function  frame2D_C1_L2_defl (scale) 
% Copyright 2004, J.E. Akin.  All rights reserved.
%  ------------------------------------------------------
%  Matlab graph of i_p-th component value of 1 eigenvector, 
%  at mesh node locations 
%  ------------------------------------------------------

% 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, nt x nod_per_el
% loop   = corners for nod_per_el line polygon
% nod_per_el = Nodes per element
% np     = Number of Points
% nt     = Number of elements
% pre_e  = Element items before connectivity list
  pre_e  = 0 ;
% pre_p  = Nodal items before coordinates
  pre_p = 1;
pre_r=0 
% 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

  clear fid_1 fid_5 
  if ( nargin == 0 )
    scale= 1 
  end % if

%    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  
  fprintf ('Read %g mesh coordinate pairs \n', np)
  ns = size (msh_bc_xyz,2) - pre_p ;   % space dimension
  if ( ns > 2 )
    %b error ('This is not a 1D mesh')
    fprintf ('Not 2D: will use x- & y-coordinate only \n')
  end % if not 2D data
  % msh_bc_xyz has: pre_p items then: x, y
  x = msh_bc_xyz (1:np, (pre_p+1)) ; % extract x column
  fy = msh_bc_xyz (1:np, (pre_p+2)) ; % extract y column

  maxx  = max (x)    ; minx = min (x) ;
  maxy  = max (fy)    ; miny = min (fy) ;
  Max_Len= max((maxx-minx),(maxy-miny)) ;
  
%    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
  fprintf ('Read %g elements connections \n', nt)

  %b ng = 1 ; % number of generalized dof
%% ==================== 1 files ====================
%  file_1 = ['node_results'];
%  filename_1 = [file_1, '.tmp'];
%  fid_1= fopen(filename_1, 'r') ;

%    Get deflections
  load node_results.tmp
%    Get deflections
  load node_results.tmp
  nd = size (node_results, 1) ;
  if ( nd == 0 )
    error ('Error missing file node_results.tmp')
  end % if error
  fprintf ('Read %g mesh deformations \n', nd)

  [X_X, L_X] = max ( abs (node_results (:, pre_r+1)) );  %CL
  [Y_X, L_Y] = max ( abs (node_results (:, pre_r+2)) );  %CL
  Max_Disp = max (X_X, Y_X) ;
  Good_Scale=Max_Len/Max_Disp/20 ;
  %b if (nargin == 0 )
    %b d_scale = Good_Scale ;
    fprintf ('Suggested scale = %g \n', Good_Scale)
  %b end % if

%%    load the file array for this result
%  Result_1 = fscanf (fid_1, '%g  \n', [inf])  
%  NP = size (Result_1, 1)  
%  if ( NP == 0 )
%    error ('Error missing file ', file_1, '.tmp')
%  end % if error
%  if ( NP ~= np )
%    fprintf ('Read %g nodal dof  \n', NP)
%    ng = NP / np ;
%    fprintf ('with %g per node \n', ng )
%  end % if
%  max_p = ng ; 
%  Result_1 = reshape (Result_1, ng, np) ;
%  Result_1 = Result_1' 

% ==================== end 1 files ====================
  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 (nod_per_el + 1) = 0 ;   % Optional pre-allocation

%                set constants
  [loop] = get_El_Loop (nod_per_el) ;


  %b a_1  = Result_1(:, 1) ; % axial nodal disp
  a_1  = node_results (:, pre_r+1)  % axial nodal disp
  Rax  = max(a_1) ; Ran  = min(a_1);
  %b y_1  = Result_1(:, 1) ; % transverse nodal disp
  y_1  = node_results (:, pre_r+2)  % transverse nodal disp
  R1x  = max(y_1) ; R1n  = min(y_1);
  %b dy_1 = Result_1(:, 2) ; % nodal slope
  dy_1 = node_results (:, pre_r+3)   % nodal slope
  R2x  = max(dy_1) ; R2n  = min(dy_1);
  [norm, at] = max ( abs (y_1) );
  if ( norm == 0 )
    error ('Null displacement, nothing to plot')
  end % if
% scale up the displacements
  a_1 = a_1 * scale;
  y_1 = y_1 * scale;

%    Initialize plots
  xmax = max (x)      ; xmin = min (x) ;
  fymax = max (fy)      ; fymin = min (fy) ;
  y_1X = max (y_1)    ; y_1N = min (y_1) ;
  xmax = xmax + y_1X  ; 
  xmin = xmin - y_1X  ;
  fymax = fymax + y_1X  ;  
  fymin = fymin - y_1X  ; 

  ymax = max (y_1X) ;                       
  ymin = min (y_1N) ;                       
  if ( ymin == ymax )
    disp(ymin)
    error('All values are the above constant')
  end % if
  clf                               % clear graphics
  
  hold on                           % hold image for plots
  xlabel ('X')                      % add label 

%    Loop over all elements
  el_min = ymin ; el_max = ymax ;
  for it = 1:nt  ;

%      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
      t_fy  = fy (t_nodes) ;         % y original
      c_x = t_x (loop) ;       % x for nod_per_el line polygon
      c_fy = t_fy (loop) ;       % y for nod_per_el line polygon
      dx = c_x(2) - c_x(1) ; dy = c_fy(2) - c_fy(1) ;
      A = sqrt(dx*dx + dy*dy) ;
      nx = dx/A;  
      ny = dy/A;  % dir cosine normal to beam
      dir_c = [nx, ny]
      T = [nx, ny, 0,0,0,0; ...
          -ny, nx, 0,0,0,0; ...
           0,   0  1,0,0,0; ...
           0,0,0, nx, ny, 0; ...
           0,0,0,-ny, nx, 0; ...
           0,0,0,  0,  0, 1]

      t_a  = a_1 (t_nodes) ;
      t_y  = y_1 (t_nodes) ;         % y at those nodes, only
      t_dy  = dy_1 (t_nodes) ;         % dy at those nodes, only
      % D (1:2:4) = t_y ;
      % D (2:2:4) = t_dy ;
      DXY(1:3:6) = t_a;
      DXY(2:3:6) = t_y;
      DXY(3:3:6) = t_dy;

DXY
% rotate to element direction
      Dxy = T * DXY'
      D (1) = Dxy(2);
D(2)=Dxy(3);
D(3)=Dxy(5);
D(4)=Dxy(6);

%      Loop over local points on the cubic polynomial element
      n_poly = 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 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
        fy_el (k) = H * t_fy ;  % true Y value
        a_el (k) = H * t_a;
        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
        DHC1(1) = (-3 + 3*X*X) * 0.5 / A;
        DHC1(2) = (-1 - 2*X + 3*X*X) * 0.25 ;
        DHC1(3) = ( 3 - 3*X*X) * 0.5d0 / A;
        DHC1(4) = (-1 + 2*X + 3*X*X) * 0.25;
        dy_el (k) = DHC1 * D' ;  % true y value
      end % for k

      deformed_x = x_el + nx* a_el + nx*y_el ;
      deformed_y = fy_el + ny*a_el + ny*y_el ;
      format short
      plot (x, fy, 'ko') % nodal value symbols
      plot (deformed_x, deformed_y)
        max_el = max (y_el) ;
        min_el = min (y_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
  if ( el_max > ymax )
    fprintf ('Max interior deflection was %g \n', el_max)
    ymax = el_max ;
  end % if
  if ( el_min < ymin )
    ymin = el_min ;
    fprintf ('Min interior was %g \n', el_min)
  end % if
  axis ([xmin, xmax, fymin, fymax])   % set axes

    ylabel ('Y')
    title(['Frame Deformed Shape: ', int2str(nt),' Elements, ', ...
           int2str(np), ' Nodes, (', int2str(nod_per_el), ...
           ' per Element)'])
  grid
 
%       -depsc -tiff            % for an eps version
% print ('-dpsc', ['beam_', int2str(i_p), '_defl'])
  hold off
%  v_text = ['Created beam_', int2str(i_p), '_defl.ps'] ;
% fprintf (1,'%s', v_text) ; fprintf (1, ' \n' )
% end of frame2D_C1_L2_defl