def test_parEleGPAssemble(self):
(gPArray,gWArray, mCount, mSize) = gas.parEleGPAssemble(1,[-1/np.sqrt(3),1/np.sqrt(3)],[1,1])
self.assertEqual(gPArray.tolist(),[[-1/np.sqrt(3)],[1/np.sqrt(3)]])
self.assertEqual(gWArray.tolist(),[1.,1.])
self.assertEqual(mCount.tolist(),[0,1])
self.assertEqual(mSize.tolist(),[0,2])
(gPArray,gWArray, mCount, mSize) = gas.parEleGPAssemble(2,[-1/np.sqrt(3),1/np.sqrt(3)],[1,1])
self.assertEqual(gPArray.tolist(),[
[-1/np.sqrt(3), -1/np.sqrt(3),],
[ 1/np.sqrt(3), -1/np.sqrt(3)],
[-1/np.sqrt(3), 1/np.sqrt(3)],
[ 1/np.sqrt(3), 1/np.sqrt(3)],
[-1/np.sqrt(3), -1. ],
[ 1/np.sqrt(3), -1. ],
[-1/np.sqrt(3), 1. ],
[ 1/np.sqrt(3), 1. ],
[-1. , -1/np.sqrt(3)],
[-1. , 1/np.sqrt(3)],
[ 1. , -1/np.sqrt(3)],
[ 1. , 1/np.sqrt(3)]])
self.assertEqual(gWArray.tolist(),[ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])
self.assertEqual(mCount.tolist(),[0, 1, 4])
self.assertEqual(mSize.tolist(),[0, 4, 2])
def test_basisSubsetGaussPoint(self):
dim = 1
numBasis = 2
gaussPoints = [-1/np.sqrt(3),1/np.sqrt(3)]
(gPArray,gWArray, mCount, mSize) = gas.parEleGPAssemble(dim,gaussPoints,[1,1])
basisArray = bas.basisArrayAssemble(dim,numBasis,gaussPoints,gPArray,mCount, mSize)
basisSubset = geas.basisSubsetGaussPoint(0,0,dim,basisArray,mCount,mSize)
self.assertEqual(basisSubset.tolist(), [[0.7886751345948128655, -0.5],[0.211324865405187079, 0.5]])
basisSubset = geas.basisSubsetGaussPoint(0,1,dim,basisArray,mCount,mSize)
self.assertEqual(basisSubset.tolist(), [[0.21132486540518708, -0.5],[0.7886751345948129, 0.5]])
dim = 2
(gPArray,gWArray, mCount, mSize) = gas.parEleGPAssemble(dim,gaussPoints,[1,1])
basisArray = bas.basisArrayAssemble(dim,numBasis,gaussPoints,gPArray,mCount, mSize)
basisSubset = geas.basisSubsetGaussPoint(0,0,dim,basisArray,mCount,mSize)
self.assertEqual(basisSubset.tolist(), [[0.6220084679281462, -0.39433756729740643, -0.39433756729740643],
[0.16666666666666663, 0.39433756729740643, -0.10566243270259354],
[0.16666666666666663, -0.10566243270259354, 0.39433756729740643],
[0.044658198738520435, 0.10566243270259354, 0.10566243270259354]])
basisSubset = geas.basisSubsetGaussPoint(0,1,dim,basisArray,mCount,mSize)
self.assertEqual(basisSubset.tolist(), [[0.16666666666666663, -0.39433756729740643, -0.10566243270259354],
[0.6220084679281462, 0.39433756729740643, -0.39433756729740643],
[0.044658198738520435, -0.10566243270259354, 0.10566243270259354],
[0.16666666666666663, 0.10566243270259354, 0.39433756729740643]])
basisSubset = geas.basisSubsetGaussPoint(2,0,dim,basisArray,mCount,mSize)
self.assertEqual(basisSubset.tolist(), [[0.0, -0.0, -0.39433756729740643],
[0.0, 0.0, -0.10566243270259354],
[0.7886751345948129, -0.5, 0.39433756729740643],
[0.21132486540518708, 0.5, 0.10566243270259354]])
basisSubset = geas.basisSubsetGaussPoint(2,1,dim,basisArray,mCount,mSize)
self.assertEqual(basisSubset.tolist(), [[0.0, -0.0, -0.10566243270259354],
[0.0, 0.0, -0.39433756729740643],
[0.21132486540518708, -0.5, 0.10566243270259354],
[0.7886751345948129, 0.5, 0.39433756729740643]])
def test_newtonRaph(self):
dim = 2
numEle = [2]*dim
eleSize = [1]*dim
numBasis = 2
gaussPoints = [-1/np.sqrt(3),1/np.sqrt(3)]
E = 1#modulus
v = 0.0 #poisons ratio
constit = nr.fint.constitAssemble(E,v,dim)
(gPArray,gWArray, mCount, mSize) = gas.parEleGPAssemble(dim,gaussPoints =gaussPoints)
basisArray = bas.basisArrayAssemble(dim,numBasis,gaussPoints,gPArray, mCount, mSize)
(nodeCoords,eleNodesArray,edgeNodesArray) = mas.meshAssemble(numEle,eleSize)
forceType = np.zeros([np.prod(numEle),np.sum(mCount)])
forceType[[1,3],4] = 3
forces = np.zeros([np.prod(numEle),np.sum(mCount)*dim])
forces[[1,3],4*dim+0]=.5
disp = np.zeros([len(nodeCoords[:,0]),dim])
constraintes = np.ones([len(nodeCoords[:,0]),dim])
constraintes[0:9:3,:] = 0
ui = nr.newtonRaph(dim,numEle,constit,gPArray,gWArray,
mCount, mSize,basisArray,nodeCoords,eleNodesArray,forces,forceType,disp,constraintes)
self.assertEqual(ui.tolist(),
[[ 0.00000000e+00, 0.00000000e+00],
[ 2.5000000000000006e-01, -2.0816681711721685e-17],
[ 5.00000000e-01, -4.097430972836398e-17],
[ 0.00000000e+00, 0.00000000e+00],
[ 2.500000000000001e-01, -2.270991192460361e-17],
[ 5.000000000000001e-01, -5.972088998909374e-17],
[ 0.00000000e+00, 0.00000000e+00],
[ 2.5000000000000006e-01, -2.0809619091596192e-17],
[ 5.000000000000001e-01, -5.205264538381372e-17]])
a = 1
def test_basisArrayAssemble(self):
dim = 1
numBasis = 2
gaussPoints = [-1/np.sqrt(3),1/np.sqrt(3)]
(gPArray,gWArray, mCount, mSize) = gas.parEleGPAssemble(dim,gaussPoints,[1,1])
basisArray = bas.basisArrayAssemble(dim,numBasis,gaussPoints,gPArray,mCount, mSize)
self.assertAlmostEqual(basisArray.tolist(),
[[0.7886751345948129, -0.5, 0.21132486540518708, -0.5],
[0.21132486540518708, 0.5, 0.7886751345948129, 0.5]])
dim = 2
(gPArray,gWArray, mCount, mSize) = gas.parEleGPAssemble(dim,gaussPoints,[1,1])
basisArray = bas.basisArrayAssemble(dim,numBasis,gaussPoints,gPArray, mCount, mSize)
self.assertTrue((np.around(basisArray,8)==
np.array([[ 0.62200847, -0.39433757, -0.39433757, 0.16666667, -0.39433757,
-0.10566243, 0.16666667, -0.10566243, -0.39433757, 0.0446582 ,
-0.10566243, -0.10566243, 0.78867513, -0.5 , -0.39433757,
0.21132487, -0.5 , -0.10566243, 0. , -0. ,
-0.39433757, 0. , -0. , -0.10566243, 0.78867513,
-0.39433757, -0.5 , 0.21132487, -0.10566243, -0.5 ,
0. , -0.39433757, -0. , 0. , -0.10566243,
-0. ],
[ 0.16666667, 0.39433757, -0.10566243, 0.62200847, 0.39433757,
-0.39433757, 0.0446582 , 0.10566243, -0.10566243, 0.16666667,
0.10566243, -0.39433757, 0.21132487, 0.5 , -0.10566243,
0.78867513, 0.5 , -0.39433757, 0. , 0. ,
-0.10566243, 0. , 0. , -0.39433757, 0. ,
0.39433757, -0. , 0. , 0.10566243, -0. ,
0.78867513, 0.39433757, -0.5 , 0.21132487, 0.10566243,
-0.5 ],
[ 0.16666667, -0.10566243, 0.39433757, 0.0446582 , -0.10566243,
0.10566243, 0.62200847, -0.39433757, 0.39433757, 0.16666667,
-0.39433757, 0.10566243, 0. , -0. , 0.39433757,
0. , -0. , 0.10566243, 0.78867513, -0.5 ,
0.39433757, 0.21132487, -0.5 , 0.10566243, 0.21132487,
-0.10566243, 0.5 , 0.78867513, -0.39433757, 0.5 ,
0. , -0.10566243, 0. , 0. , -0.39433757,
0. ],
[ 0.0446582 , 0.10566243, 0.10566243, 0.16666667, 0.10566243,
0.39433757, 0.16666667, 0.39433757, 0.10566243, 0.62200847,
0.39433757, 0.39433757, 0. , 0. , 0.10566243,
0. , 0. , 0.39433757, 0.21132487, 0.5 ,
0.10566243, 0.78867513, 0.5 , 0.39433757, 0. ,
0.10566243, 0. , 0. , 0.39433757, 0. ,
0.21132487, 0.10566243, 0.5 , 0.78867513, 0.39433757,
0.5 ]])).all())
def test_basisSubsetAssemble(self):
dim = 1
numBasis = 2
gaussPoints = [-1/np.sqrt(3),1/np.sqrt(3)]
(gPArray,gWArray, mCount, mSize) = gas.parEleGPAssemble(dim,gaussPoints,[1,1])
basisArray = bas.basisArrayAssemble(dim,numBasis,gaussPoints,gPArray,mCount, mSize)
basisSubsetGP = geas.basisSubsetAssemble(0,dim,basisArray,mCount,mSize,divDim = 0)
self.assertEqual(basisSubsetGP.tolist(),[[0.7886751345948129, 0.21132486540518708], [0.21132486540518708, 0.7886751345948129]])
dim = 2
(gPArray,gWArray, mCount, mSize) = gas.parEleGPAssemble(dim,gaussPoints,[1,1])
basisArray = bas.basisArrayAssemble(dim,numBasis,gaussPoints,gPArray,mCount, mSize)
basisSubsetGP = geas.basisSubsetAssemble(0,dim,basisArray,mCount,mSize,divDim = 0)
self.assertEqual(basisSubsetGP.tolist(),[[0.6220084679281462,0.16666666666666663,0.16666666666666663,0.044658198738520435],
[0.16666666666666663,0.6220084679281462,0.044658198738520435,0.16666666666666663],
[0.16666666666666663,0.044658198738520435,0.6220084679281462,0.16666666666666663],
[0.044658198738520435,0.16666666666666663,0.16666666666666663,0.6220084679281462]])
basisSubsetGP = geas.basisSubsetAssemble(2,dim,basisArray,mCount,mSize,divDim = 0)
self.assertEqual(basisSubsetGP.tolist(),[[0.21132486540518708, 0.0],
[0.7886751345948129, 0.0],
[0.0, 0.7886751345948129],
[0.0, 0.21132486540518708]])
def test_gaussJacobian(self):
dim = 1
numBasis = 2
numEle = [1]*dim
eleSize = [1]*dim
gaussPoints = [-1/np.sqrt(3),1/np.sqrt(3)]
(gPArray,gWArray, mCount, mSize) = gas.parEleGPAssemble(dim,gaussPoints,[1,1])
(nodeCoords,eleNodesArray,edgeNodesArray) = mas.meshAssemble(numEle,eleSize)
basisArray = bas.basisArrayAssemble(dim,numBasis,gaussPoints,gPArray,mCount, mSize)
(intScalFact,hardCodedJac) = geas.gaussJacobian(0,0,0,dim,basisArray,mCount,mSize,nodeCoords,eleNodesArray)
self.assertEqual(intScalFact,0.5)
self.assertEqual(hardCodedJac.tolist(),[[0.5, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]])
(intScalFact,hardCodedJac) = geas.gaussJacobian(0,0,1,dim,basisArray,mCount,mSize,nodeCoords,eleNodesArray)
self.assertEqual(intScalFact,0.5)
self.assertEqual(hardCodedJac.tolist(),[[0.5, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]])
dim = 2
numBasis = 2
numEle = [1]*dim
eleSize = [1]*dim
gaussPoints = [-1/np.sqrt(3),1/np.sqrt(3)]
(gPArray,gWArray, mCount, mSize) = gas.parEleGPAssemble(dim,gaussPoints,[1,1])
(nodeCoords,eleNodesArray,edgeNodesArray) = mas.meshAssemble(numEle,eleSize)
basisArray = bas.basisArrayAssemble(dim,numBasis,gaussPoints,gPArray,mCount, mSize)
(intScalFact,hardCodedJac) = geas.gaussJacobian(0,0,0,dim,basisArray,mCount,mSize,nodeCoords,eleNodesArray)
self.assertEqual(intScalFact,0.25)
self.assertEqual(hardCodedJac.tolist(),[[0.5, 0.0, 0.0], [0.0, 0.5, 0.0], [0.0, 0.0, 0.0]])
(intScalFact,hardCodedJac) = geas.gaussJacobian(0,0,1,dim,basisArray,mCount,mSize,nodeCoords,eleNodesArray)
self.assertEqual(intScalFact,0.25)
self.assertEqual(hardCodedJac.tolist(),[[0.5, 0.0, 0.0], [0.0, 0.5, 0.0], [0.0, 0.0, 0.0]])
(intScalFact,hardCodedJac) = geas.gaussJacobian(0,0,3,dim,basisArray,mCount,mSize,nodeCoords,eleNodesArray)
self.assertEqual(intScalFact,0.25)
self.assertEqual(hardCodedJac.tolist(),[[0.5, 0.0, 0.0], [0.0, 0.5, 0.0], [0.0, 0.0, 0.0]])
(intScalFact,hardCodedJac) = geas.gaussJacobian(1,0,0,dim,basisArray,mCount,mSize,nodeCoords,eleNodesArray)
self.assertEqual(intScalFact,0.5)
self.assertEqual(hardCodedJac.tolist(),[[0.5, 0.0, 0.0], [0.0, 0.5, 0.0], [0.0, 0.0, 0.0]])
# print(Fa)
Fint[eleNodesArray[:, i], :] = Fa + Fint[eleNodesArray[:, i], :]
return (Fint)
if __name__ == '__main__':
dim = 2
numEle = [2] * dim
eleSize = [1] * dim
numBasis = 2
gaussPoints = [-1 / np.sqrt(3), 1 / np.sqrt(3)]
E = 200 * 10**9 #modulus
v = 0 #poisons ratio
#gaussPoints = [-1,1]
(gPArray, gWArray, mCount,
mSize) = gas.parEleGPAssemble(dim, gaussPoints=gaussPoints)
basisArray = bas.basisArrayAssemble(dim, numBasis, gaussPoints, gPArray,
mCount, mSize)
(nodeCoords, eleNodesArray,
edgeNodesArray) = mas.meshAssemble(numEle, eleSize)
disp = np.zeros([len(nodeCoords[:, 0]), dim]) * 0
disp[0:9:3, :] = 0
# disp[1:9:3,:] = .05
disp[2:9:3, 0] = .1
constit = constitAssemble(E, v, dim)
Fin = fintAssemble(dim, numEle, gWArray, mCount, mSize, basisArray,
Fext[tempNodes,:] += fa
return(Fext)
if __name__ == '__main__':
dim = 2
numEle = [1]*dim
eleSize = [1]*dim
numBasis = 2
gaussPoints = [-1/np.sqrt(3),1/np.sqrt(3)]
#gaussPoints = [-1,1]
(gPArray,gWArray, mCount, mSize) = gas.parEleGPAssemble(dim,gaussPoints =gaussPoints)
basisArray = bas.basisArrayAssemble(dim,numBasis,gaussPoints,gPArray, mCount, mSize)
(nodeCoords,eleNodesArray,edgeNodesArray) = mas.meshAssemble(numEle,eleSize)
r = (nodeCoords[:,1]+1)
theta = np.pi/2*(nodeCoords[:,0]/np.max(nodeCoords[:,0]))
nodeCoords[:,0] = r*np.sin(theta)
nodeCoords[:,1] = r*np.cos(theta)
side = 1
forceType = np.zeros([np.prod(numEle),np.sum(mCount)])
forceType[0:numEle[0],side] = 2
forces = np.zeros([np.prod(numEle),np.sum(mCount)*dim])
forces[0:numEle[0],side*dim+0]=1