function  cubic_beam_pressure_bed   (F_k) 
% Copyright 2008, J.E. Akin.  All rights reserved.
%  ------------------------------------------------------
%  Matlab graph of BEF pressure distribution    m
%  ------------------------------------------------------
% c_x    = x coordinates of nod_per_el line polygon
% c_y    = y coordinates of nod_per_el line polygon
% msh_typ_nodes   = connectivity list for elements
% loop   = corners for nod_per_el line polygon
% nod_per_el = Nodes per element
% np     = Number of Points
% nt     = Number of elements
  pre_e  = 0 ; % Element items before connectivity list
  pre_p = 1; % Nodal items before coordinates
% msh_bc_xyz = Nodal coordinates (with preceeding data)
% t_x    = x coordinates of nod_per_el corners
% t_y    = y coordinates of nod_per_el corners
  i_p = 1 ; % temp
  n_fk = size (F_k, 2) ; % number of different foundationS

%    Read coordinate file and connectivity file
%    integer bc code, real xy pairs for np points (pre_p = 1)
  load msh_bc_xyz.tmp ;  

%    Set control data: number of points
  np = size (msh_bc_xyz,1) ;   % number of nodal points  
  %b fprintf ('Read %g mesh coordinate pairs \n', np)
  ns = size (msh_bc_xyz,2) - pre_p ;   % space dimension
  if ( ns > 1 )
    fprintf ('Not 1D: will use x-coordinate only \n')
  end % if not 2D data
  null (1:np) = 0      ;
  Pts_wide = 2 ;  % fat lines
  
%    Set control data: number elements
  load  msh_typ_nodes.tmp ; % nod_per_el nodes per element
  nt = size (msh_typ_nodes,1) ;          % number of elements in mesh 
  nod_per_el = size (msh_typ_nodes,2) - pre_e -1 ; % nodes per elem
  %b fprintf ('Read %g elements connections \n', nt)

  load node_results.tmp
  nr = size (node_results, 1);
  if ( nr == 0 )
    error ('Error missing file node_results.tmp')
  end % if error
  max_p = size (node_results, 2) ; % number of columns

  H (2)       = 0. ;
  HC1 (4)     = 0. ;
  DHC1 (4)     = 0. ;
  x (np)      = 0.       ;       % pre-allocate array x
  
  t_nodes (nod_per_el) = 0 ;    % Optional pre-allocation
  t_x (nod_per_el) = 0 ;        % Optional pre-allocation
  t_y (nod_per_el) = 0 ;        % Optional pre-allocation
  c_x (nod_per_el + 1) = 0 ;    % Optional pre-allocation
  c_y (nod_per_el + 1) = 0 ;    % Optional pre-allocation

  loop = [1:nod_per_el] ;
  % msh_bc_xyz has: pre_p items then: x, y
  x = msh_bc_xyz (1:np, (pre_p+1)) ; % extract x column
  xmax = max (x)      ; xmin = min (x) ;
  y  = node_results(:, 1) ;
  dy = node_results(:, 2) ;

   clf                               % clear graphics
   hold on                           % hold image for plots
   %b xlabel (['X, Node at 45 deg (', int2str(nod_per_el), ...
     %b ' per element), Element at 90 deg'])
   xlabel ('Height from foot (ft)')

%    Loop over all elements
  %B Pmax = -max (node_results(:, i_p)) * max (F_k) ;
  %B Pmin = -min (node_results(:, i_p)) * max (F_k) ;
  Pmax = -1e6 ; % -min (node_results(:, i_p)) * max (F_k) 
  Pmin =  1e6 ; % max (node_results(:, i_p)) * max (F_k)
  el_max  = Pmax ; el_min= Pmin  ;

%    Loop over all elements
  for it = 1:nt  ;
%      Element foundation stiffness, if any
    if ( n_fk == 1 ) % then homogeneous
      k_f = F_k (1)  ;
    else
      k_f = F_k (it)  ;
    end % if 

%      Extract element connectivity 
    t_nodes = msh_typ_nodes (it, (pre_e+2):(nod_per_el+pre_e+1)); 

%      Skip point elements, if any
    if ( all (t_nodes) ) % then valid line

%      Extract element coordinates & values
      t_x  = x (t_nodes) ;         % x at those nodes, only
      A = t_x(2) - t_x(1) ;        % element length
      t_y  = y (t_nodes) ;       % y at those nodes, only
      t_dy  = dy (t_nodes) ;     % dy at those nodes, only
      D (1:2:4) = t_y ; D (2:2:4) = t_dy ;

%      Loop over local points on the cubic polynomial element
      n_poly = 20 ;   % ceil ( 95 / nt) ;
      for k = 1: (n_poly + 1) % points in parametric space
%          get element parametric interpolation functions
        R     = (k - 1)/n_poly ;   % on 0 to 1
        X     = 2*R - 1 ;          % on -1 to 1
%       H = ELEMENT CUBIC SHAPE FUNCTIONS
%       X = LOCAL COORDINATE OF POINT,    -1 TO +1
%       LOCAL NODE COORD. ARE -1,+1    1------------2
        H (1) = 0.5*(1 - X) ;
        H (2) = 0.5*(1 + X) ;
        x_el (k) = H * t_x ;               % true X value
        HC1(1) = (2 - 3*X + X^3)/4;        
        HC1(2) = (1 - X - X^2 + X^3)*A/8;
        HC1(3) = (2 + 3*X - X^3)/4;    
        HC1(4) = (-1 - X + X^2 + X^3)*A/8;
        y_el (k) = HC1 * D' ;              % true y value
      end % for k
      p_el = -y_el * k_f ;       % true pressure
      plot(x_el, p_el, 'b-', 'LineWidth',Pts_wide)

% Plot the element number
       x_bar = mean (x_el) ;
       y_bar = mean (p_el) ;
       t_text = sprintf ('   (%g)', it);  % offset # from pt
       text (x_bar, y_bar, t_text) % incline

      format short
      max_el = max (p_el)  ;
      min_el = min (p_el)  ;
      if ( max_el > el_max )
        el_max = max_el 
      end % if
      if ( min_el < el_min )
        el_min = min_el 
      end % if
    end % if has non-zero nodes
  end % for all elements
  fprintf ('Max interior pressure was %g \n', el_max)
  fprintf ('Min interior pressure was %g \n', el_min)

%B  % plot node points on axis
  %B  inc_p = 1 ;
  %B  if ( inc_p > 0 )
    %B  for i = 1:np
      %B  t_text = sprintf ('   %g', i);  % offset # from pt
      %B  text (x(i), null(i), t_text, 'Rotation', 45) % incline
    %B  end % for all
    %B  plot (x, null, 'k*')
  %B  end % if

  ylabel (['Pressure (max = ', num2str(el_max), ...
           ', min = ', num2str(el_min), ')'])
  %B ylabel (['Pressure (max = ', num2str(Pmax), ')'])
            %B num2str(Pmax), ', min = ', num2str(Pmin), ')'])
  title(['Bed Pressure: ', int2str(nt),' Elements, ', ...
         int2str(np), ' Nodes, (', int2str(nod_per_el), ...
         ' per Element)'])
  grid
  print -dpng pressure_plot
  hold off
  fprintf ('Saved pressure plot as pressure_plot.png \n')
% end of cubic_beam_pressure_bed