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))
K1 = zero123
K3 = zero123
K2 = mdotm(-L2, (M3 * Szu + M2 * Sxu)) + mdotm(L3, (M3 * Syu - M1 * Sxu))
K4 = mdotm( L2, (M3 * Szv - M5 * Sxv)) - mdotm(L3, (M3 * Syv + M4 * Sxv))
Kg3 = hstack((K1, K2, K3, K4))
K11 *= 0.
K13 *= 0.
K31 *= 0.
K33 *= 0.
Sr0Syu = mdotm(-Sr0, Syu)
Sr0Syv = mdotm(-Sr0, Syv)
Sr0Szu = mdotm(-Sr0, Szu)
Sr0Szv = mdotm(-Sr0, Szv)
Sr1Sxu = mdotm(Sr1, Sxu)
Sr1Sxv = mdotm(Sr1, Sxv)
Sr1Szu = mdotm(Sr1, Szu)
Sr1Szv = mdotm(Sr1, Szv)
Sr2Sxu = mdotm(Sr2, Sxu)
Sr2Sxv = mdotm(Sr2, Sxv)
Sr2Syu = mdotm(Sr2, Syu)
Sr2Syv = mdotm(Sr2, Syv)
K22 = +M3 * (Sr1Szu - Sr2Syu) + M2 * (Sr0Syu + Sr1Sxu) + M1 * (Sr0Szu + Sr2Sxu)
K44 = -M3 * (Sr1Szv - Sr2Syv) + M5 * (Sr0Syv + Sr1Sxv) + M4 * (Sr0Szv + Sr2Sxv)
Kg4 = vstack((
hstack((K11, K12, K13, K14)),
K11 *= 0.
K13 *= 0.
K31 *= 0.
K33 *= 0.
Sr0Syu = mdotm(-Sr0, Syu)
Sr0Syv = mdotm(-Sr0, Syv)
Sr0Szu = mdotm(-Sr0, Szu)
Sr0Szv = mdotm(-Sr0, Szv)
Sr1Sxu = mdotm(Sr1, Sxu)
Sr1Sxv = mdotm(Sr1, Sxv)
Sr1Szu = mdotm(Sr1, Szu)
Sr1Szv = mdotm(Sr1, Szv)
Sr2Sxu = mdotm(Sr2, Sxu)
Sr2Sxv = mdotm(Sr2, Sxv)
Sr2Syu = mdotm(Sr2, Syu)
Sr2Syv = mdotm(Sr2, Syv)
K22 = +M3 * (Sr1Szu - Sr2Syu) + M2 * (Sr0Syu + Sr1Sxu) + M1 * (Sr0Szu + Sr2Sxu)
K44 = -M3 * (Sr1Szv - Sr2Syv) + M5 * (Sr0Syv + Sr1Sxv) + M4 * (Sr0Szv + Sr2Sxv)
Kg4 = vstack((
hstack((K11, K12, K13, K14)),
hstack((K21, K22, K23, K24)),
hstack((K31, K32, K33, K34)),
hstack((K41, K42, K43, K44))
))
k = 1. / li * (M2 * yu + M1 * zu + M5 * yv + M4 * zv)
K22 *= 0.
K44 *= 0.
mu = 2. * abs(arctan(normq / q_0))
if mu == 0.:
e = array([1., 1., 1.])
else:
e = q / normq
S = zeros((3, 3))
S[0, 1] = -e[2]
S[0, 2] = e[1]
S[1, 0] = e[2]
S[1, 2] = -e[0]
S[2, 0] = -e[1]
S[2, 1] = e[0]
dRm = eye(3) + sin(0.5 * mu) * S + (1. - cos(0.5 * mu)) * multiply_matrices_numba(S, S)
R_e = multiply_matrices_numba(dRm, T_u)
return R_e
hstack((K41, K42, K43, K44))
))
k = 1. / li * (M2 * yu + M1 * zu + M5 * yv + M4 * zv)
K22 *= 0.
K44 *= 0.
K12 = -(M2 * mdotm(B, Syu) + M1 * mdotm(B, Szu))
K32 = -K12
K21 = K12.transpose()
K23 = -K12.transpose()
K14 = -(M5 * mdotm(B, Syv) + M4 * mdotm(B, Szv))
K34 = -K14
K41 = K14.transpose()
K43 = -K14.transpose()
K11 = mdotm(mdotm(B, k), xet) + mdotm(mdotm(xe, k.transpose()), B) + (mdotm(xet, k) * B)
K33 = K11
K13 = -K11
K31 = -K11
Kg5 = vstack((hstack((K11, K12, K13, K14)), hstack((K21, K22, K23, K24)), hstack((K31, K32, K33, K34)), hstack((K41, K42, K43, K44))))
Df = zeros((6, 6))
Df[0, 0] = f_[1][0] * tan(theta[0])
Df[1, 1] = f_[2][0] * tan(theta[2])
Df[2, 2] = f_[3][0] * tan(theta[4])
Df[3, 3] = f_[4][0] * tan(theta[1])
Df[4, 4] = f_[5][0] * tan(theta[3])
Df[5, 5] = f_[6][0] * tan(theta[5])
Kg6 = mdotm(mdotm(T[:, 1:7], Df), T[:, 1:7].transpose())
k = 1 / li * (M[2] * yu + M[1] * zu + M[5] * yv + M[4] * zv)
K11 = multiply_matrices_numba(multiply_matrices_numba(B, k), xe.transpose()) + multiply_matrices_numba(multiply_matrices_numba(xe, k.transpose()), B) + (multiply_matrices_numba(xe.transpose(), k) * B)
K33 = K11
K13 = -K11
K31 = -K11
K_g5 = vstack((hstack((K11, K12, K13, K14)), hstack((K21, K22, K23, K24)), hstack((K31, K32, K33, K34)), hstack((K41, K42, K43, K44))))
Df = zeros((6, 6))
Df[0, 0] = f_[1][0] * tan(theta[0])
Df[1, 1] = f_[2][0] * tan(theta[2])
Df[2, 2] = f_[3][0] * tan(theta[4])
Df[3, 3] = f_[4][0] * tan(theta[1])
Df[4, 4] = f_[5][0] * tan(theta[3])
Df[5, 5] = f_[6][0] * tan(theta[5])
K_g6 = multiply_matrices_numba(multiply_matrices_numba(T[:, 1:7], Df), T[:, 1:7].transpose())
Sx = _skew_(Sx, xe.transpose()[0])
Szuzv = _skew_(Szuzv, zuzv.transpose()[0])
Syvyu = _skew_(Syvyu, yvyu.transpose()[0])
r1T_B = multiply_matrices_numba(r1.transpose(), B)
r2T_B = multiply_matrices_numba(r2.transpose(), B)
r1T_xe = multiply_matrices_numba(r1.transpose(), xe)
r2T_xe = multiply_matrices_numba(r2.transpose(), xe)
B_r1 = multiply_matrices_numba(B, r1)
B_r2 = multiply_matrices_numba(B, r2)
B_r1_xeT = multiply_matrices_numba(B_r1, xe.transpose())
B_r2_xeT = multiply_matrices_numba(B_r2, xe.transpose())
r1T_xe = multiply_matrices_numba(r1.transpose(), xe) / (2 * li)
r2T_xe = multiply_matrices_numba(r2.transpose(), xe) / (2 * li)
xeT_Sr1 = multiply_matrices_numba(xe.transpose(), Sr1)
Kg6 = mdotm(mdotm(T[:, 1:7], Df), T[:, 1:7].transpose())
Sx = _skew_(Sx, xet[0])
Szuzv = _skew_(Szuzv, zuzv.transpose()[0])
Syvyu = _skew_(Syvyu, yvyu.transpose()[0])
r1t = r1.transpose()
r2t = r2.transpose()
r1T_B = mdotm(r1t, B)
r2T_B = mdotm(r2t, B)
r1T_xe = mdotm(r1t, xe)
r2T_xe = mdotm(r2t, xe)
Br1 = mdotm(B, r1)
Br2 = mdotm(B, r2)
Br1_xet = mdotm(Br1, xet)
Br2_xet = mdotm(Br2, xet)
r1T_xe = mdotm(r1t, xe) / (2 * li)
r2T_xe = mdotm(r2t, xe) / (2 * li)
xeT_Sr1 = mdotm(xet, Sr1)
xeT_Sr2 = mdotm(xet, Sr2)
BSr1 = mdotm(B, Sr1)
BSr2 = mdotm(B, Sr2)
Sr1_xe = mdotm(Sr1, xe)
Sr2_xe = mdotm(Sr2, xe)
SxSr1 = mdotm(Sx, Sr1)
SxSr2 = mdotm(Sx, Sr2)
Kg21 = Kg2(r1, zuzv, B, li, xe, r0, Sr0, Sx, Sr1, Szuzv, r1T_B, r1T_xe, Br1, Br1_xet, xeT_Sr1, BSr1, Sr1_xe, SxSr1)
Kg22 = Kg2(r2, yvyu, B, li, xe, r0, Sr0, Sx, Sr2, Syvyu, r2T_B, r2T_xe, Br2, Br2_xet, xeT_Sr2, BSr2, Sr2_xe, SxSr2)
Kg23 = Kg2(r1, xu, B, li, xe, r0, Sr0, Sx, Sr1, Sxu, r1T_B, r1T_xe, Br1, Br1_xet, xeT_Sr1, BSr1, Sr1_xe, SxSr1)
Kg24 = Kg2(r2, xu, B, li, xe, r0, Sr0, Sx, Sr2, Sxu, r2T_B, r2T_xe, Br2, Br2_xet, xeT_Sr2, BSr2, Sr2_xe, SxSr2)
Kg25 = Kg2(r1, xv, B, li, xe, r0, Sr0, Sx, Sr1, Sxv, r1T_B, r1T_xe, Br1, Br1_xet, xeT_Sr1, BSr1, Sr1_xe, SxSr1)
U = -0.5 * mdotm(Bo, riT_B) + (riT_xe / (2 * l)) * mdotm(Bo, xt) + (oT_xr0 / (2 * l)) * B_ri_xeT
K11 = U + U.transpose() + riT_xe * (2 * mdotm(xt, o) + mdotm(ot, r_0)) * B
K33 = K11
K13 = -K11
K31 = -K11
K12 = 0.25 * (mdotm(-Bo, xeT_Sri) - mdotm(B_ri, mdotm(ot, Sr0)) - oT_xr0 * B_Sri)
K14 = K12
K32 = -K12
K34 = -K12
K21 = K12.transpose()
K41 = K12.transpose()
K23 = -K12.transpose()
K43 = -K12.transpose()
K22 = ((-riT_xe * mdotm(So, Sr0) + mdotm(mdotm(Sr0, o), xeT_Sri) + mdotm(Sri_xe, mdotm(ot, Sr0)) -
mdotm(xt + r_0.transpose(), o) * Sx_Sri + 2 * mdotm(So, Sri)) / 8)
K24 = K22
K42 = K22
K44 = K22
Kg2 = vstack((
hstack((K11, K12, K13, K14)),
hstack((K21, K22, K23, K24)),
hstack((K31, K32, K33, K34)),
hstack((K41, K42, K43, K44))
))
return Kg2
K11 *= 0.
K13 *= 0.
K31 *= 0.
K33 *= 0.
Sr0Syu = mdotm(-Sr0, Syu)
Sr0Syv = mdotm(-Sr0, Syv)
Sr0Szu = mdotm(-Sr0, Szu)
Sr0Szv = mdotm(-Sr0, Szv)
Sr1Sxu = mdotm(Sr1, Sxu)
Sr1Sxv = mdotm(Sr1, Sxv)
Sr1Szu = mdotm(Sr1, Szu)
Sr1Szv = mdotm(Sr1, Szv)
Sr2Sxu = mdotm(Sr2, Sxu)
Sr2Sxv = mdotm(Sr2, Sxv)
Sr2Syu = mdotm(Sr2, Syu)
Sr2Syv = mdotm(Sr2, Syv)
K22 = +M3 * (Sr1Szu - Sr2Syu) + M2 * (Sr0Syu + Sr1Sxu) + M1 * (Sr0Szu + Sr2Sxu)
K44 = -M3 * (Sr1Szv - Sr2Syv) + M5 * (Sr0Syv + Sr1Sxv) + M4 * (Sr0Szv + Sr2Sxv)
Kg4 = vstack((
hstack((K11, K12, K13, K14)),
hstack((K21, K22, K23, K24)),
hstack((K31, K32, K33, K34)),
hstack((K41, K42, K43, K44))
))
k = 1. / li * (M2 * yu + M1 * zu + M5 * yv + M4 * zv)
K22 *= 0.
K11 = 0 * K11
K13 = 0 * K13
K31 = 0 * K31
K33 = 0 * K33
K22 = M[3] * (multiply_matrices_numba(Sr1, Szu) - multiply_matrices_numba(Sr2, Syu)) + M[2] * (multiply_matrices_numba(-Sr0, Syu) + multiply_matrices_numba(Sr1, Sxu)) + M[1] * (multiply_matrices_numba(-Sr0, Szu) + multiply_matrices_numba(Sr2, Sxu))
K44 = -M[3] * (multiply_matrices_numba(Sr1, Szv) - multiply_matrices_numba(Sr2, Syv)) + M[5] * (multiply_matrices_numba(-Sr0, Syv) + multiply_matrices_numba(Sr1, Sxv)) + M[4] * (multiply_matrices_numba(-Sr0, Szv) + multiply_matrices_numba(Sr2, Sxv))
K_g4 = vstack((hstack((K11, K12, K13, K14)), hstack((K21, K22, K23, K24)), hstack((K31, K32, K33, K34)), hstack((K41, K42, K43, K44))))
K22 = 0 * K22
K44 = 0 * K44
K12 = -(M[2] * multiply_matrices_numba(B, Syu) + M[1] * multiply_matrices_numba(B, Szu))
K32 = -K12
K21 = K12.transpose()
K23 = -K12.transpose()
K14 = -(M[5] * multiply_matrices_numba(B, Syv) + M[4] * multiply_matrices_numba(B, Szv))
K34 = -K14
K41 = K14.transpose()
K43 = -K14.transpose()
k = 1 / li * (M[2] * yu + M[1] * zu + M[5] * yv + M[4] * zv)
K11 = multiply_matrices_numba(multiply_matrices_numba(B, k), xe.transpose()) + multiply_matrices_numba(multiply_matrices_numba(xe, k.transpose()), B) + (multiply_matrices_numba(xe.transpose(), k) * B)
K33 = K11
K13 = -K11
K31 = -K11
K_g5 = vstack((hstack((K11, K12, K13, K14)), hstack((K21, K22, K23, K24)), hstack((K31, K32, K33, K34)), hstack((K41, K42, K43, K44))))
K1 = zero123
K3 = zero123
K2 = mdotm(-L2, (M3 * Szu + M2 * Sxu)) + mdotm(L3, (M3 * Syu - M1 * Sxu))
K4 = mdotm( L2, (M3 * Szv - M5 * Sxv)) - mdotm(L3, (M3 * Syv + M4 * Sxv))
Kg3 = hstack((K1, K2, K3, K4))
K11 *= 0.
K13 *= 0.
K31 *= 0.
K33 *= 0.
Sr0Syu = mdotm(-Sr0, Syu)
Sr0Syv = mdotm(-Sr0, Syv)
Sr0Szu = mdotm(-Sr0, Szu)
Sr0Szv = mdotm(-Sr0, Szv)
Sr1Sxu = mdotm(Sr1, Sxu)
Sr1Sxv = mdotm(Sr1, Sxv)
Sr1Szu = mdotm(Sr1, Szu)
Sr1Szv = mdotm(Sr1, Szv)
Sr2Sxu = mdotm(Sr2, Sxu)
Sr2Sxv = mdotm(Sr2, Sxv)
Sr2Syu = mdotm(Sr2, Syu)
Sr2Syv = mdotm(Sr2, Syv)
K22 = +M3 * (Sr1Szu - Sr2Syu) + M2 * (Sr0Syu + Sr1Sxu) + M1 * (Sr0Szu + Sr2Sxu)
K44 = -M3 * (Sr1Szv - Sr2Syv) + M5 * (Sr0Syv + Sr1Sxv) + M4 * (Sr0Szv + Sr2Sxv)
Kg4 = vstack((
hstack((K11, K12, K13, K14)),
hstack((K21, K22, K23, K24)),
hstack((K31, K32, K33, K34)),