boundary_shape_function

BOUNDSHAPEFUNC  Shape functions on the boundary in local coordiantes
SHAPE = boundshapefunc(TYPE,X,Y)

NOTES - On boundary, dimension is smaller e.g. tri6 element, boundary has 
3 node (quadratic) and is 1D

INPUT:
1. X, Y, Z - local coordinates
2. TYPE - string describing different element typeswhat kind of element
   'tri3' - Linear, 2 node 1D shape function 
   'tri 6'- Quadratic, 3 node 1D shape function
   'tet4' - Linear, 3 node triangle shape function
   'tet10' - Quadratic, 6 node triangle shape function

OUTPUT
1. SHAPE - vector of shape functions on this segment of boundary

M Crabb - 29.06.2012

0001 function shape=boundary_shape_function(type,x,y)
0002 %BOUNDSHAPEFUNC  Shape functions on the boundary in local coordiantes
0003 %SHAPE = boundshapefunc(TYPE,X,Y)
0004 %
0005 %NOTES - On boundary, dimension is smaller e.g. tri6 element, boundary has
0006 %3 node (quadratic) and is 1D
0007 %
0008 %INPUT:
0009 %1. X, Y, Z - local coordinates
0010 %2. TYPE - string describing different element typeswhat kind of element
0011 %   'tri3' - Linear, 2 node 1D shape function
0012 %   'tri 6'- Quadratic, 3 node 1D shape function
0013 %   'tet4' - Linear, 3 node triangle shape function
0014 %   'tet10' - Quadratic, 6 node triangle shape function
0015 %
0016 %OUTPUT
0017 %1. SHAPE - vector of shape functions on this segment of boundary
0018 %
0019 %M Crabb - 29.06.2012
0020 
0021 if(strcmp(type,'tri3'))
0022     shape = boundshapetri3(x,y);
0023 elseif(strcmp(type,'tri6'))
0024     shape = boundshapetri6(x,y);
0025 elseif(strcmp(type,'tri10'))
0026     shape = boundshapetri10(x,y);
0027 elseif(strcmp(type,'tet4'))
0028     shape = boundshapetet4(x,y);
0029 elseif(strcmp(type,'tet10'))
0030     shape = boundshapetet10(x,y);
0031 else
0032     error('Incorrect number of input arguments')
0033 end
0034 
0035 
0036 
0037 %1D Shape functions : Equidistant placed in region [-1,1]
0038 
0039 function shape = boundshapetri3(x,y)
0040 shape(1) = 0.5*(1-x);
0041 shape(2) = 0.5*(1+x);
0042 end
0043 
0044 %Ordered correctly (vertex basis functions are first : (1,3,2) order)
0045 function shape = boundshapetri6(x,y)
0046 shape(1) = 0.5*x*(x-1);
0047 shape(2) = 0.5*x*(x+1);
0048 shape(3) = (1-x)*(1+x);
0049 end
0050 
0051 %Ordered correctly (vertex basis functions are first : (1,3,4,2) order)
0052 function shape = boundshapetri10(x,y)
0053 shape(1) = 0.0625*(1-x)*(3*x-1)*(3*x+1);
0054 shape(2) = 0.0625*(1+x)*(3*x-1)*(3*x+1);
0055 shape(3) = -0.5625*(1+x)*(3*x-1)*(1-x);
0056 shape(4) = 0.5625*(1+x)*(3*x+1)*(1-x);
0057 end
0058 
0059 
0060 
0061 
0062 
0063 %2D Shape functions : Place on the unit triangle [0,1]*[0,1] axes
0064 
0065 function shape = boundshapetet4(x,y)
0066 shape(1) = 1-x-y;
0067 shape(2) = x;
0068 shape(3) = y;
0069 end
0070 
0071 %Ordered correctly (i.e. vertex basis function (first 3) are first)
0072 function shape = boundshapetet10(x,y)
0073 shape(1) = (1-x-y)*(1-2*x-2*y);
0074 shape(2) = x*(2*x-1);
0075 shape(3) = y*(2*y-1);
0076 shape(4) = 4*x*(1-x-y);
0077 shape(5) = 4*y*(1-x-y);
0078 shape(6) = 4*x*y;
0079 end
0080 
0081 end