def coeff_tau_eq(x, y):
result = [0, _c['h_0'][3]]
for i in range(M):
result.append((_c['h_n'][0][0] * sinh(a_[0][0] * alpha[i] * y) +
_c['h_n'][0][1] * sinh(a_[0][1] * alpha[i] * y)) *
cos(alpha[i] * x) * alpha[i])
result.append((_c['h_n'][1][0] * cosh(a_[0][0] * alpha[i] * y) +
_c['h_n'][1][1] * cosh(a_[0][1] * alpha[i] * y)) *
cos(alpha[i] * x) * alpha[i])
result.append((_c['h_n'][2][0] * sinh(a_[0][0] * alpha[i] * y) +
_c['h_n'][2][1] * sinh(a_[0][1] * alpha[i] * y)) *
cos(alpha[i] * x))
result.append((_c['h_n'][3][0] * cosh(a_[0][0] * alpha[i] * y) +
_c['h_n'][3][1] * cosh(a_[0][1] * alpha[i] * y)) *
cos(alpha[i] * x))
result.extend([0, _c['g_0'][3]])
for i in range(M):
result.append((_c['g_n'][0][0] * cosh(a_[1][0] * beta[i] * x) +
_c['g_n'][0][1] * cosh(a_[1][1] * beta[i] * x)) *
cos(beta[i] * y) * beta[i])
result.append((_c['g_n'][1][0] * sinh(a_[1][0] * beta[i] * x) +
_c['g_n'][1][1] * sinh(a_[1][1] * beta[i] * x)) *
cos(beta[i] * y) * beta[i])
result.append((_c['g_n'][2][0] * sinh(a_[1][0] * beta[i] * x) +
_c['g_n'][2][1] * sinh(a_[1][1] * beta[i] * x)) *
cos(beta[i] * y))
result.append((_c['g_n'][3][0] * cosh(a_[1][0] * beta[i] * x) +
_c['g_n'][3][1] * cosh(a_[1][1] * beta[i] * x)) *
cos(beta[i] * y))
return result
def coeff_sigma_y_eq(x, y):
result = [0, 0]
'''
if x == 0:
result.extend([0, ] * (4*M + 2))
for i in range(M):
result.extend(
[
0,
sum(_c['g_n'][1]) * beta[i] * sin(beta[i]*y),
sum(_c['g_n'][2]) * sin(beta[i]*y),
0
]
)
elif y == 0:
for i in range(M):
result.extend(
[0, 0, sum(_c['h_n'][2]) * sin(alpha[i]*x), 0]
)
result.extend([0, ] * (4*M + 2))
else:
for i in range(M):
result.append(
(
_c['h_n'][0][0] * cosh(a_[0][0] * alpha[i] * y) +
_c['h_n'][0][1] * cosh(a_[0][1] * alpha[i] * y)
) * sin(alpha[i]*x) * alpha[i]
)
result.append(
(
_c['h_n'][1][0] * sinh(a_[0][0] * alpha[i] * y) +
_c['h_n'][1][1] * sinh(a_[0][1] * alpha[i] * y)
) * sin(alpha[i]*x) * alpha[i]
)
result.append(
(
_c['h_n'][2][0] * cosh(a_[0][0] * alpha[i] * y) +
_c['h_n'][2][1] * cosh(a_[0][1] * alpha[i] * y)
) * sin(alpha[i]*x)
)
result.append(
(
_c['h_n'][3][0] * sinh(a_[0][0] * alpha[i] * y) +
_c['h_n'][3][1] * sinh(a_[0][1] * alpha[i] * y)
) * sin(alpha[i]*x)
)
result.extend([0, 0])
for i in range(M):
result.append(
(
_c['g_n'][0][0] * sinh(a_[1][0] * beta[i] * x) +
_c['g_n'][0][1] * sinh(a_[1][1] * beta[i] * x)
) * sin(beta[i]*y) * beta[i]
)
result.append(
(
_c['g_n'][1][0] * cosh(a_[1][0] * beta[i] * x) +
_c['g_n'][1][1] * cosh(a_[1][1] * beta[i] * x)
) * sin(beta[i]*y) * beta[i]
)
result.append(
(
_c['g_n'][2][0] * cosh(a_[1][0] * beta[i] * x) +
_c['g_n'][2][1] * cosh(a_[1][1] * beta[i] * x)
) * sin(beta[i]*y)
)
result.append(
(
_c['g_n'][3][0] * sinh(a_[1][0] * beta[i] * x) +
_c['g_n'][3][1] * sinh(a_[1][1] * beta[i] * x)
) * sin(beta[i]*y)
)
'''
for i in range(M):
result.append((_c['h_n'][0][0] * cosh(a_[0][0] * alpha[i] * y) +
_c['h_n'][0][1] * cosh(a_[0][1] * alpha[i] * y)) *
sin(alpha[i] * x) * alpha[i])
result.append((_c['h_n'][1][0] * sinh(a_[0][0] * alpha[i] * y) +
_c['h_n'][1][1] * sinh(a_[0][1] * alpha[i] * y)) *
sin(alpha[i] * x) * alpha[i])
result.append((_c['h_n'][2][0] * cosh(a_[0][0] * alpha[i] * y) +
_c['h_n'][2][1] * cosh(a_[0][1] * alpha[i] * y)) *
sin(alpha[i] * x))
result.append((_c['h_n'][3][0] * sinh(a_[0][0] * alpha[i] * y) +
_c['h_n'][3][1] * sinh(a_[0][1] * alpha[i] * y)) *
sin(alpha[i] * x))
result.extend([0, 0])
for i in range(M):
result.append((_c['g_n'][0][0] * sinh(a_[1][0] * beta[i] * x) +
_c['g_n'][0][1] * sinh(a_[1][1] * beta[i] * x)) *
sin(beta[i] * y) * beta[i])
result.append((_c['g_n'][1][0] * cosh(a_[1][0] * beta[i] * x) +
_c['g_n'][1][1] * cosh(a_[1][1] * beta[i] * x)) *
sin(beta[i] * y) * beta[i])
result.append((_c['g_n'][2][0] * cosh(a_[1][0] * beta[i] * x) +
_c['g_n'][2][1] * cosh(a_[1][1] * beta[i] * x)) *
sin(beta[i] * y))
result.append((_c['g_n'][3][0] * sinh(a_[1][0] * beta[i] * x) +
_c['g_n'][3][1] * sinh(a_[1][1] * beta[i] * x)) *
sin(beta[i] * y))
return result
def coeff_u_eq(x, y):
result = [_c['h_0'][0], _c['h_0'][3] * y]
if x == 0:
for i in range(M):
result.append(_c['h_n'][0][0] * cosh(a_[0][0] * alpha[i] * y) +
_c['h_n'][0][1] * cosh(a_[0][1] * alpha[i] * y))
result.append(_c['h_n'][1][0] * sinh(a_[0][0] * alpha[i] * y) +
_c['h_n'][1][1] * sinh(a_[0][1] * alpha[i] * y))
result.append(
(_c['h_n'][2][0] * cosh(a_[0][0] * alpha[i] * y) +
_c['h_n'][2][1] * cosh(a_[0][1] * alpha[i] * y)) /
alpha[i])
result.append(
(_c['h_n'][3][0] * sinh(a_[0][0] * alpha[i] * y) +
_c['h_n'][3][1] * sinh(a_[0][1] * alpha[i] * y)) /
alpha[i])
result.extend([0, 0])
for i in range(M):
result.extend([sum(_c['g_n'][0]) * sin(beta[i] * y), 0, 0, 0])
elif y == 0:
for i in range(M):
result.extend([sum(_c['h_n'][0]) * cos(alpha[i] * x), 0, 0, 0])
result.extend([
0,
] * (2 + 4 * M))
else:
for i in range(M):
result.append(
(_c['h_n'][0][0] * cosh(a_[0][0] * alpha[i] * y) +
_c['h_n'][0][1] * cosh(a_[0][1] * alpha[i] * y)) *
cos(alpha[i] * x))
result.append(
(_c['h_n'][1][0] * sinh(a_[0][0] * alpha[i] * y) +
_c['h_n'][1][1] * sinh(a_[0][1] * alpha[i] * y)) *
cos(alpha[i] * x))
result.append(
(_c['h_n'][2][0] * cosh(a_[0][0] * alpha[i] * y) +
_c['h_n'][2][1] * cosh(a_[0][1] * alpha[i] * y)) *
cos(alpha[i] * x) / alpha[i])
result.append(
(_c['h_n'][3][0] * sinh(a_[0][0] * alpha[i] * y) +
_c['h_n'][3][1] * sinh(a_[0][1] * alpha[i] * y)) *
cos(alpha[i] * x) / alpha[i])
result.extend([0, 0])
for i in range(M):
result.append(
(_c['g_n'][0][0] * cosh(a_[1][0] * beta[i] * x) +
_c['g_n'][0][1] * cosh(a_[1][1] * beta[i] * x)) *
sin(beta[i] * y))
result.append(
(_c['g_n'][1][0] * sinh(a_[1][0] * beta[i] * x) +
_c['g_n'][1][1] * sinh(a_[1][1] * beta[i] * x)) *
sin(beta[i] * y))
result.append(
(_c['g_n'][2][0] * sinh(a_[1][0] * beta[i] * x) +
_c['g_n'][2][1] * sinh(a_[1][1] * beta[i] * x)) *
sin(beta[i] * y) / beta[i])
result.append(
(_c['g_n'][3][0] * cosh(a_[1][0] * beta[i] * x) +
_c['g_n'][3][1] * cosh(a_[1][1] * beta[i] * x)) *
sin(beta[i] * y) / beta[i])
return result