theta = 1/2.0 + epsilon # theta for MoreauJeanOSI integrator
#theta = 1.0
E = 210e9 # young Modulus
S = 0.000314 # Beam Section 1 cm for the diameter
#S=0.1
L = 1.0 # length of the beam
l = L/nDof # length of an element
rho = 7800.0 # specific mass
#rho=1.0
g = 9.81 # Gravity
g=0.0
M= SimpleMatrix(nDof,nDof,SPARSE,nDof)
K= SimpleMatrix(nDof,nDof,SPARSE,nDof)
K.setValue(0,0, 1.*E*S/l)
K.setValue(0,1,-1.*E*S/l)
M.setValue(0,0, 1/3.*rho*S*l)
M.setValue(0,1, 1/6.*rho*S*l)
for i in range(1,nDof-1):
K.setValue(i,i,2.*E*S/l)
K.setValue(i,i-1,-1.*E*S/l)
K.setValue(i,i+1,-1.*E*S/l)
M.setValue(i,i,2/3.*rho*S*l)
M.setValue(i,i-1,1/6.*rho*S*l)
M.setValue(i,i+1,1/6.*rho*S*l)
K.setValue(nDof-1,nDof-2,-1.*E*S/l)
K.setValue(nDof-1,nDof-1, 1.*E*S/l)
#nnz=0
# for i in range(n_dof):
# idx = np.where(stiffness_mat_np[i,:]>=1e-14)
# for j in idx[0]:
# K.setValue(i,j,stiffness_mat_np[i,j])
# idx = np.where(mass_mat_np[i,:]>=1e-14)
# nnz = nnz + len(idx[0])
# for j in idx[0]:
# M.setValue(i,j,mass_mat_np[i,j])
# nnz=0
for i in range(n_dof):
for j in range(n_dof):
K.setValue(i, j, stiffness_mat_np[i, j])
M.setValue(i, j, mass_mat_np[i, j])
#print('nnz=', nnz)
#M.display()
print(' -- set initial conditions -- ')
q_0 = u_old.vector().get_local()
v_0 = v_old.vector().get_local()
t0 = 0.0
print(' -- build dynamical system -- ')
body = LagrangianLinearTIDS(q_0, v_0, M)