_3:do iel = 1 , nels
         write(11,'(a,i5)') "Element No.  ",iel 
    num = g_num(: , iel); g = g_g(: , iel)
    coord = transpose(g_coord(:,num)); eld=loads(g)
       call shape_der (der,points,i); jac= matmul(der,coord)
       call invert(jac) ;    deriv= matmul(jac,der)
       call beemat(bee,deriv) ;  sigma = matmul (dee,matmul(bee,eld)) 
       write(11,'(a,i5)') "Point  ",i   ;  write(11,'(3e12.4)') sigma
 end do elements_3
end program p53