circle_spline_crack.asv

efg code with matlab

% *************************************************************************
%                 TWO DIMENSIONAL ELEMENT FREE GALERKIN CODE
%                            Nguyen Vinh Phu
%                        LTDS, ENISE, Juillet 2006
% *************************************************************************
function [w,dwdx,dwdy] = circle_spline(x,xI,d,form,xCr)
% Compute cubic and quartic spline function which take account the 
% presence of 1 crack xCr 
% Inputs:
% x (1x2)  : coordinate of point at which w is to be evaluated
% xI (1x2) : coord of node I
% d        : size of the support
% xCr(2,2) : points defining the crack line


% Only normal level sets are computed and stored in nodes
x0  = xCr(1,1); y0 = xCr(1,2);
x1  = xCr(2,1); y1 = xCr(2,2);
t   = 1/norm(seg)*seg;
for i = 1 : numnode
    x = node(i,1);
    y = node(i,2);
    l   = sqrt((x1-x0)*(x1-x0)+(y1-y0)*(y1-y0)) ;
    phi = (y0-y1)*x + (x1-x0)*y + (x0*y1-x1*y0);
    ls(i,1) = phi/l;            % normal LS
    ls(i,2) = ([x y]-xTip)*t';  % tangent LS
    dt(i)   = norm([x y]-xTip); % distances from node I to tip
end

r = sqrt( (x(1,1) - xI(1,1)) .* (x(1,1) - xI(1,1)) + (x(1,2) - xI(1,2)).*(x(1,2) - xI(1,2)) )/d ;

switch form
  case 'cubic_spline' 
     [w,dwdr] = cubic_spline(r);
  case 'quartic_spline'
     [w,dwdr] = quartic_spline(r);
  otherwise 
     error('Grr. Unknown functional form');
end

if (r ~= 0)
    drdx = (x(1,1) - xI(1,1))/(r*d*d) ;
    drdy = (x(1,2) - xI(1,2))/(r*d*d) ;
else
    drdx = 0 ;
    drdy = 0 ;
end

dwdx = dwdr * drdx ;
dwdy = dwdr * drdy ;