def lowerOrderAMORE(coordTri,Dmat,coord1,rho1,coord2=None,rho2=None):
if coord2 is None:
coord2=coord1
rho2=rho1
if coord1.shape[0]+coord2.shape[0]==6: nInt=3
elif coord1.shape[0]+coord2.shape[0]==7: nInt=4
else: nInt=6
pos,wei=numericalIntegration.gaussTri(nInt)
LCmat1=getLC(coordTri,rho1)
if rho2 is rho1: LCmat2=LCmat1
else: LCmat2=getLC(coordTri,rho2)
Kloc=np.zeros((2*coord1.shape[0],2*coord2.shape[0]))
for i in range(nInt):
Nmat,_,Jacobian=shapeFunction.shapeTriFE2(coordTri,pos[i,0],pos[i,1])
rho1Value=(Nmat@rho1)[0]
xy=(Nmat@coordTri).reshape(-1)
Bmat1=getStrainMatrix(LCmat1,coord1,xy,rho1Value)
if rho2 is rho1: Bmat2=Bmat1
else:
rho2Value=(Nmat@rho2)[0]
Bmat2=getStrainMatrix(LCmat2,coord2,xy,rho2Value)
Kloc+=0.5*np.matmul(Bmat1.transpose(),np.matmul(Dmat,Bmat2))*Jacobian*wei[i]
return Kloc
def quadraticAMORE(coordTri,Dmat,coord1,rho1,coord2=None,rho2=None):
"""For a straight-edge triangle. It can be curved only at the boundary."""
if coord2 is None:
coord2=coord1
rho2=rho1
if coord1.shape[0]+coord2.shape[0]==6: nInt=3 # 3+3
elif coord1.shape[0]+coord2.shape[0]==7: nInt=4 # 3+4
elif coord1.shape[0]+coord2.shape[0]==8: nInt=6 # 4+4
elif coord1.shape[0]+coord2.shape[0]==9: nInt=4 # 3+6
elif coord1.shape[0]+coord2.shape[0]==10: nInt=6 # 4+6
elif coord1.shape[0]+coord2.shape[0]==12: nInt=9 # 3+9
elif coord1.shape[0]+coord2.shape[0]==13: nInt=12 # 4+9
else: nInt=16 # 9+9
pos,wei=numericalIntegration.gaussTri(nInt)
Kloc=np.zeros((2*coord1.shape[0],2*coord2.shape[0]))
if len(coordTri)==3:
LCmat1=getLC(coordTri,rho1) # A constant matrix
if rho2 is rho1: LCmat2=LCmat1
else: LCmat2=getLC(coordTri,rho2)
for i in range(nInt):
Nmat,_,Jacobian=shapeFunction.shapeTriFE2(coordTri,pos[i,0],pos[i,1])
rho1Value=(Nmat@rho1)[0]
xy=(Nmat@coordTri).reshape(-1)
Bmat1=getStrainMatrix(LCmat1,coord1,xy,rho1Value)
if rho2 is rho1: Bmat2=Bmat1
else:
rho2Value=(Nmat@rho2)[0]
Bmat2=getStrainMatrix(LCmat2,coord2,xy,rho2Value)
Kloc+=0.5*np.matmul(Bmat1.transpose(),np.matmul(Dmat,Bmat2))*Jacobian*wei[i]
elif len(coordTri)==6:
for i in range(nInt):
LCmat1=getLC(coordTri,rho1,pos[i,0],pos[i,1]) # No longer constant
if rho2 is rho1: LCmat2=LCmat1
else: LCmat2=getLC(coordTri,rho2,pos[i,0],pos[i,1])
Nmat,_,Jacobian=shapeFunction.shapeTriQuadFE2(coordTri,pos[i,0],pos[i,1])
rho1Value=pos[i,0]*rho1[0]+pos[i,1]*rho1[1]+pos[i,2]*rho1[2]
xy=(Nmat@coordTri).reshape(-1)
Bmat1=getStrainMatrix(LCmat1,coord1,xy,rho1Value)
if rho2 is rho1: Bmat2=Bmat1
else:
rho2Value=pos[i,0]*rho2[0]+pos[i,1]*rho2[1]+pos[i,2]*rho2[2]
Bmat2=getStrainMatrix(LCmat2,coord2,xy,rho2Value)
Kloc+=0.5*np.matmul(Bmat1.transpose(),np.matmul(Dmat,Bmat2))*Jacobian*wei[i]
else: raise ValueError
return Kloc
def triFE(coord,Dmat):
nInt=1
(pos,wei)=numericalIntegration.gaussTri(nInt)
Kloc=np.zeros((2*len(coord),2*len(coord)))
for i in range(nInt):
(Bmat,Jacobian)=shapeFunction.shapeTriFE(coord,pos[i,0],pos[i,1])[1:3]
Kloc+=0.5*np.matmul(Bmat.transpose(),np.matmul(Dmat,Bmat))*Jacobian*wei[i]
return Kloc