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Modify Member.getHydrostatics #67

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Modify Member.getHydrostatics #67

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8b28cfc
A small correction of Member.getHydrostatics()
YangHaoran12 Dec 4, 2024
04b401d
Change Fvec in getHydrostatics()
YangHaoran12 Dec 4, 2024
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39 changes: 25 additions & 14 deletions raft/raft_member.py
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Original file line number Diff line number Diff line change
Expand Up @@ -766,19 +766,30 @@ def getHydrostatics(self, rPRP=np.zeros(3), rho=1025, g=9.81):
xWP = intrp(0, rA[2], rB[2], rA[0], rB[0]) # x coordinate where member axis cross the waterplane [m]
yWP = intrp(0, rA[2], rB[2], rA[1], rB[1]) # y coordinate where member axis cross the waterplane [m]
if self.shape=='circular':
dWP = intrp(0, rA[2], rB[2], self.d[i], self.d[i-1]) # diameter of member where its axis crosses the waterplane [m]
AWP = (np.pi/4)*dWP**2 # waterplane area of member [m^2]
IWP = (np.pi/64)*dWP**4 # waterplane moment of inertia [m^4] approximates as a circle
IxWP = IWP # MoI of circular waterplane is the same all around
IyWP = IWP # MoI of circular waterplane is the same all around
dWP = intrp(0, rA[2], rB[2], self.d[i-1], self.d[i]) # diameter of member where its axis crosses the waterplane [m]
AWP = np.pi*(dWP/2)**2/cosPhi # waterplane area of member [m^2]
# note that clipped waterplane area should be an ellipse generally @Yang

IxWP = np.pi/64*dWP**4/cosPhi # waterplane moment of inertia [m^4] approximates as an ellipse (short side)
IyWP = IxWP/(cosPhi**2) # waterplane moment of inertia [m^4] approximates as an ellipse (Long side)

I = np.diag([IxWP, IyWP])
T = np.array([[cosBeta, sinBeta], [-sinBeta, cosBeta]]) # 2D rotation matrix: R_z(-Beta)

I_rot = np.matmul(T, np.matmul(I, T.T)) # I_rot = T*diag(IxWP', IyWP')*T.T
IxWP = I_rot[0,0] # the transformation matrix to unrotate the member's local axes
IyWP = I_rot[1,1] # area moment of inertia tensor where MoI axes are now in the same direction as PRP
elif self.shape=='rectangular':
slWP = intrp(0, rA[2], rB[2], self.sl[i], self.sl[i-1]) # side lengths of member where its axis crosses the waterplane [m]
AWP = slWP[0]*slWP[1] # waterplane area of rectangular member [m^2]
IxWP = (1/12)*slWP[0]*slWP[1]**3 # waterplane MoI [m^4] about the member's LOCAL x-axis, not the global x-axis
IyWP = (1/12)*slWP[0]**3*slWP[1] # waterplane MoI [m^4] about the member's LOCAL y-axis, not the global y-axis
I = np.diag([IxWP, IyWP, 0]) # area moment of inertia tensor
T = self.R.T # the transformation matrix to unrotate the member's local axes
I_rot = np.matmul(T.T, np.matmul(I,T)) # area moment of inertia tensor where MoI axes are now in the same direction as PRP
slWP = intrp(0, rA[2], rB[2], self.sl[i-1], self.sl[i]) # side lengths of member where its axis crosses the waterplane [m]
AWP = slWP[0]*slWP[1] / cosPhi # waterplane area of rectangular member [m^2]

IxWP = (1/12)*slWP[0]*slWP[1]**3 / cosPhi # waterplane MoI [m^4] about the member's LOCAL x-axis, not the global x-axis
IyWP = (1/12)*slWP[0]**3*slWP[1] / (cosPhi**3) # waterplane MoI [m^4] about the member's LOCAL y-axis, not the global y-axis

I = np.diag([IxWP, IyWP]) # area moment of inertia tensor
T = np.array([[cosBeta, sinBeta], [-sinBeta, cosBeta]]) # the transformation matrix to unrotate the member's local axes

I_rot = np.matmul(T, np.matmul(I,T.T)) # area moment of inertia tensor where MoI axes are now in the same direction as PRP
IxWP = I_rot[0,0]
IyWP = I_rot[1,1]

Expand Down Expand Up @@ -817,8 +828,8 @@ def getHydrostatics(self, rPRP=np.zeros(3), rho=1025, g=9.81):
My = M*dPhi_dThy

Fvec[2] += Fz # vertical buoyancy force [N]
Fvec[3] += Mx + Fz*rA[1] # moment about x axis [N-m]
Fvec[4] += My - Fz*rA[0] # moment about y axis [N-m]
Fvec[3] += Mx + Fz*r_center[1] # moment about x axis [N-m]
Fvec[4] += My - Fz*r_center[0] # moment about y axis [N-m]


# normal approach to hydrostatic stiffness, using this temporarily until above fancier approach is verified
Expand Down