def getStiffnessA(self, lines_only=False):
'''Gets the analytical stiffness matrix of the Body with other objects fixed.
Returns
-------
K : matrix
6x6 analytic stiffness matrix.
'''
#print("Getting Body "+str(self.number)+" stiffness matrix...")
K = np.zeros([6, 6])
for PointID, rPointRel in zip(self.attachedP, self.rPointRel):
r = rotatePosition(
rPointRel, self.r6[3:]
) # relative position of Point about body ref point in unrotated reference frame
f3 = self.sys.pointList[PointID - 1].getForces(
) # total force on point (for additional rotational stiffness term due to change in moment arm)
K3 = self.sys.pointList[
PointID -
1].getStiffnessA() # local 3D stiffness matrix of the point
# following are from functions translateMatrix3to6
H = getH(r)
K[:3, :3] += K3
K[:3, 3:] += np.matmul(
K3, H
) # only add up one off-diagonal sub-matrix for now, then we'll mirror at the end
K[3:, 3:] += np.matmul(np.matmul(H, K3), H.T) + np.matmul(
getH(f3), H.T)
#K[3:,3:] += np.matmul(np.matmul(H, K3), H.T) - np.matmul( getH(f3), H) # <<< should be the same
K[3:, :3] = K[:3, 3:].T # copy over other off-diagonal sub-matrix
if lines_only == False:
# rotational stiffness effect of weight
rCG_rotated = rotatePosition(
self.rCG, self.r6[3:]
) # relative position of CG about body ref point in unrotated reference frame
Kw = -np.matmul(getH([0, 0, -self.m * self.sys.g]),
getH(rCG_rotated))
# rotational stiffness effect of buoyancy at metacenter
rM_rotated = rotatePosition(
self.rM, self.r6[3:]
) # relative position of metacenter about body ref point in unrotated reference frame
Kb = -np.matmul(getH([0, 0, self.sys.rho * self.sys.g * self.v]),
getH(rM_rotated))
# hydrostatic heave stiffness (if AWP is nonzero)
Kwp = self.sys.rho * self.sys.g * self.AWP
K[3:, 3:] += Kw + Kb
K[2, 2] += Kwp
return K
def getForces(self, lines_only=False):
'''Sums the forces and moments on the Body, including its own plus those from any attached objects.
Parameters
----------
lines_only : boolean, optional
An option for calculating forces from just the mooring lines or not. The default is False.
Returns
-------
f6 : array
The 6DOF forces and moments applied to the body in its current position [N, Nm]
'''
f6 = np.zeros(6)
# TODO: could save time in below by storing the body's rotation matrix when it's position is set rather than
# recalculating it in each of the following function calls.
if lines_only == False:
# add weight, which may result in moments as well as a force
rCG_rotated = rotatePosition(
self.rCG, self.r6[3:]
) # relative position of CG about body ref point in unrotated reference frame
f6 += translateForce3to6DOF(rCG_rotated,
np.array([
0, 0, -self.m * self.sys.g
])) # add to net forces/moments
# add buoyancy force and moments if applicable (this can include hydrostatic restoring moments
# if rM is considered the metacenter location rather than the center of buoyancy)
rM_rotated = rotatePosition(
self.rM, self.r6[3:]
) # relative position of metacenter about body ref point in unrotated reference frame
f6 += translateForce3to6DOF(rM_rotated,
np.array([
0, 0,
self.sys.rho * self.sys.g * self.v
])) # add to net forces/moments
# add hydrostatic heave stiffness (if AWP is nonzero)
f6[2] -= self.sys.rho * self.sys.g * self.AWP * self.r6[2]
# add any externally applied forces/moments (in global orientation)
f6 += self.f6Ext
# add forces from any attached Points (and their attached lines)
for PointID, rPointRel in zip(self.attachedP, self.rPointRel):
fPoint = self.sys.pointList[PointID - 1].getForces(
lines_only=lines_only) # get net force on attached Point
rPoint_rotated = rotatePosition(
rPointRel, self.r6[3:]
) # relative position of Point about body ref point in unrotated reference frame
f6 += translateForce3to6DOF(
rPoint_rotated, fPoint
) # add net force and moment resulting from its position to the Body
# All forces and moments on the body should now be summed, and are in global/unrotated orientations.
# For application to the body DOFs, convert the moments to be about the body's local/rotated x/y/z axes <<< do we want this in all cases?
rotMat = rotationMatrix(*self.r6[3:]) # get rotation matrix for body
moment_about_body_ref = np.matmul(
rotMat.T, f6[3:]
) # transform moments so that they are about the body's local/rotated axes
f6[3:] = moment_about_body_ref # use these moments
return f6