y2 = np.sin(x2) / np.cos(1) - x2
plt.plot(x2, y2, 'k--')
plt.title('1D FEM')
plt.xlabel('x')
plt.ylabel('u')
#plt.savefig("1D_Fig3.png")
plt.show()
if __name__ == '__main__':
# Preprocessor
nodes, elements = preprocessor()
# Solver
numberOfNodes = nodes.shape[0]
K, b = totalmatrices(nodes, elements)
# Take account of Dirichlet boundary condition.
# Assumption Dirichlet boundary condition u0 = 0
# Assumption diri = [[node number, value]] example: diri = [[0, 0]]
diris = [[0, 0]]
#K, b = fem.dis_to_force(diris, numberOfNodes, K, b)
K, b = fem.dis_to_force2(diris, K, b)
u = solve(K, b)
# Postprocessor
postprocessor(nodes) # Visualize solution.
"""
# Solver: Method 1
K = array([[9, 5, -2, -3, -7, -2, 0, 0], [5, 9, -2, -7, -3, -2, 0, 0],
[-2, -2, 9, 0, 0, 5, -7, -3], [-3, -7, 0, 9, 5, 0, -2, -2],
[-7, -3, 0, 5, 9, 0, -2, -2], [-2, -2, 5, 0, 0, 9, -3, -7],
[0, 0, -7, -2, -2, -3, 9, 5], [0, 0, -3, -2, -2, -7, 5, 9]
]) * 50000 / 2.6
unval = 100 # unknown value
f = array([unval, unval, unval, 0, 10, unval, 10, 0])
# "discon" is a list of displcement constraint.
# discon = [[index number in the K matrix, value], ...]
discon = [[0, 0], [1, 0], [2, 0], [5, 0]]
K, f = fem.dis_to_force2(discon, K, f)
d1 = solve(K, f)
d1 = d1.reshape((4, 2))
new_nodes1 = nodes + d1 * 500
"""
# Solver: Method 2
# Convert displacement constraint into force constraint.
# NewK is a converted matrix.
newK = array([[1, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 9, 5, 0, -2, -2],
[0, 0, 0, 5, 9, 0, -2, -2],
[0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, -2, -2, 0, 9, 5],
[0, 0, 0, -2, -2, 0, 5, 9]])*50000/2.6
plt.plot(x2, y2, 'k--')
plt.title('1D FEM')
plt.xlabel('x')
plt.ylabel('u')
#plt.savefig("1D_Fig3.png")
plt.show()
if __name__ == '__main__':
# Preprocessor
nodes, elements = preprocessor()
# Solver
numberOfNodes = nodes.shape[0]
K, b = totalmatrices(nodes, elements)
# Take account of Dirichlet boundary condition.
# Assumption Dirichlet boundary condition u0 = 0
# Assumption diri = [[node number, value]] example: diri = [[0, 0]]
diris = [[0, 0]]
#K, b = fem.dis_to_force(diris, numberOfNodes, K, b)
K, b = fem.dis_to_force2(diris, K, b)
u = solve(K, b)
# Postprocessor
postprocessor(nodes) # Visualize solution.
# Solver
# Young's modulus and Poisson's ration of soft iron
Young = 200*10**3 # MPa
Poisson = 0.3
D = createDmatrix()
K, B = totalmatrices(nodes, elements)
unval = 100 # unkown value
f = array([unval, unval, unval, 0, 10, unval, 10, 0])
# "discon" is a list of displcement constraint.
# ex) discon = [[index number in the K matrix, value], ...]
discon = [[0, 0], [1, 0], [2, 0], [5, 0]]
K, f = fem.dis_to_force2(discon, K, f)
d = solve(K, f)
d = d.reshape((d.shape[0]/2, 2))
dis_scale = 500 # displacement scale
new_nodes = nodes + d * dis_scale
#eps = total_strain()
# Print Debug
#print "matrixK\n", K
#print "displacement\n", d
# Postprocessor
#plot_displacement(nodes, new_nodes)
